TSTP Solution File: ANA045-1 by Prover9---1109a

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : ANA045-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n011.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 19:22:03 EDT 2022

% Result   : Unsatisfiable 26.84s 26.89s
% Output   : Refutation 26.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA045-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 02:46:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.60/1.86  ============================== Prover9 ===============================
% 1.60/1.86  Prover9 (32) version 2009-11A, November 2009.
% 1.60/1.86  Process 23542 was started by sandbox on n011.cluster.edu,
% 1.60/1.86  Fri Jul  8 02:46:10 2022
% 1.60/1.86  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23388_n011.cluster.edu".
% 1.60/1.86  ============================== end of head ===========================
% 1.60/1.86  
% 1.60/1.86  ============================== INPUT =================================
% 1.60/1.86  
% 1.60/1.86  % Reading from file /tmp/Prover9_23388_n011.cluster.edu
% 1.60/1.86  
% 1.60/1.86  set(prolog_style_variables).
% 1.60/1.86  set(auto2).
% 1.60/1.86      % set(auto2) -> set(auto).
% 1.60/1.86      % set(auto) -> set(auto_inference).
% 1.60/1.86      % set(auto) -> set(auto_setup).
% 1.60/1.86      % set(auto_setup) -> set(predicate_elim).
% 1.60/1.86      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.60/1.86      % set(auto) -> set(auto_limits).
% 1.60/1.86      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.60/1.86      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.60/1.86      % set(auto) -> set(auto_denials).
% 1.60/1.86      % set(auto) -> set(auto_process).
% 1.60/1.86      % set(auto2) -> assign(new_constants, 1).
% 1.60/1.86      % set(auto2) -> assign(fold_denial_max, 3).
% 1.60/1.86      % set(auto2) -> assign(max_weight, "200.000").
% 1.60/1.86      % set(auto2) -> assign(max_hours, 1).
% 1.60/1.86      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.60/1.86      % set(auto2) -> assign(max_seconds, 0).
% 1.60/1.86      % set(auto2) -> assign(max_minutes, 5).
% 1.60/1.86      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.60/1.86      % set(auto2) -> set(sort_initial_sos).
% 1.60/1.86      % set(auto2) -> assign(sos_limit, -1).
% 1.60/1.86      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.60/1.86      % set(auto2) -> assign(max_megs, 400).
% 1.60/1.86      % set(auto2) -> assign(stats, some).
% 1.60/1.86      % set(auto2) -> clear(echo_input).
% 1.60/1.86      % set(auto2) -> set(quiet).
% 1.60/1.86      % set(auto2) -> clear(print_initial_clauses).
% 1.60/1.86      % set(auto2) -> clear(print_given).
% 1.60/1.86  assign(lrs_ticks,-1).
% 1.60/1.86  assign(sos_limit,10000).
% 1.60/1.86  assign(order,kbo).
% 1.60/1.86  set(lex_order_vars).
% 1.60/1.86  clear(print_given).
% 1.60/1.86  
% 1.60/1.86  % formulas(sos).  % not echoed (2784 formulas)
% 1.60/1.86  
% 1.60/1.86  ============================== end of input ==========================
% 1.60/1.86  
% 1.60/1.86  % From the command line: assign(max_seconds, 300).
% 1.60/1.86  
% 1.60/1.86  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.60/1.86  
% 1.60/1.86  % Formulas that are not ordinary clauses:
% 1.60/1.86  
% 1.60/1.86  ============================== end of process non-clausal formulas ===
% 1.60/1.86  
% 1.60/1.86  ============================== PROCESS INITIAL CLAUSES ===============
% 1.60/1.86  
% 1.60/1.86  ============================== PREDICATE ELIMINATION =================
% 1.60/1.86  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].
% 1.60/1.86  2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom).  [assumption].
% 1.60/1.86  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)].
% 1.60/1.86  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].
% 1.60/1.86  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)].
% 1.60/1.86  4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom).  [assumption].
% 1.60/1.86  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(4,a,1,a)].
% 1.60/1.86  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(4,a,3,a)].
% 1.60/1.86  5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom).  [assumption].
% 1.60/1.86  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(5,a,1,a)].
% 1.60/1.86  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(5,a,3,a)].
% 1.60/1.86  6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom).  [assumption].
% 1.60/1.86  Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(6,b,1,a)].
% 1.60/1.86  Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(6,b,3,a)].
% 1.60/1.86  7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom).  [assumption].
% 1.60/1.89  Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(7,b,1,a)].
% 1.60/1.89  Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(7,b,3,a)].
% 1.60/1.89  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].
% 1.60/1.89  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)].
% 1.60/1.89  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)].
% 1.60/1.89  9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom).  [assumption].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(9,a,2,a)].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(9,a,4,a)].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(9,a,5,a)].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(9,a,6,b)].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(9,a,7,b)].
% 1.60/1.89  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(9,a,8,b)].
% 1.60/1.89  10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom).  [assumption].
% 1.60/1.89  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(10,a,2,a)].
% 1.60/1.89  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(10,a,4,a)].
% 1.60/1.89  Derived: class_HOL_Oplus(tc_nat).  [resolve(10,a,5,a)].
% 1.60/1.89  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(10,a,6,b)].
% 1.60/1.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(10,a,7,b)].
% 1.60/1.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(10,a,8,b)].
% 1.60/1.89  11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom).  [assumption].
% 1.60/1.89  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(11,b,1,a)].
% 1.60/1.89  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(11,b,3,a)].
% 1.60/1.89  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].
% 1.60/1.89  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)].
% 1.60/1.89  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)].
% 1.60/1.89  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].
% 1.60/1.89  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)].
% 1.60/1.89  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)].
% 1.60/1.89  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].
% 1.60/1.89  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)].
% 1.60/1.89  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)].
% 1.60/1.89  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(18,b,9,a)].
% 1.60/1.91  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(18,b,10,a)].
% 1.60/1.91  19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom).  [assumption].
% 1.60/1.91  Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(19,b,1,a)].
% 1.60/1.91  Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(19,b,3,a)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A).  [resolve(20,b,10,a)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.60/1.91  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(22,b,10,a)].
% 1.60/1.91  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].
% 1.60/1.91  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)].
% 1.60/1.91  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)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(23,b,9,a)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A).  [resolve(23,b,10,a)].
% 1.68/1.96  24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom).  [assumption].
% 1.68/1.96  Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(24,b,1,a)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(24,b,3,a)].
% 1.68/1.96  25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom).  [assumption].
% 1.68/1.96  Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(25,b,1,a)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(25,b,3,a)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(27,b,10,a)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(30,b,9,a)].
% 1.68/1.96  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(30,b,10,a)].
% 1.68/1.96  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].
% 1.68/1.96  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)].
% 1.68/1.96  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)].
% 1.68/1.96  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(33,b,9,a)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A).  [resolve(33,b,10,a)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A).  [resolve(34,b,10,a)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(36,b,9,a)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(36,b,10,a)].
% 1.74/1.99  37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom).  [assumption].
% 1.74/1.99  Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(37,b,1,a)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(37,b,3,a)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(38,b,9,a)].
% 1.74/1.99  Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A).  [resolve(38,b,10,a)].
% 1.74/1.99  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].
% 1.74/1.99  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)].
% 1.74/1.99  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)].
% 1.74/1.99  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].
% 1.90/2.14  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)].
% 1.90/2.14  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)].
% 1.90/2.14  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].
% 1.90/2.14  42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom).  [assumption].
% 1.90/2.14  43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom).  [assumption].
% 1.90/2.14  44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom).  [assumption].
% 1.90/2.14  45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom).  [assumption].
% 1.90/2.14  46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom).  [assumption].
% 1.90/2.14  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(41,a,42,a)].
% 1.90/2.14  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(41,a,43,a)].
% 1.90/2.14  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(41,a,44,a)].
% 1.90/2.14  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(41,a,45,b)].
% 1.90/2.14  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(41,a,46,b)].
% 1.90/2.14  47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom).  [assumption].
% 1.90/2.14  48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom).  [assumption].
% 1.90/2.14  49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom).  [assumption].
% 1.90/2.14  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].
% 1.90/2.14  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(50,b,41,a)].
% 1.90/2.14  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(50,b,47,a)].
% 1.90/2.14  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A).  [resolve(50,b,48,a)].
% 1.90/2.14  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].
% 1.90/2.14  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].
% 1.90/2.14  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].
% 1.90/2.14  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].
% 1.90/2.14  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].
% 1.90/2.14  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].
% 1.90/2.19  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(56,b,41,a)].
% 1.90/2.19  57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom).  [assumption].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(61,b,41,a)].
% 1.90/2.19  62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom).  [assumption].
% 1.90/2.19  63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom).  [assumption].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(68,b,41,a)].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(71,b,41,a)].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  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].
% 1.90/2.19  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(74,b,41,a)].
% 1.90/2.19  75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom).  [assumption].
% 1.90/2.21  Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(75,b,41,a)].
% 1.90/2.21  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].
% 1.90/2.21  Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(76,b,41,a)].
% 1.90/2.21  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].
% 1.90/2.21  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(77,b,41,a)].
% 1.90/2.21  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(77,b,47,a)].
% 1.90/2.21  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(77,b,48,a)].
% 1.90/2.21  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].
% 1.90/2.21  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)].
% 1.90/2.21  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)].
% 1.90/2.21  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(79,a,43,a)].
% 1.90/2.21  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(79,a,44,a)].
% 1.90/2.21  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(79,a,45,b)].
% 1.90/2.21  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C).  [resolve(79,a,46,b)].
% 1.90/2.21  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)].
% 1.90/2.21  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)].
% 1.90/2.21  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(80,a,43,a)].
% 1.90/2.21  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(80,a,44,a)].
% 1.90/2.21  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(80,a,45,b)].
% 1.90/2.21  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C).  [resolve(80,a,46,b)].
% 1.90/2.21  81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(9,a,8,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(81,b,42,a)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(81,b,43,a)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(81,b,44,a)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(81,b,45,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(81,b,46,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(81,b,49,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(81,b,51,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(81,b,52,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(81,b,53,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(81,b,54,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(81,b,55,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(81,b,57,b)].
% 1.90/2.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(81,b,58,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(81,b,59,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(81,b,60,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(81,b,62,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(81,b,63,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(81,b,64,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(81,b,65,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(81,b,66,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(81,b,67,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(81,b,69,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(81,b,70,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(81,b,72,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(81,b,73,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(81,b,75,b)].
% 2.05/2.35  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(81,b,78,b)].
% 2.05/2.35  82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(10,a,8,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(82,b,42,a)].
% 2.05/2.35  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(82,b,43,a)].
% 2.05/2.35  Derived: class_HOL_Oplus(tc_nat).  [resolve(82,b,44,a)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(82,b,45,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(82,b,46,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(82,b,49,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(82,b,51,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(82,b,52,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(82,b,53,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(82,b,54,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(82,b,55,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(82,b,57,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(82,b,59,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(82,b,62,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(82,b,63,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(82,b,64,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(82,b,66,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(82,b,67,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(82,b,69,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(82,b,70,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(82,b,73,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A).  [resolve(82,b,75,b)].
% 2.05/2.35  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(82,b,78,b)].
% 2.05/2.35  83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom).  [assumption].
% 2.13/2.37  84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom).  [assumption].
% 2.13/2.37  85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom).  [assumption].
% 2.13/2.37  86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom).  [assumption].
% 2.13/2.37  87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom).  [assumption].
% 2.13/2.37  88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom).  [assumption].
% 2.13/2.37  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(83,a,84,a)].
% 2.13/2.37  Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(83,a,85,a)].
% 2.13/2.37  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(83,a,86,a)].
% 2.13/2.37  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(83,a,87,a)].
% 2.13/2.37  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(83,a,88,b)].
% 2.13/2.37  89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom).  [assumption].
% 2.13/2.37  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(89,a,84,a)].
% 2.13/2.37  Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(89,a,85,a)].
% 2.13/2.37  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(89,a,86,a)].
% 2.13/2.37  Derived: class_HOL_Otimes(tc_nat).  [resolve(89,a,87,a)].
% 2.13/2.37  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(89,a,88,b)].
% 2.13/2.37  90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom).  [assumption].
% 2.13/2.37  91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom).  [assumption].
% 2.13/2.37  Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(91,b,83,a)].
% 2.13/2.37  Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A).  [resolve(91,b,89,a)].
% 2.13/2.37  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].
% 2.13/2.37  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].
% 2.13/2.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(93,b,83,a)].
% 2.13/2.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A).  [resolve(93,b,89,a)].
% 2.13/2.37  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].
% 2.13/2.37  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].
% 2.13/2.37  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].
% 2.13/2.37  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].
% 2.13/2.37  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].
% 2.13/2.37  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(98,b,83,a)].
% 2.13/2.37  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(98,b,89,a)].
% 2.13/2.37  99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom).  [assumption].
% 2.27/2.53  100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom).  [assumption].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(106,b,83,a)].
% 2.27/2.53  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A).  [resolve(106,b,89,a)].
% 2.27/2.53  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].
% 2.27/2.53  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].
% 2.27/2.53  109 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom).  [assumption].
% 2.27/2.53  110 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom).  [assumption].
% 2.27/2.53  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C).  [resolve(108,a,109,a)].
% 2.27/2.53  Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(108,a,110,a)].
% 2.27/2.53  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].
% 2.27/2.53  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C).  [resolve(111,a,109,a)].
% 2.27/2.53  Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(111,a,110,a)].
% 2.27/2.53  112 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom).  [assumption].
% 2.27/2.53  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(112,a,108,a)].
% 2.27/2.53  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(112,a,111,a)].
% 2.27/2.53  113 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom).  [assumption].
% 2.27/2.53  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(113,a,108,a)].
% 2.27/2.53  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(113,a,111,a)].
% 2.27/2.53  114 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom).  [assumption].
% 2.27/2.53  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B.  [resolve(114,b,108,a)].
% 2.27/2.53  Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B.  [resolve(114,b,111,a)].
% 2.27/2.53  115 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom).  [assumption].
% 2.27/2.53  Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B.  [resolve(115,b,108,a)].
% 2.27/2.53  Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B.  [resolve(115,b,111,a)].
% 2.27/2.53  116 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom).  [assumption].
% 2.27/2.57  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(116,a,109,a)].
% 2.27/2.57  Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(116,a,110,a)].
% 2.27/2.57  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(116,a,112,a)].
% 2.27/2.57  Derived: class_HOL_Oone(tc_nat).  [resolve(116,a,113,a)].
% 2.27/2.57  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(116,a,114,b)].
% 2.27/2.57  Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(116,a,115,b)].
% 2.27/2.57  117 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom).  [assumption].
% 2.27/2.57  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(117,a,115,b)].
% 2.27/2.57  118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom).  [assumption].
% 2.27/2.57  Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(118,a,115,b)].
% 2.27/2.57  119 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom).  [assumption].
% 2.27/2.57  Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B.  [resolve(119,b,108,a)].
% 2.27/2.57  Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B.  [resolve(119,b,111,a)].
% 2.27/2.57  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].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B.  [resolve(120,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B.  [resolve(120,b,111,a)].
% 2.27/2.57  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].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B.  [resolve(121,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B.  [resolve(121,b,111,a)].
% 2.27/2.57  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].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(122,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(122,b,111,a)].
% 2.27/2.57  123 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom).  [assumption].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B.  [resolve(123,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B.  [resolve(123,b,111,a)].
% 2.27/2.57  124 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom).  [assumption].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B.  [resolve(124,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B.  [resolve(124,b,111,a)].
% 2.27/2.57  125 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom).  [assumption].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B.  [resolve(125,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B.  [resolve(125,b,111,a)].
% 2.27/2.57  126 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom).  [assumption].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B.  [resolve(126,b,108,a)].
% 2.27/2.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B.  [resolve(126,b,111,a)].
% 2.27/2.57  127 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom).  [assumption].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B.  [resolve(127,b,108,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B.  [resolve(127,b,111,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(127,b,117,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A).  [resolve(127,b,118,a)].
% 2.45/2.69  128 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom).  [assumption].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B.  [resolve(128,b,108,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B.  [resolve(128,b,111,a)].
% 2.45/2.69  129 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom).  [assumption].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B.  [resolve(129,b,108,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B.  [resolve(129,b,111,a)].
% 2.45/2.69  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].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(130,b,108,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(130,b,111,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(130,b,116,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(130,b,117,a)].
% 2.45/2.69  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(130,b,118,a)].
% 2.45/2.69  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].
% 2.45/2.69  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].
% 2.45/2.69  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)].
% 2.45/2.69  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].
% 2.45/2.69  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)].
% 2.45/2.69  134 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom).  [assumption].
% 2.45/2.69  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)].
% 2.45/2.69  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)].
% 2.48/2.72  135 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom).  [assumption].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  136 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom).  [assumption].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  137 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom).  [assumption].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  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].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  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].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  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].
% 2.48/2.72  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)].
% 2.48/2.72  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)].
% 2.48/2.72  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].
% 2.48/2.72  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)].
% 2.48/2.73  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)].
% 2.48/2.73  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].
% 2.48/2.73  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)].
% 2.48/2.73  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)].
% 2.48/2.73  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].
% 2.48/2.73  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)].
% 2.48/2.73  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)].
% 2.48/2.73  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].
% 2.48/2.73  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)].
% 2.48/2.73  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)].
% 2.48/2.73  145 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom).  [assumption].
% 2.48/2.73  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)].
% 2.48/2.73  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)].
% 2.48/2.73  146 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom).  [assumption].
% 2.48/2.73  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)].
% 2.48/2.73  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)].
% 2.48/2.73  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].
% 2.48/2.73  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.76  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)].
% 2.48/2.76  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].
% 2.48/2.76  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  160 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom).  [assumption].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  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].
% 2.48/2.77  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)].
% 2.48/2.77  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)].
% 2.48/2.77  162 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom).  [assumption].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(162,a,132,a)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(162,a,137,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(162,a,138,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(162,a,139,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(162,a,140,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(162,a,141,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(162,a,142,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(162,a,143,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(162,a,145,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(162,a,146,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(162,a,147,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(162,a,148,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(162,a,149,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(162,a,150,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(162,a,152,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(162,a,153,b)].
% 2.48/2.77  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(162,a,155,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(162,a,156,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(162,a,157,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(162,a,159,b)].
% 2.48/2.78  163 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom).  [assumption].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(163,a,132,a)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(163,a,140,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(163,a,141,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(163,a,143,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(163,a,157,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(163,a,159,b)].
% 2.48/2.78  164 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom).  [assumption].
% 2.48/2.78  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(164,a,132,a)].
% 2.48/2.78  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(164,a,140,b)].
% 2.48/2.78  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(164,a,141,b)].
% 2.48/2.78  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(164,a,143,b)].
% 2.48/2.78  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(164,a,157,b)].
% 2.48/2.78  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(164,a,159,b)].
% 2.48/2.78  165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom).  [assumption].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(165,a,132,a)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(165,a,138,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(165,a,140,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(165,a,141,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(165,a,142,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(165,a,143,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(165,a,145,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(165,a,146,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(165,a,147,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(165,a,148,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(165,a,149,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(165,a,150,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(165,a,151,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(165,a,153,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(165,a,154,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(165,a,155,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(165,a,157,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(165,a,158,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(165,a,159,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A).  [resolve(165,a,160,b)].
% 2.48/2.78  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(165,a,161,b)].
% 2.48/2.78  166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom).  [assumption].
% 2.48/2.78  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(166,a,132,a)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(166,a,138,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(166,a,140,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(166,a,141,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(166,a,142,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(166,a,143,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(166,a,145,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(166,a,146,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(166,a,147,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(166,a,148,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(166,a,149,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(166,a,150,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(166,a,151,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(166,a,153,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(166,a,154,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(166,a,155,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(166,a,157,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(166,a,158,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(166,a,159,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A).  [resolve(166,a,160,b)].
% 2.48/2.78  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(166,a,161,b)].
% 2.48/2.78  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].
% 2.48/2.78  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)].
% 2.48/2.78  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)].
% 2.48/2.78  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].
% 2.48/2.78  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)].
% 2.48/2.78  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)].
% 2.65/2.93  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].
% 2.65/2.93  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)].
% 2.65/2.93  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)].
% 2.65/2.93  Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A).  [resolve(169,b,164,a)].
% 2.65/2.93  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].
% 2.65/2.93  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)].
% 2.65/2.93  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)].
% 2.65/2.93  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].
% 2.65/2.93  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].
% 2.65/2.93  173 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom).  [assumption].
% 2.65/2.93  174 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom).  [assumption].
% 2.65/2.93  175 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom).  [assumption].
% 2.65/2.93  176 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom).  [assumption].
% 2.65/2.93  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].
% 2.65/2.93  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].
% 2.65/2.93  179 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom).  [assumption].
% 2.65/2.93  180 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom).  [assumption].
% 2.65/2.93  181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom).  [assumption].
% 2.65/2.93  182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom).  [assumption].
% 2.65/2.93  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].
% 2.65/2.93  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].
% 2.65/2.93  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].
% 2.65/2.93  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].
% 2.65/2.98  187 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom).  [assumption].
% 2.65/2.98  188 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom).  [assumption].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.65/2.98  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  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)].
% 2.75/2.99  198 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(162,a,140,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(198,b,172,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(198,b,173,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(198,b,174,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(198,b,175,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(198,b,176,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(198,b,177,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(198,b,178,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(198,b,186,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(198,b,193,b)].
% 2.75/2.99  199 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(163,a,140,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(199,b,172,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(199,b,173,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(199,b,174,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(199,b,175,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(199,b,176,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(199,b,177,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(199,b,178,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(199,b,184,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(199,b,186,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(199,b,187,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(199,b,188,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(199,b,189,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(199,b,190,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(199,b,191,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(199,b,192,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(199,b,193,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(199,b,194,b)].
% 2.75/2.99  200 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(164,a,140,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(200,b,172,a)].
% 2.75/2.99  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(200,b,173,a)].
% 2.75/2.99  Derived: class_HOL_Oplus(tc_nat).  [resolve(200,b,174,a)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(200,b,175,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(200,b,176,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(200,b,177,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(200,b,178,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(200,b,184,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(200,b,186,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(200,b,187,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(200,b,188,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(200,b,189,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(200,b,190,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(200,b,191,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(200,b,192,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(200,b,193,b)].
% 2.75/2.99  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(200,b,194,b)].
% 2.75/2.99  201 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(165,a,140,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(201,b,172,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(201,b,173,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(201,b,174,a)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(201,b,175,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A).  [resolve(201,b,176,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(201,b,177,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(201,b,178,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(201,b,186,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(201,b,192,b)].
% 2.75/2.99  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(201,b,194,b)].
% 2.75/2.99  202 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(166,a,140,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(202,b,172,a)].
% 2.87/3.16  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(202,b,173,a)].
% 2.87/3.16  Derived: class_HOL_Otimes(tc_nat).  [resolve(202,b,174,a)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(202,b,175,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A).  [resolve(202,b,176,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(202,b,177,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(202,b,178,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(202,b,186,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(202,b,192,b)].
% 2.87/3.16  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(202,b,194,b)].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  205 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom).  [assumption].
% 2.87/3.16  206 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom).  [assumption].
% 2.87/3.16  207 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom).  [assumption].
% 2.87/3.16  208 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom).  [assumption].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  215 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom).  [assumption].
% 2.87/3.16  216 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom).  [assumption].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.16  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  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].
% 2.87/3.17  230 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom).  [assumption].
% 2.87/3.17  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].
% 2.87/3.17  232 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom).  [assumption].
% 2.87/3.17  233 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom).  [assumption].
% 2.87/3.17  234 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom).  [assumption].
% 2.87/3.17  235 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom).  [assumption].
% 2.87/3.17  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].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(236,a,204,a)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(236,a,205,a)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(236,a,206,a)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(236,a,207,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A).  [resolve(236,a,208,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(236,a,209,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(236,a,210,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(236,a,211,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(236,a,212,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(236,a,213,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(236,a,214,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(236,a,215,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(236,a,216,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(236,a,217,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(236,a,218,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(236,a,219,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(236,a,220,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(236,a,221,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(236,a,222,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(236,a,223,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(236,a,224,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(236,a,225,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(236,a,226,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(236,a,227,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(236,a,228,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(236,a,229,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(236,a,230,b)].
% 2.87/3.17  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(236,a,231,b)].
% 2.87/3.17  237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom).  [assumption].
% 2.87/3.17  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(237,a,204,a)].
% 2.87/3.17  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(237,a,205,a)].
% 2.87/3.17  Derived: class_HOL_Ozero(tc_nat).  [resolve(237,a,206,a)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(237,a,207,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(237,a,208,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(237,a,209,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(237,a,210,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(237,a,211,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(237,a,212,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(237,a,213,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(237,a,214,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(237,a,215,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(237,a,216,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(237,a,217,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(237,a,218,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(237,a,219,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(237,a,220,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(237,a,221,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(237,a,222,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(237,a,223,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(237,a,224,b)].
% 2.87/3.17  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(237,a,225,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(237,a,226,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(237,a,227,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(237,a,228,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(237,a,229,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A).  [resolve(237,a,230,b)].
% 2.95/3.21  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(237,a,231,b)].
% 2.95/3.21  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].
% 2.95/3.21  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].
% 2.95/3.21  Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A).  [resolve(239,b,237,a)].
% 2.95/3.21  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].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 2.95/3.21  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)].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  245 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom).  [assumption].
% 3.08/3.36  246 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom).  [assumption].
% 3.08/3.36  247 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom).  [assumption].
% 3.08/3.36  248 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom).  [assumption].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.36  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].
% 3.08/3.41  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].
% 3.08/3.41  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].
% 3.08/3.41  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)].
% 3.08/3.41  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)].
% 3.08/3.41  271 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(162,a,141,b)].
% 3.08/3.41  272 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(163,a,141,b)].
% 3.08/3.41  273 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(164,a,141,b)].
% 3.08/3.41  274 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(165,a,141,b)].
% 3.08/3.41  275 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(166,a,141,b)].
% 3.08/3.41  276 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(236,a,211,b)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(276,b,244,a)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(276,b,245,a)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(276,b,246,a)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(276,b,247,b)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A).  [resolve(276,b,248,b)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(276,b,249,b)].
% 3.08/3.41  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(276,b,250,b)].
% 3.08/3.41  277 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(237,a,211,b)].
% 3.08/3.41  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(277,b,244,a)].
% 3.08/3.41  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(277,b,245,a)].
% 3.08/3.41  Derived: class_HOL_Ozero(tc_nat).  [resolve(277,b,246,a)].
% 3.08/3.41  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(277,b,247,b)].
% 3.08/3.41  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(277,b,248,b)].
% 3.08/3.41  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(277,b,249,b)].
% 3.08/3.41  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(277,b,250,b)].
% 3.08/3.41  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)].
% 3.08/3.41  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)].
% 3.08/3.41  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)].
% 3.08/3.41  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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(279,c,244,a)].
% 3.28/3.51  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(279,c,245,a)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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)].
% 3.28/3.51  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].
% 3.28/3.51  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].
% 3.28/3.51  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)].
% 3.28/3.51  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].
% 3.28/3.51  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)].
% 3.28/3.51  283 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom).  [assumption].
% 3.28/3.55  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(283,a,280,a)].
% 3.28/3.55  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(283,a,282,a)].
% 3.28/3.55  284 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom).  [assumption].
% 3.28/3.55  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(284,a,280,a)].
% 3.28/3.55  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(284,a,282,a)].
% 3.28/3.55  285 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom).  [assumption].
% 3.28/3.55  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(285,b,280,a)].
% 3.28/3.55  Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(285,b,282,a)].
% 3.28/3.55  286 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom).  [assumption].
% 3.28/3.55  Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0.  [resolve(286,b,280,a)].
% 3.28/3.55  Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0.  [resolve(286,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(287,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(287,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(288,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(288,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(289,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(289,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(290,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(290,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0.  [resolve(291,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0.  [resolve(291,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0.  [resolve(292,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0.  [resolve(292,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(293,b,280,a)].
% 3.28/3.55  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(293,b,282,a)].
% 3.28/3.55  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].
% 3.28/3.55  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(294,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(294,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0.  [resolve(295,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0.  [resolve(295,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0.  [resolve(296,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0.  [resolve(296,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(297,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(297,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0.  [resolve(298,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0.  [resolve(298,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(299,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(299,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(300,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(300,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(301,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(301,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(302,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(302,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(303,b,280,a)].
% 3.28/3.57  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(303,b,282,a)].
% 3.28/3.57  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].
% 3.28/3.57  Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0.  [resolve(304,b,280,a)].
% 3.36/3.60  Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0.  [resolve(304,b,282,a)].
% 3.36/3.60  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].
% 3.36/3.60  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(305,b,280,a)].
% 3.36/3.60  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(305,b,282,a)].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  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].
% 3.36/3.60  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(313,b,280,a)].
% 3.36/3.60  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(313,b,282,a)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C).  [resolve(314,a,286,b)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(314,a,291,b)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(314,a,292,b)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C).  [resolve(314,a,304,b)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C).  [resolve(315,a,286,b)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(315,a,291,b)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(315,a,292,b)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  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)].
% 3.36/3.60  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C).  [resolve(315,a,304,b)].
% 3.36/3.60  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)].
% 3.36/3.60  316 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(77,b,41,a)].
% 3.36/3.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(316,a,297,b)].
% 3.36/3.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(316,a,303,b)].
% 3.36/3.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(316,a,304,b)].
% 3.36/3.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(316,a,305,b)].
% 3.36/3.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(316,a,313,b)].
% 3.36/3.60  317 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(77,b,47,a)].
% 3.50/3.75  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(317,a,297,b)].
% 3.50/3.75  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(317,a,303,b)].
% 3.50/3.75  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(317,a,305,b)].
% 3.50/3.75  318 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(77,b,48,a)].
% 3.50/3.75  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(318,a,297,b)].
% 3.50/3.75  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(318,a,301,b)].
% 3.50/3.75  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(318,a,303,b)].
% 3.50/3.75  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(318,a,305,b)].
% 3.50/3.75  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)].
% 3.50/3.75  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)].
% 3.50/3.75  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].
% 3.50/3.75  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].
% 3.50/3.75  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)].
% 3.50/3.75  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].
% 3.50/3.75  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)].
% 3.50/3.75  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].
% 3.50/3.75  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)].
% 3.50/3.75  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].
% 3.50/3.75  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)].
% 3.50/3.75  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].
% 3.50/3.75  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)].
% 3.50/3.75  327 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom).  [assumption].
% 3.50/3.75  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  328 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom).  [assumption].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.77  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)].
% 3.50/3.78  331 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom).  [assumption].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  332 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom).  [assumption].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.78  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)].
% 3.50/3.80  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].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  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)].
% 3.50/3.80  339 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom).  [assumption].
% 3.50/3.80  340 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom).  [assumption].
% 3.50/3.80  341 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom).  [assumption].
% 3.50/3.80  342 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom).  [assumption].
% 3.50/3.80  343 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom).  [assumption].
% 3.50/3.80  344 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom).  [assumption].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(344,a,322,a)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(344,a,327,a)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(344,a,328,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(344,a,329,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(344,a,330,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(344,a,331,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(344,a,332,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(344,a,333,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(344,a,334,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(344,a,335,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(344,a,336,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(344,a,337,b)].
% 3.50/3.80  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(344,a,338,b)].
% 3.50/3.80  345 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom).  [assumption].
% 3.50/3.80  Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(345,a,322,a)].
% 3.50/3.80  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(345,a,327,a)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(345,a,328,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(345,a,329,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(345,a,330,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(345,a,331,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(345,a,332,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(345,a,333,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(345,a,334,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(345,a,335,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(345,a,336,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(345,a,337,b)].
% 3.50/3.80  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(345,a,338,b)].
% 3.59/3.84  346 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom).  [assumption].
% 3.59/3.84  347 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom).  [assumption].
% 3.59/3.84  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].
% 3.59/3.84  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)].
% 3.59/3.84  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)].
% 3.59/3.84  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)].
% 3.59/3.84  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)].
% 3.59/3.84  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)].
% 3.59/3.84  349 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(37,b,1,a)].
% 3.59/3.84  350 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(37,b,3,a)].
% 3.59/3.84  351 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(75,b,41,a)].
% 3.59/3.84  352 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(81,b,75,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(352,b,333,b)].
% 3.59/3.84  353 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A).  [resolve(82,b,75,b)].
% 3.59/3.84  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(353,b,333,b)].
% 3.59/3.84  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)].
% 3.59/3.84  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)].
% 3.59/3.84  356 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A).  [resolve(165,a,160,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(356,b,331,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(356,b,332,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(356,b,333,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(356,b,334,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(356,b,335,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(356,b,336,b)].
% 3.59/3.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(356,b,338,b)].
% 3.59/3.84  357 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A).  [resolve(166,a,160,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(357,b,331,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(357,b,332,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(357,b,333,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(357,b,334,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(357,b,335,b)].
% 3.59/3.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(357,b,336,b)].
% 3.59/3.85  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(357,b,338,b)].
% 3.59/3.85  358 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(236,a,230,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(358,b,331,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(358,b,332,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(358,b,333,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(358,b,334,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(358,b,335,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(358,b,336,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(358,b,337,b)].
% 3.59/3.85  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(358,b,338,b)].
% 3.59/3.85  359 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A).  [resolve(237,a,230,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(359,b,331,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(359,b,332,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(359,b,333,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(359,b,334,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(359,b,335,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(359,b,336,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(359,b,337,b)].
% 3.59/3.85  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(359,b,338,b)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.85  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  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)].
% 3.59/3.86  362 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0.  [resolve(304,b,280,a)].
% 3.59/3.86  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)].
% 3.59/3.86  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(362,a,327,a)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(362,a,328,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(362,a,329,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(362,a,330,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(362,a,331,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(362,a,332,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(362,a,333,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(362,a,334,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(362,a,335,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(362,a,336,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(362,a,337,b)].
% 3.59/3.86  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(362,a,338,b)].
% 3.59/3.86  363 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0.  [resolve(304,b,282,a)].
% 3.59/3.86  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)].
% 3.59/3.86  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(363,a,327,a)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(363,a,328,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(363,a,329,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(363,a,330,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(363,a,331,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(363,a,332,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(363,a,333,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(363,a,334,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(363,a,335,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(363,a,336,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(363,a,337,b)].
% 3.59/3.87  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(363,a,338,b)].
% 3.59/3.87  364 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C).  [resolve(314,a,304,b)].
% 3.59/3.87  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)].
% 3.59/3.87  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(364,c,327,a)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(364,c,328,b)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(364,c,331,b)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(364,c,332,b)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  365 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C).  [resolve(315,a,304,b)].
% 3.59/3.87  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)].
% 3.59/3.87  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(365,c,327,a)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(365,c,328,b)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(365,c,331,b)].
% 3.59/3.87  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(365,c,332,b)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.59/3.87  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)].
% 3.78/4.01  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)].
% 3.78/4.01  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)].
% 3.78/4.01  366 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(316,a,304,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(366,b,322,a)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(366,b,327,a)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(366,b,328,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(366,b,329,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(366,b,330,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(366,b,331,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(366,b,332,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(366,b,333,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(366,b,334,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(366,b,335,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(366,b,336,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(366,b,337,b)].
% 3.78/4.01  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(366,b,338,b)].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  369 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom).  [assumption].
% 3.78/4.01  370 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom).  [assumption].
% 3.78/4.01  371 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom).  [assumption].
% 3.78/4.01  372 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom).  [assumption].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.78/4.01  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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].
% 3.81/4.08  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)].
% 3.81/4.08  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)].
% 3.81/4.08  390 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(22,b,10,a)].
% 3.81/4.08  391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(81,b,60,b)].
% 3.81/4.08  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)].
% 3.81/4.08  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)].
% 3.81/4.08  394 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(162,a,142,b)].
% 3.81/4.08  395 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(165,a,142,b)].
% 3.81/4.08  396 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(166,a,142,b)].
% 3.81/4.08  397 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(199,b,184,b)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(397,b,368,a)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(397,b,369,a)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(397,b,370,a)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(397,b,371,b)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(397,b,372,b)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(397,b,373,b)].
% 3.81/4.08  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(397,b,374,b)].
% 3.81/4.08  398 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(200,b,184,b)].
% 3.81/4.08  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(398,b,368,a)].
% 3.81/4.08  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(398,b,369,a)].
% 3.81/4.08  Derived: class_HOL_Oplus(tc_nat).  [resolve(398,b,370,a)].
% 3.81/4.08  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(398,b,371,b)].
% 3.95/4.23  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(398,b,372,b)].
% 3.95/4.23  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(398,b,373,b)].
% 3.95/4.23  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(398,b,374,b)].
% 3.95/4.23  399 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(236,a,212,b)].
% 3.95/4.23  400 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(237,a,212,b)].
% 3.95/4.23  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)].
% 3.95/4.23  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)].
% 3.95/4.23  403 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(289,b,280,a)].
% 3.95/4.23  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(403,a,370,a)].
% 3.95/4.23  Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B).  [resolve(403,a,372,b)].
% 3.95/4.23  404 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(289,b,282,a)].
% 3.95/4.23  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(404,a,370,a)].
% 3.95/4.23  Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B).  [resolve(404,a,372,b)].
% 3.95/4.23  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)].
% 3.95/4.23  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(405,c,370,a)].
% 3.95/4.23  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C).  [resolve(405,c,372,b)].
% 3.95/4.23  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)].
% 3.95/4.23  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(406,c,370,a)].
% 3.95/4.23  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C).  [resolve(406,c,372,b)].
% 3.95/4.23  407 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom).  [assumption].
% 3.95/4.23  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].
% 3.95/4.23  409 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom).  [assumption].
% 3.95/4.23  410 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom).  [assumption].
% 3.95/4.23  411 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom).  [assumption].
% 3.95/4.23  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].
% 3.95/4.23  413 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom).  [assumption].
% 3.95/4.23  414 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom).  [assumption].
% 3.95/4.23  415 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom).  [assumption].
% 3.95/4.23  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].
% 3.95/4.23  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].
% 3.95/4.23  418 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom).  [assumption].
% 3.95/4.23  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].
% 4.06/4.30  420 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom).  [assumption].
% 4.06/4.30  421 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom).  [assumption].
% 4.06/4.30  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].
% 4.06/4.30  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].
% 4.06/4.30  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].
% 4.06/4.30  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)].
% 4.06/4.30  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)].
% 4.06/4.30  427 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A).  [resolve(20,b,10,a)].
% 4.06/4.30  428 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(81,b,58,b)].
% 4.06/4.30  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)].
% 4.06/4.30  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)].
% 4.06/4.30  431 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(162,a,138,b)].
% 4.06/4.30  432 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(165,a,138,b)].
% 4.06/4.30  433 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(166,a,138,b)].
% 4.06/4.30  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)].
% 4.06/4.30  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)].
% 4.06/4.30  436 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(198,b,177,b)].
% 4.06/4.30  437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(199,b,177,b)].
% 4.06/4.30  438 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(200,b,177,b)].
% 4.06/4.30  439 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(201,b,177,b)].
% 4.06/4.30  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(439,b,408,a)].
% 4.06/4.30  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(439,b,409,a)].
% 4.06/4.30  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(439,b,410,b)].
% 4.06/4.30  440 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(202,b,177,b)].
% 4.06/4.30  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(440,b,408,a)].
% 4.06/4.30  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(440,b,409,a)].
% 4.06/4.30  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(440,b,410,b)].
% 4.06/4.30  441 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(236,a,209,b)].
% 4.06/4.30  442 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(237,a,209,b)].
% 4.06/4.30  443 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(276,b,249,b)].
% 4.06/4.30  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(443,b,408,a)].
% 4.06/4.31  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(443,b,409,a)].
% 4.06/4.31  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(443,b,410,b)].
% 4.06/4.31  444 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(277,b,249,b)].
% 4.06/4.31  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(444,b,408,a)].
% 4.06/4.31  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(444,b,409,a)].
% 4.06/4.31  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(444,b,410,b)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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(446,c,409,a)].
% 4.06/4.31  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)].
% 4.06/4.31  447 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(287,b,280,a)].
% 4.06/4.31  448 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(287,b,282,a)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.06/4.31  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  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)].
% 4.10/4.32  456 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(344,a,329,b)].
% 4.10/4.32  Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(456,b,408,a)].
% 4.10/4.32  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(456,b,409,a)].
% 4.10/4.32  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(456,b,410,b)].
% 4.10/4.32  457 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(345,a,329,b)].
% 4.10/4.32  Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(457,b,408,a)].
% 4.10/4.32  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(457,b,409,a)].
% 4.10/4.32  Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(457,b,410,b)].
% 4.10/4.32  458 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(362,a,329,b)].
% 4.19/4.41  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)].
% 4.19/4.41  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(458,b,409,a)].
% 4.19/4.41  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(458,b,410,b)].
% 4.19/4.41  459 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(363,a,329,b)].
% 4.19/4.41  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)].
% 4.19/4.41  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(459,b,409,a)].
% 4.19/4.41  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(459,b,410,b)].
% 4.19/4.41  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)].
% 4.19/4.41  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)].
% 4.19/4.41  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(460,c,409,a)].
% 4.19/4.41  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(460,c,410,b)].
% 4.19/4.41  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)].
% 4.19/4.41  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)].
% 4.19/4.41  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(461,c,409,a)].
% 4.19/4.41  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(461,c,410,b)].
% 4.19/4.41  462 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(366,b,329,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(462,b,408,a)].
% 4.19/4.41  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(462,b,409,a)].
% 4.19/4.41  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(462,b,410,b)].
% 4.19/4.41  463 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(397,b,373,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(463,b,408,a)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(463,b,409,a)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(463,b,410,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(463,b,420,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(463,b,421,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(463,b,422,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(463,b,423,b)].
% 4.19/4.41  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(463,b,424,b)].
% 4.19/4.41  464 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(398,b,373,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(464,b,408,a)].
% 4.19/4.41  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(464,b,409,a)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(464,b,410,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(464,b,420,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(464,b,421,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(464,b,422,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(464,b,423,b)].
% 4.19/4.41  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(464,b,424,b)].
% 4.19/4.41  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].
% 4.19/4.41  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].
% 4.42/4.69  Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(465,a,466,a)].
% 4.42/4.69  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].
% 4.42/4.69  Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(467,a,466,a)].
% 4.42/4.69  468 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom).  [assumption].
% 4.42/4.69  Derived: c_0 != c_1.  [resolve(468,a,465,a)].
% 4.42/4.69  Derived: c_1 != c_0.  [resolve(468,a,467,a)].
% 4.42/4.69  469 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom).  [assumption].
% 4.42/4.69  470 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom).  [assumption].
% 4.42/4.69  471 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom).  [assumption].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(473,a,466,a)].
% 4.42/4.69  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(473,a,471,b)].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(476,b,473,a)].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  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].
% 4.42/4.69  485 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom).  [assumption].
% 4.42/4.69  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].
% 4.42/4.69  487 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom).  [assumption].
% 4.42/4.69  488 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom).  [assumption].
% 4.42/4.71  489 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom).  [assumption].
% 4.42/4.71  490 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom).  [assumption].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  494 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom).  [assumption].
% 4.42/4.71  495 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom).  [assumption].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  500 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom).  [assumption].
% 4.42/4.71  501 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom).  [assumption].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(501,a,491,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(501,a,492,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(501,a,494,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(501,a,495,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(501,a,496,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(501,a,497,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(501,a,498,b)].
% 4.42/4.71  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(501,a,499,b)].
% 4.42/4.71  502 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom).  [assumption].
% 4.42/4.71  503 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom).  [assumption].
% 4.42/4.71  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].
% 4.42/4.71  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].
% 4.42/4.71  506 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom).  [assumption].
% 4.42/4.71  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].
% 4.42/4.71  508 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B.  [resolve(129,b,108,a)].
% 4.42/4.71  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(508,a,486,a)].
% 4.42/4.71  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(508,a,487,a)].
% 4.64/4.89  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(508,a,488,a)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(508,a,489,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B).  [resolve(508,a,490,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(508,a,491,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(508,a,492,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(508,a,493,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(508,a,494,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(508,a,495,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(508,a,496,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(508,a,497,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(508,a,498,b)].
% 4.64/4.89  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(508,a,499,b)].
% 4.64/4.89  509 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B.  [resolve(129,b,111,a)].
% 4.64/4.89  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(509,a,486,a)].
% 4.64/4.89  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(509,a,487,a)].
% 4.64/4.89  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(509,a,488,a)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(509,a,489,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B).  [resolve(509,a,490,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(509,a,491,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(509,a,492,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(509,a,493,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(509,a,494,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(509,a,495,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(509,a,496,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(509,a,497,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(509,a,498,b)].
% 4.64/4.89  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(509,a,499,b)].
% 4.64/4.89  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)].
% 4.64/4.89  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)].
% 4.64/4.89  512 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A).  [resolve(169,b,164,a)].
% 4.64/4.89  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(512,a,492,b)].
% 4.64/4.89  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(512,a,507,b)].
% 4.64/4.89  513 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A).  [resolve(239,b,237,a)].
% 4.64/4.89  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(513,a,492,b)].
% 4.64/4.89  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(513,a,493,b)].
% 4.64/4.89  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(513,a,498,b)].
% 4.64/4.89  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(513,a,499,b)].
% 4.64/4.89  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(513,a,507,b)].
% 4.64/4.89  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].
% 4.69/4.94  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].
% 4.69/4.94  516 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom).  [assumption].
% 4.69/4.94  517 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom).  [assumption].
% 4.69/4.94  518 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom).  [assumption].
% 4.69/4.94  519 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom).  [assumption].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(525,a,515,a)].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint).  [resolve(525,a,516,a)].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat).  [resolve(525,a,517,a)].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(525,a,518,b)].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A).  [resolve(525,a,519,b)].
% 4.69/4.94  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(525,a,520,b)].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  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].
% 4.69/4.94  535 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B.  [resolve(121,b,108,a)].
% 4.69/4.94  536 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B.  [resolve(121,b,111,a)].
% 4.73/5.01  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)].
% 4.73/5.01  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)].
% 4.73/5.01  539 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(162,a,143,b)].
% 4.73/5.01  540 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(163,a,143,b)].
% 4.73/5.01  541 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(164,a,143,b)].
% 4.73/5.01  542 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(165,a,143,b)].
% 4.73/5.01  543 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(166,a,143,b)].
% 4.73/5.01  544 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(236,a,213,b)].
% 4.73/5.01  545 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(237,a,213,b)].
% 4.73/5.01  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)].
% 4.73/5.01  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)].
% 4.73/5.01  548 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(501,a,492,b)].
% 4.73/5.01  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(548,b,515,a)].
% 4.73/5.01  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(548,b,516,a)].
% 4.73/5.01  Derived: class_HOL_Oone(tc_nat).  [resolve(548,b,517,a)].
% 4.73/5.01  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(548,b,518,b)].
% 4.73/5.01  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(548,b,519,b)].
% 4.73/5.01  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(548,b,520,b)].
% 4.73/5.01  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(548,b,529,b)].
% 4.73/5.01  549 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(508,a,492,b)].
% 4.73/5.01  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(549,b,515,a)].
% 4.73/5.01  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(549,b,516,a)].
% 4.73/5.01  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(549,b,517,a)].
% 4.73/5.01  Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(549,b,518,b)].
% 4.73/5.01  Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B).  [resolve(549,b,519,b)].
% 4.73/5.01  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(549,b,520,b)].
% 4.73/5.01  550 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(509,a,492,b)].
% 4.73/5.01  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(550,b,515,a)].
% 4.73/5.01  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(550,b,516,a)].
% 4.73/5.01  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(550,b,517,a)].
% 4.73/5.01  Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(550,b,518,b)].
% 4.73/5.01  Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B).  [resolve(550,b,519,b)].
% 4.73/5.01  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(550,b,520,b)].
% 4.73/5.01  551 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(512,a,492,b)].
% 4.73/5.01  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(551,b,515,a)].
% 4.73/5.01  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(551,b,516,a)].
% 4.73/5.01  Derived: class_HOL_Oplus(tc_nat).  [resolve(551,b,517,a)].
% 4.73/5.01  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(551,b,518,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(551,b,519,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(551,b,520,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(551,b,529,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(551,b,530,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(551,b,531,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(551,b,532,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(551,b,533,b)].
% 4.88/5.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(551,b,534,b)].
% 4.88/5.13  552 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(513,a,492,b)].
% 4.88/5.13  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(552,b,515,a)].
% 4.88/5.14  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(552,b,516,a)].
% 4.88/5.14  Derived: class_HOL_Ozero(tc_nat).  [resolve(552,b,517,a)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(552,b,518,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(552,b,519,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(552,b,520,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(552,b,530,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(552,b,531,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(552,b,532,b)].
% 4.88/5.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(552,b,533,b)].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  555 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom).  [assumption].
% 4.88/5.14  556 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom).  [assumption].
% 4.88/5.14  557 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom).  [assumption].
% 4.88/5.14  558 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom).  [assumption].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.88/5.14  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].
% 4.96/5.19  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].
% 4.96/5.19  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].
% 4.96/5.19  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].
% 4.96/5.19  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].
% 4.96/5.19  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].
% 4.96/5.19  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].
% 4.96/5.19  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)].
% 4.96/5.19  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)].
% 4.96/5.19  576 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(81,b,78,b)].
% 4.96/5.19  577 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(82,b,78,b)].
% 4.96/5.19  578 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(130,b,108,a)].
% 4.96/5.19  579 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(130,b,111,a)].
% 4.96/5.19  580 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(130,b,116,a)].
% 4.96/5.19  581 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(130,b,117,a)].
% 4.96/5.19  582 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(130,b,118,a)].
% 4.96/5.19  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)].
% 4.96/5.19  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)].
% 4.96/5.19  585 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(313,b,280,a)].
% 4.96/5.19  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(585,a,560,b)].
% 4.96/5.19  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(585,a,565,b)].
% 4.96/5.19  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(585,a,566,b)].
% 4.96/5.19  586 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(313,b,282,a)].
% 4.96/5.19  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(586,a,560,b)].
% 4.96/5.19  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(586,a,565,b)].
% 4.96/5.19  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(586,a,566,b)].
% 4.96/5.19  587 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(316,a,313,b)].
% 4.96/5.19  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(587,b,556,a)].
% 4.96/5.19  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(587,b,558,b)].
% 4.96/5.19  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(587,b,560,b)].
% 4.96/5.19  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(587,b,565,b)].
% 4.96/5.19  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(587,b,566,b)].
% 5.17/5.39  588 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(512,a,507,b)].
% 5.17/5.39  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(588,b,566,b)].
% 5.17/5.39  589 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(513,a,507,b)].
% 5.17/5.39  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(589,b,560,b)].
% 5.17/5.39  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(589,b,565,b)].
% 5.17/5.39  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(589,b,566,b)].
% 5.17/5.39  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].
% 5.17/5.39  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].
% 5.17/5.39  592 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom).  [assumption].
% 5.17/5.39  593 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom).  [assumption].
% 5.17/5.39  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].
% 5.17/5.39  595 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom).  [assumption].
% 5.17/5.39  596 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom).  [assumption].
% 5.17/5.39  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].
% 5.17/5.39  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].
% 5.17/5.39  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].
% 5.17/5.39  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].
% 5.17/5.39  601 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom).  [assumption].
% 5.17/5.39  602 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom).  [assumption].
% 5.17/5.39  603 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom).  [assumption].
% 5.17/5.39  604 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom).  [assumption].
% 5.17/5.39  605 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom).  [assumption].
% 5.17/5.39  606 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom).  [assumption].
% 5.17/5.39  607 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom).  [assumption].
% 5.17/5.39  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)].
% 5.17/5.39  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)].
% 5.17/5.39  610 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(38,b,9,a)].
% 5.17/5.39  611 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A).  [resolve(38,b,10,a)].
% 5.17/5.39  612 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(76,b,41,a)].
% 5.17/5.39  613 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B.  [resolve(128,b,108,a)].
% 5.17/5.39  614 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B.  [resolve(128,b,111,a)].
% 5.17/5.39  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)].
% 5.17/5.43  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)].
% 5.17/5.43  617 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(165,a,161,b)].
% 5.17/5.43  618 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(166,a,161,b)].
% 5.17/5.43  619 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(236,a,231,b)].
% 5.17/5.43  620 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(237,a,231,b)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  623 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(305,b,280,a)].
% 5.17/5.43  624 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(305,b,282,a)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  627 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(316,a,305,b)].
% 5.17/5.43  628 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(317,a,305,b)].
% 5.17/5.43  629 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(318,a,305,b)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.43  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  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)].
% 5.17/5.45  635 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(501,a,499,b)].
% 5.17/5.45  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(635,b,595,b)].
% 5.17/5.45  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(635,b,596,b)].
% 5.17/5.45  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(635,b,597,b)].
% 5.17/5.45  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(635,b,598,b)].
% 5.17/5.45  636 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(508,a,499,b)].
% 5.17/5.45  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(636,b,595,b)].
% 5.17/5.45  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(636,b,596,b)].
% 5.17/5.45  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(636,b,597,b)].
% 5.17/5.45  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(636,b,598,b)].
% 5.24/5.46  637 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(509,a,499,b)].
% 5.24/5.46  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(637,b,595,b)].
% 5.24/5.46  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(637,b,596,b)].
% 5.24/5.46  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(637,b,597,b)].
% 5.24/5.46  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(637,b,598,b)].
% 5.24/5.46  638 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(513,a,499,b)].
% 5.24/5.46  639 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(585,a,566,b)].
% 5.24/5.46  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)].
% 5.24/5.46  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(639,b,592,a)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(639,b,593,b)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(639,b,594,b)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(639,b,595,b)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(639,b,596,b)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(639,b,597,b)].
% 5.24/5.46  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(639,b,598,b)].
% 5.24/5.46  640 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(586,a,566,b)].
% 5.24/5.46  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)].
% 5.24/5.46  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(640,b,592,a)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(640,b,593,b)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(640,b,594,b)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(640,b,595,b)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(640,b,596,b)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(640,b,597,b)].
% 5.24/5.46  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(640,b,598,b)].
% 5.24/5.46  641 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(587,b,566,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(641,b,591,a)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(641,b,592,a)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(641,b,593,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(641,b,594,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(641,b,595,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(641,b,596,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(641,b,597,b)].
% 5.24/5.46  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(641,b,598,b)].
% 5.24/5.46  642 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(588,b,566,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(642,b,591,a)].
% 5.24/5.46  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(642,b,592,a)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(642,b,593,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(642,b,594,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(642,b,595,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(642,b,596,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(642,b,597,b)].
% 5.24/5.46  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(642,b,598,b)].
% 5.30/5.52  643 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(589,b,566,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(643,b,591,a)].
% 5.30/5.52  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(643,b,592,a)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(643,b,593,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(643,b,594,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(643,b,595,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(643,b,596,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(643,b,597,b)].
% 5.30/5.52  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(643,b,598,b)].
% 5.30/5.52  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].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.30/5.52  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)].
% 5.30/5.52  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].
% 5.32/5.57  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)].
% 5.32/5.57  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].
% 5.32/5.57  Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(654,a,645,a)].
% 5.32/5.57  655 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom).  [assumption].
% 5.32/5.57  Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,644,a)].
% 5.32/5.57  Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,646,a)].
% 5.32/5.57  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)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,649,a)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1.  [resolve(655,a,651,a)].
% 5.32/5.57  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)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint).  [resolve(655,a,654,a)].
% 5.32/5.57  656 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom).  [assumption].
% 5.32/5.57  Derived: c_in(c_0,c_IntDef_ONats,tc_nat).  [resolve(656,a,644,a)].
% 5.32/5.57  Derived: c_in(c_1,c_IntDef_ONats,tc_nat).  [resolve(656,a,646,a)].
% 5.32/5.57  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)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(656,a,649,a)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1.  [resolve(656,a,651,a)].
% 5.32/5.57  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)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: -c_IntDef_Oiszero(c_1,tc_nat).  [resolve(656,a,654,a)].
% 5.32/5.57  657 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom).  [assumption].
% 5.32/5.57  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(657,b,644,a)].
% 5.32/5.57  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(657,b,646,a)].
% 5.32/5.57  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)].
% 5.32/5.57  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)].
% 5.32/5.57  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(657,b,649,a)].
% 5.32/5.57  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)].
% 5.32/5.59  Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(657,b,651,a)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(657,b,654,a)].
% 5.32/5.59  658 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom).  [assumption].
% 5.32/5.59  Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(658,b,644,a)].
% 5.32/5.59  Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(658,b,646,a)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(658,b,649,a)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(658,b,651,a)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(658,b,654,a)].
% 5.32/5.59  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].
% 5.32/5.59  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(659,b,644,a)].
% 5.32/5.59  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(659,b,646,a)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(659,b,651,a)].
% 5.32/5.59  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)].
% 5.32/5.59  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)].
% 5.32/5.59  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(659,b,654,a)].
% 5.32/5.59  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].
% 5.32/5.59  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].
% 5.32/5.59  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  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].
% 5.32/5.60  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(669,b,644,a)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(669,b,646,a)].
% 5.32/5.60  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)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(669,b,649,a)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(669,b,651,a)].
% 5.32/5.60  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)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(669,b,654,a)].
% 5.32/5.60  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].
% 5.32/5.60  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(670,b,644,a)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(670,b,646,a)].
% 5.32/5.60  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)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(670,b,649,a)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(670,b,651,a)].
% 5.32/5.60  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)].
% 5.32/5.60  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)].
% 5.32/5.60  Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(670,b,654,a)].
% 5.32/5.62  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].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(671,b,644,a)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(671,b,646,a)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(671,b,651,a)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(671,b,654,a)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(671,b,667,a)].
% 5.32/5.62  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].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(672,b,644,a)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(672,b,646,a)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(672,b,651,a)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(672,b,654,a)].
% 5.32/5.62  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].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(673,b,644,a)].
% 5.32/5.62  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(673,b,646,a)].
% 5.32/5.62  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)].
% 5.32/5.62  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)].
% 5.41/5.66  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)].
% 5.41/5.66  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)].
% 5.41/5.66  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(673,b,651,a)].
% 5.41/5.66  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)].
% 5.41/5.66  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)].
% 5.41/5.66  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(673,b,654,a)].
% 5.41/5.66  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)].
% 5.41/5.66  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)].
% 5.41/5.66  676 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(23,b,9,a)].
% 5.41/5.66  677 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A).  [resolve(23,b,10,a)].
% 5.41/5.66  678 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(61,b,41,a)].
% 5.41/5.66  679 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(98,b,83,a)].
% 5.41/5.66  680 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(98,b,89,a)].
% 5.41/5.66  681 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(122,b,108,a)].
% 5.41/5.66  682 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(122,b,111,a)].
% 5.41/5.66  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)].
% 5.41/5.66  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)].
% 5.41/5.66  685 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(198,b,186,b)].
% 5.41/5.66  686 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(199,b,186,b)].
% 5.41/5.66  687 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(200,b,186,b)].
% 5.41/5.66  688 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(201,b,186,b)].
% 5.41/5.66  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(688,b,656,a)].
% 5.41/5.66  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A).  [resolve(688,b,658,b)].
% 5.41/5.66  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(688,b,659,b)].
% 5.41/5.66  689 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(202,b,186,b)].
% 5.41/5.66  Derived: class_HOL_Otimes(tc_nat).  [resolve(689,b,656,a)].
% 5.41/5.66  Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A).  [resolve(689,b,658,b)].
% 5.41/5.66  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(689,b,659,b)].
% 5.41/5.66  690 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(236,a,214,b)].
% 5.41/5.66  691 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(237,a,214,b)].
% 5.41/5.66  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)].
% 5.61/5.82  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)].
% 5.61/5.82  694 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(290,b,280,a)].
% 5.61/5.82  695 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(290,b,282,a)].
% 5.61/5.82  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)].
% 5.61/5.82  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)].
% 5.61/5.82  698 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(476,b,473,a)].
% 5.61/5.82  699 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(508,a,493,b)].
% 5.61/5.82  700 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(509,a,493,b)].
% 5.61/5.82  701 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(513,a,493,b)].
% 5.61/5.82  702 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(548,b,529,b)].
% 5.61/5.82  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(702,b,645,a)].
% 5.61/5.82  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(702,b,655,a)].
% 5.61/5.82  Derived: class_HOL_Oone(tc_nat).  [resolve(702,b,656,a)].
% 5.61/5.82  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(702,b,657,b)].
% 5.61/5.82  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(702,b,658,b)].
% 5.61/5.82  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(702,b,659,b)].
% 5.61/5.82  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(702,b,673,b)].
% 5.61/5.82  703 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(551,b,529,b)].
% 5.61/5.82  Derived: class_HOL_Oplus(tc_nat).  [resolve(703,b,656,a)].
% 5.61/5.82  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(703,b,658,b)].
% 5.61/5.82  704 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(585,a,560,b)].
% 5.61/5.82  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(704,b,656,a)].
% 5.61/5.82  Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B).  [resolve(704,b,658,b)].
% 5.61/5.82  705 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(586,a,560,b)].
% 5.61/5.82  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(705,b,656,a)].
% 5.61/5.82  Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B).  [resolve(705,b,658,b)].
% 5.61/5.82  706 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(587,b,560,b)].
% 5.61/5.82  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(706,b,656,a)].
% 5.61/5.82  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(706,b,658,b)].
% 5.61/5.82  707 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(589,b,560,b)].
% 5.61/5.82  Derived: class_HOL_Ozero(tc_nat).  [resolve(707,b,656,a)].
% 5.61/5.82  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(707,b,658,b)].
% 5.61/5.82  708 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom).  [assumption].
% 5.61/5.82  709 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom).  [assumption].
% 5.61/5.82  710 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom).  [assumption].
% 5.61/5.82  711 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom).  [assumption].
% 5.61/5.82  712 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom).  [assumption].
% 5.61/5.82  713 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom).  [assumption].
% 5.61/5.82  714 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom).  [assumption].
% 5.61/5.84  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B).  [resolve(708,a,709,a)].
% 5.61/5.84  Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(708,a,710,a)].
% 5.61/5.84  715 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom).  [assumption].
% 5.61/5.84  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B).  [resolve(715,a,709,a)].
% 5.61/5.84  Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(715,a,710,a)].
% 5.61/5.84  716 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom).  [assumption].
% 5.61/5.84  717 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom).  [assumption].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  726 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom).  [assumption].
% 5.61/5.84  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].
% 5.61/5.84  728 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom).  [assumption].
% 5.61/5.84  729 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom).  [assumption].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.84  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  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].
% 5.61/5.87  743 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(41,a,42,a)].
% 5.61/5.87  744 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(41,a,43,a)].
% 5.61/5.87  745 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(41,a,44,a)].
% 5.61/5.87  746 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(41,a,45,b)].
% 5.61/5.87  747 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(41,a,46,b)].
% 5.61/5.87  748 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(50,b,41,a)].
% 5.61/5.87  749 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(56,b,41,a)].
% 5.61/5.87  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(749,b,708,a)].
% 5.61/5.87  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(749,b,715,a)].
% 5.61/5.87  750 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(68,b,41,a)].
% 5.61/5.87  751 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(71,b,41,a)].
% 5.61/5.87  752 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(74,b,41,a)].
% 5.61/5.87  753 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(162,a,132,a)].
% 5.61/5.87  754 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(162,a,137,b)].
% 5.61/5.87  755 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(162,a,139,b)].
% 5.61/5.87  756 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(162,a,145,b)].
% 5.61/5.87  757 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(162,a,146,b)].
% 5.61/5.87  758 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(162,a,147,b)].
% 5.61/5.87  759 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(162,a,148,b)].
% 5.61/5.87  760 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(162,a,149,b)].
% 5.61/5.87  761 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(162,a,150,b)].
% 5.61/5.87  762 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(162,a,152,b)].
% 5.70/5.92  763 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(162,a,153,b)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(763,a,708,a)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(763,a,715,a)].
% 5.70/5.92  764 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(162,a,155,b)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(764,a,708,a)].
% 5.70/5.92  765 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(162,a,156,b)].
% 5.70/5.92  766 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(162,a,157,b)].
% 5.70/5.92  767 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(162,a,159,b)].
% 5.70/5.92  768 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(198,b,172,a)].
% 5.70/5.92  769 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(198,b,173,a)].
% 5.70/5.92  770 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(198,b,174,a)].
% 5.70/5.92  771 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(198,b,175,b)].
% 5.70/5.92  772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(198,b,176,b)].
% 5.70/5.92  773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(198,b,178,b)].
% 5.70/5.92  774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(198,b,193,b)].
% 5.70/5.92  775 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(316,a,297,b)].
% 5.70/5.92  776 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(316,a,303,b)].
% 5.70/5.92  777 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(366,b,322,a)].
% 5.70/5.92  778 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(366,b,327,a)].
% 5.70/5.92  779 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(366,b,328,b)].
% 5.70/5.92  780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(366,b,330,b)].
% 5.70/5.92  781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(366,b,331,b)].
% 5.70/5.92  782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(366,b,332,b)].
% 5.70/5.92  783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(366,b,333,b)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(783,a,708,a)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A).  [resolve(783,a,715,a)].
% 5.70/5.92  784 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(366,b,334,b)].
% 5.70/5.92  785 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(366,b,335,b)].
% 5.70/5.92  786 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(366,b,336,b)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(786,a,708,a)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(786,a,715,a)].
% 5.70/5.92  787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(366,b,337,b)].
% 5.70/5.92  788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(366,b,338,b)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(788,a,708,a)].
% 5.70/5.92  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(788,a,715,a)].
% 5.70/5.92  789 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(462,b,408,a)].
% 5.78/6.04  790 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(462,b,409,a)].
% 5.78/6.04  791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(462,b,410,b)].
% 5.78/6.04  792 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(587,b,556,a)].
% 5.78/6.04  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(792,a,708,a)].
% 5.78/6.04  793 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(587,b,558,b)].
% 5.78/6.04  Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(793,a,708,a)].
% 5.78/6.04  794 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(587,b,565,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(794,a,708,a)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A).  [resolve(794,a,715,a)].
% 5.78/6.04  795 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(641,b,591,a)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)).  [resolve(795,a,708,a)].
% 5.78/6.04  796 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(641,b,592,a)].
% 5.78/6.04  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(796,a,708,a)].
% 5.78/6.04  797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(641,b,593,b)].
% 5.78/6.04  Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(797,a,708,a)].
% 5.78/6.04  798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(641,b,594,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(798,a,708,a)].
% 5.78/6.04  799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(641,b,595,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(799,a,708,a)].
% 5.78/6.04  800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(641,b,596,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(800,a,708,a)].
% 5.78/6.04  801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(641,b,597,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(801,a,708,a)].
% 5.78/6.04  802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(641,b,598,b)].
% 5.78/6.04  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(802,a,708,a)].
% 5.78/6.04  803 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(706,b,656,a)].
% 5.78/6.04  Derived: class_HOL_Oplus(tc_nat).  [resolve(803,a,715,a)].
% 5.78/6.04  804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(706,b,658,b)].
% 5.78/6.04  Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A).  [resolve(804,a,715,a)].
% 5.78/6.04  805 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom).  [assumption].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.04  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,815,a)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.05  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,825,a)].
% 5.78/6.05  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)].
% 5.78/6.05  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(805,a,840,a)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(805,a,845,a)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,851,a)].
% 5.78/6.06  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,852,a)].
% 5.78/6.06  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,853,a)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,861,a)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  864 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom).  [assumption].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.06  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(864,a,815,a)].
% 5.78/6.06  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)].
% 5.78/6.06  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(864,a,825,a)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(864,a,831,a)].
% 5.78/6.07  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(864,a,832,a)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(864,a,834,a)].
% 5.78/6.07  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(864,a,835,a)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(864,a,837,a)].
% 5.78/6.07  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(864,a,838,a)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(864,a,840,a)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(864,a,842,a)].
% 5.78/6.07  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(864,a,843,a)].
% 5.78/6.07  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)].
% 5.78/6.07  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(864,a,845,a)].
% 5.78/6.07  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)].
% 5.87/6.08  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(864,a,847,a)].
% 5.87/6.08  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(864,a,848,a)].
% 5.87/6.08  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(864,a,849,a)].
% 5.87/6.08  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(864,a,850,a)].
% 5.87/6.08  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(864,a,851,a)].
% 5.87/6.08  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(864,a,852,a)].
% 5.87/6.08  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(864,a,853,a)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(864,a,861,a)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.08  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.87/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(865,b,840,a)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(865,b,845,a)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.09  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  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)].
% 5.88/6.10  866 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom).  [assumption].
% 5.88/6.10  Derived: class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(866,a,805,a)].
% 5.88/6.10  Derived: class_LOrder_Olorder(tc_nat).  [resolve(866,a,864,a)].
% 5.88/6.10  Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(866,a,865,b)].
% 5.88/6.10  867 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom).  [assumption].
% 5.88/6.10  Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint).  [resolve(867,a,805,a)].
% 5.88/6.10  Derived: class_LOrder_Ojoin__semilorder(tc_nat).  [resolve(867,a,864,a)].
% 5.88/6.10  Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(867,a,865,b)].
% 5.88/6.10  868 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom).  [assumption].
% 5.88/6.10  Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint).  [resolve(868,a,805,a)].
% 5.88/6.10  Derived: class_LOrder_Omeet__semilorder(tc_nat).  [resolve(868,a,864,a)].
% 5.88/6.10  Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(868,a,865,b)].
% 5.88/6.10  869 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom).  [assumption].
% 5.88/6.10  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(869,a,805,a)].
% 5.88/6.10  Derived: class_Orderings_Oord(tc_nat).  [resolve(869,a,864,a)].
% 5.88/6.10  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(869,a,865,b)].
% 5.88/6.10  870 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom).  [assumption].
% 5.88/6.10  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(870,a,805,a)].
% 5.88/6.10  Derived: class_Orderings_Oorder(tc_nat).  [resolve(870,a,864,a)].
% 5.88/6.10  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(870,a,865,b)].
% 5.88/6.11  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].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(871,b,840,a)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  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)].
% 5.88/6.11  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(871,b,845,a)].
% 5.88/6.11  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  872 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom).  [assumption].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.91/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.12  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(872,b,840,a)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(872,b,845,a)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.13  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  873 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom).  [assumption].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.14  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)].
% 5.92/6.15  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)].
% 5.92/6.15  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(873,b,840,a)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(873,b,845,a)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.15  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)].
% 5.92/6.16  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].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(874,b,840,a)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(874,b,845,a)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.16  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  875 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom).  [assumption].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.17  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(875,b,840,a)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(875,b,845,a)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.18  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.19  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)].
% 5.92/6.20  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)].
% 5.92/6.20  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(876,b,840,a)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(876,b,845,a)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.20  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  877 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom).  [assumption].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,815,a)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,825,a)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(877,b,840,a)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 5.92/6.21  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(877,b,845,a)].
% 5.92/6.21  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)].
% 5.92/6.21  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(877,b,851,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(877,b,852,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(877,b,853,a)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(877,b,861,a)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A).  [resolve(877,b,866,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A).  [resolve(877,b,867,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A).  [resolve(877,b,868,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(877,b,869,a)].
% 6.20/6.48  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A).  [resolve(877,b,870,a)].
% 6.20/6.48  878 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom).  [assumption].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.48  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.49  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)].
% 6.20/6.50  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)].
% 6.20/6.50  Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint).  [resolve(878,a,920,a)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,932,a)].
% 6.20/6.50  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,933,a)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.20/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0.  [resolve(878,a,944,a)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  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)].
% 6.31/6.50  948 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom).  [assumption].
% 6.31/6.50  949 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom).  [assumption].
% 6.31/6.50  950 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom).  [assumption].
% 6.31/6.50  951 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom).  [assumption].
% 6.31/6.50  952 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom).  [assumption].
% 6.31/6.50  953 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom).  [assumption].
% 6.31/6.50  954 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom).  [assumption].
% 6.31/6.50  Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint).  [resolve(954,a,878,a)].
% 6.31/6.50  955 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom).  [assumption].
% 6.31/6.50  956 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom).  [assumption].
% 6.31/6.50  Derived: class_Numeral_Onumber(tc_IntDef_Oint).  [resolve(956,a,878,a)].
% 6.31/6.50  957 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom).  [assumption].
% 6.31/6.50  958 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom).  [assumption].
% 6.31/6.50  959 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom).  [assumption].
% 6.31/6.57  960 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(6,b,1,a)].
% 6.31/6.57  961 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(6,b,3,a)].
% 6.31/6.57  962 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(9,a,6,b)].
% 6.31/6.57  963 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(10,a,6,b)].
% 6.31/6.57  964 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(79,a,45,b)].
% 6.31/6.57  965 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(80,a,45,b)].
% 6.31/6.57  966 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(81,b,45,b)].
% 6.31/6.57  967 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(82,b,45,b)].
% 6.31/6.57  968 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(83,a,88,b)].
% 6.31/6.57  969 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(89,a,88,b)].
% 6.31/6.57  970 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B.  [resolve(114,b,108,a)].
% 6.31/6.57  971 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B.  [resolve(114,b,111,a)].
% 6.31/6.57  972 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(116,a,114,b)].
% 6.31/6.57  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)].
% 6.31/6.57  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)].
% 6.31/6.57  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)].
% 6.31/6.57  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)].
% 6.31/6.57  977 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(199,b,175,b)].
% 6.31/6.57  978 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(200,b,175,b)].
% 6.31/6.57  979 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(201,b,175,b)].
% 6.31/6.57  980 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(202,b,175,b)].
% 6.31/6.57  981 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(236,a,207,b)].
% 6.31/6.57  982 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(237,a,207,b)].
% 6.31/6.57  983 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(276,b,247,b)].
% 6.31/6.57  984 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(277,b,247,b)].
% 6.31/6.57  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)].
% 6.31/6.57  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)].
% 6.31/6.57  987 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(285,b,280,a)].
% 6.31/6.57  988 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(285,b,282,a)].
% 6.31/6.57  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)].
% 6.31/6.57  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  994 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(344,a,328,b)].
% 6.31/6.58  995 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(345,a,328,b)].
% 6.31/6.58  996 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(362,a,328,b)].
% 6.31/6.58  997 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(363,a,328,b)].
% 6.31/6.58  998 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(364,c,328,b)].
% 6.31/6.58  999 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(365,c,328,b)].
% 6.31/6.58  1000 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(397,b,371,b)].
% 6.31/6.58  1001 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(398,b,371,b)].
% 6.31/6.58  1002 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(439,b,410,b)].
% 6.31/6.58  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(1002,b,878,a)].
% 6.31/6.58  1003 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(440,b,410,b)].
% 6.31/6.58  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(1003,b,878,a)].
% 6.31/6.58  1004 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(443,b,410,b)].
% 6.31/6.58  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(1004,b,878,a)].
% 6.31/6.58  1005 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(444,b,410,b)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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)].
% 6.31/6.58  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(1009,c,878,a)].
% 6.31/6.58  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)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.40/6.61  1013 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(456,b,410,b)].
% 6.40/6.61  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(1013,b,878,a)].
% 6.40/6.61  1014 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(457,b,410,b)].
% 6.40/6.61  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(1014,b,878,a)].
% 6.40/6.61  1015 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(458,b,410,b)].
% 6.40/6.61  1016 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(459,b,410,b)].
% 6.40/6.61  1017 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(460,c,410,b)].
% 6.40/6.61  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1017,c,878,a)].
% 6.40/6.61  1018 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(461,c,410,b)].
% 6.40/6.61  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1018,c,878,a)].
% 6.40/6.61  1019 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(463,b,410,b)].
% 6.40/6.61  1020 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(464,b,410,b)].
% 6.40/6.61  1021 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(508,a,489,b)].
% 6.40/6.61  1022 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(509,a,489,b)].
% 6.40/6.61  1023 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(525,a,518,b)].
% 6.40/6.61  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint).  [resolve(1023,b,878,a)].
% 6.40/6.61  1024 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(548,b,518,b)].
% 6.40/6.61  1025 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(549,b,518,b)].
% 6.40/6.61  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(1025,b,878,a)].
% 6.40/6.61  1026 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(550,b,518,b)].
% 6.40/6.61  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(1026,b,878,a)].
% 6.40/6.61  1027 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(551,b,518,b)].
% 6.40/6.61  1028 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(552,b,518,b)].
% 6.40/6.61  1029 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(639,b,593,b)].
% 6.40/6.61  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(1029,b,878,a)].
% 6.40/6.61  1030 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(640,b,593,b)].
% 6.40/6.61  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(1030,b,878,a)].
% 6.40/6.61  1031 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(642,b,593,b)].
% 6.40/6.61  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1031,b,878,a)].
% 6.40/6.61  1032 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(643,b,593,b)].
% 6.40/6.61  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(1032,b,878,a)].
% 6.40/6.61  1033 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(657,b,644,a)].
% 6.40/6.61  Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1033,a,878,a)].
% 6.40/6.61  1034 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(657,b,646,a)].
% 6.40/6.61  Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1034,a,878,a)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.40/6.61  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)].
% 6.52/6.81  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)].
% 6.52/6.81  1037 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(657,b,649,a)].
% 6.52/6.81  Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1037,a,878,a)].
% 6.52/6.81  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)].
% 6.52/6.81  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)].
% 6.52/6.81  1039 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(657,b,651,a)].
% 6.52/6.81  Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1.  [resolve(1039,a,878,a)].
% 6.52/6.81  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)].
% 6.52/6.81  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)].
% 6.52/6.81  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)].
% 6.52/6.81  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)].
% 6.52/6.81  1042 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(657,b,654,a)].
% 6.52/6.81  Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint).  [resolve(1042,a,878,a)].
% 6.52/6.81  1043 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(702,b,657,b)].
% 6.52/6.81  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(1043,b,878,a)].
% 6.52/6.81  1044 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(797,a,708,a)].
% 6.52/6.81  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1044,a,878,a)].
% 6.52/6.81  1045 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom).  [assumption].
% 6.52/6.81  1046 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom).  [assumption].
% 6.52/6.81  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1045,a,1046,a)].
% 6.52/6.81  1047 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom).  [assumption].
% 6.52/6.81  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(1047,a,1046,a)].
% 6.52/6.81  1048 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom).  [assumption].
% 6.52/6.81  1049 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom).  [assumption].
% 6.52/6.81  1050 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom).  [assumption].
% 6.52/6.81  Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1050,b,1046,a)].
% 6.52/6.81  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1050,b,1048,a)].
% 6.52/6.81  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A).  [resolve(1050,b,1049,a)].
% 6.52/6.81  1051 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom).  [assumption].
% 6.52/6.81  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1051,b,1046,a)].
% 6.52/6.81  1052 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom).  [assumption].
% 6.52/6.81  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1052,b,1046,a)].
% 6.52/6.81  1053 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1053,b,1046,a)].
% 6.79/7.07  1054 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1054,b,1046,a)].
% 6.79/7.07  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].
% 6.79/7.07  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1055,b,1046,a)].
% 6.79/7.07  1056 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1056,b,1046,a)].
% 6.79/7.07  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A).  [resolve(1056,b,1048,a)].
% 6.79/7.07  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1056,b,1049,a)].
% 6.79/7.07  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].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1057,b,1046,a)].
% 6.79/7.07  1058 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1058,b,1046,a)].
% 6.79/7.07  1059 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1059,b,1046,a)].
% 6.79/7.07  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].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1060,b,1046,a)].
% 6.79/7.07  1061 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1061,b,1046,a)].
% 6.79/7.07  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].
% 6.79/7.07  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1062,b,1046,a)].
% 6.79/7.07  1063 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom).  [assumption].
% 6.79/7.07  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1063,b,1046,a)].
% 6.79/7.07  1064 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint).  [resolve(867,a,805,a)].
% 6.79/7.07  1065 class_LOrder_Ojoin__semilorder(tc_nat).  [resolve(867,a,864,a)].
% 6.79/7.07  1066 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(867,a,865,b)].
% 6.79/7.07  1067 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A).  [resolve(877,b,867,a)].
% 6.79/7.07  1068 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom).  [assumption].
% 6.79/7.07  1069 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom).  [assumption].
% 6.79/7.07  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1068,a,1069,a)].
% 6.79/7.07  1070 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom).  [assumption].
% 6.89/7.10  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(1070,a,1069,a)].
% 6.89/7.10  1071 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1071,b,1069,a)].
% 6.89/7.10  1072 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom).  [assumption].
% 6.89/7.10  1073 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom).  [assumption].
% 6.89/7.10  1074 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1074,b,1069,a)].
% 6.89/7.10  1075 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1075,b,1069,a)].
% 6.89/7.10  1076 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1076,b,1069,a)].
% 6.89/7.10  1077 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1077,b,1069,a)].
% 6.89/7.10  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].
% 6.89/7.10  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1078,b,1069,a)].
% 6.89/7.10  1079 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1079,b,1069,a)].
% 6.89/7.10  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].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1080,b,1069,a)].
% 6.89/7.10  1081 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1081,b,1069,a)].
% 6.89/7.10  1082 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1082,b,1069,a)].
% 6.89/7.10  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].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1083,b,1069,a)].
% 6.89/7.10  1084 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom).  [assumption].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1084,b,1069,a)].
% 6.89/7.10  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].
% 6.89/7.10  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1085,b,1069,a)].
% 7.09/7.35  1086 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom).  [assumption].
% 7.09/7.35  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1086,b,1069,a)].
% 7.09/7.35  1087 class_LOrder_Omeet__semilorder(tc_IntDef_Oint).  [resolve(868,a,805,a)].
% 7.09/7.35  1088 class_LOrder_Omeet__semilorder(tc_nat).  [resolve(868,a,864,a)].
% 7.09/7.35  1089 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(868,a,865,b)].
% 7.09/7.35  1090 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A).  [resolve(877,b,868,a)].
% 7.09/7.35  1091 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom).  [assumption].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  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].
% 7.09/7.35  Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A.  [resolve(1091,a,1092,a)].
% 7.09/7.35  Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint).  [resolve(1091,a,1093,a)].
% 7.09/7.35  Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1094,a)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1091,a,1097,a)].
% 7.09/7.35  Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0.  [resolve(1091,a,1098,a)].
% 7.09/7.35  Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B.  [resolve(1091,a,1099,a)].
% 7.09/7.35  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(1091,a,1100,a)].
% 7.09/7.35  Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1091,a,1101,a)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1091,a,1104,a)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.09/7.35  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)].
% 7.19/7.38  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)].
% 7.19/7.38  Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint).  [resolve(1091,a,1112,a)].
% 7.19/7.38  Derived: -c_less(c_1,c_0,tc_IntDef_Oint).  [resolve(1091,a,1113,a)].
% 7.19/7.38  Derived: c_less(c_0,c_1,tc_IntDef_Oint).  [resolve(1091,a,1114,a)].
% 7.19/7.38  Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint).  [resolve(1091,a,1115,a)].
% 7.19/7.38  1116 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom).  [assumption].
% 7.19/7.38  Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A.  [resolve(1116,a,1092,a)].
% 7.19/7.38  Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat).  [resolve(1116,a,1093,a)].
% 7.19/7.38  Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat).  [resolve(1116,a,1094,a)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0.  [resolve(1116,a,1097,a)].
% 7.19/7.38  Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0.  [resolve(1116,a,1098,a)].
% 7.19/7.38  Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B.  [resolve(1116,a,1099,a)].
% 7.19/7.38  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0.  [resolve(1116,a,1100,a)].
% 7.19/7.38  Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat).  [resolve(1116,a,1101,a)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat).  [resolve(1116,a,1104,a)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.38  Derived: -c_lessequals(c_1,c_0,tc_nat).  [resolve(1116,a,1112,a)].
% 7.19/7.38  Derived: -c_less(c_1,c_0,tc_nat).  [resolve(1116,a,1113,a)].
% 7.19/7.38  Derived: c_less(c_0,c_1,tc_nat).  [resolve(1116,a,1114,a)].
% 7.19/7.38  Derived: c_lessequals(c_0,c_1,tc_nat).  [resolve(1116,a,1115,a)].
% 7.19/7.38  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].
% 7.19/7.38  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B.  [resolve(1117,b,1092,a)].
% 7.19/7.38  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A).  [resolve(1117,b,1093,a)].
% 7.19/7.38  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1117,b,1094,a)].
% 7.19/7.38  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)].
% 7.19/7.38  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)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0.  [resolve(1117,b,1097,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0.  [resolve(1117,b,1098,a)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A).  [resolve(1117,b,1104,a)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A).  [resolve(1117,b,1112,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A).  [resolve(1117,b,1113,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A).  [resolve(1117,b,1114,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A).  [resolve(1117,b,1115,a)].
% 7.19/7.39  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].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B.  [resolve(1118,b,1092,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A).  [resolve(1118,b,1093,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1118,b,1094,a)].
% 7.19/7.39  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)].
% 7.19/7.39  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)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0.  [resolve(1118,b,1097,a)].
% 7.19/7.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0.  [resolve(1118,b,1098,a)].
% 7.19/7.39  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A).  [resolve(1118,b,1104,a)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  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)].
% 7.19/7.40  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A).  [resolve(1118,b,1112,a)].
% 7.19/7.40  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A).  [resolve(1118,b,1113,a)].
% 7.19/7.40  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A).  [resolve(1118,b,1114,a)].
% 7.19/7.40  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A).  [resolve(1118,b,1115,a)].
% 7.19/7.40  1119 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom).  [assumption].
% 7.19/7.40  1120 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom).  [assumption].
% 7.19/7.40  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].
% 7.19/7.40  1122 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom).  [assumption].
% 7.19/7.40  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].
% 7.19/7.40  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1123,a,1118,b)].
% 7.19/7.40  1124 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom).  [assumption].
% 7.19/7.40  1125 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom).  [assumption].
% 7.19/7.40  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].
% 7.19/7.40  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint).  [resolve(1126,a,1091,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).  [resolve(1126,a,1116,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1126,a,1117,b)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1126,a,1118,b)].
% 7.21/7.40  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].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint).  [resolve(1127,a,1091,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat).  [resolve(1127,a,1116,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1127,a,1117,b)].
% 7.21/7.40  Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1127,a,1118,b)].
% 7.21/7.40  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].
% 7.21/7.40  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1128,a,1091,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1128,a,1116,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1128,a,1117,b)].
% 7.21/7.40  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1128,a,1118,b)].
% 7.21/7.40  1129 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom).  [assumption].
% 7.21/7.40  Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1129,a,1117,b)].
% 7.21/7.40  Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1129,a,1118,b)].
% 7.21/7.40  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].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1130,a,1091,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).  [resolve(1130,a,1116,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1130,a,1117,b)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1130,a,1118,b)].
% 7.21/7.40  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].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1131,a,1091,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1131,a,1116,a)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1131,a,1117,b)].
% 7.21/7.40  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1131,a,1118,b)].
% 7.21/7.40  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].
% 7.21/7.40  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint).  [resolve(1132,a,1091,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat).  [resolve(1132,a,1116,a)].
% 7.21/7.40  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1132,a,1117,b)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1132,a,1118,b)].
% 7.23/7.43  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].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint).  [resolve(1133,a,1091,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).  [resolve(1133,a,1116,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1133,a,1117,b)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1133,a,1118,b)].
% 7.23/7.43  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].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint).  [resolve(1134,a,1091,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat).  [resolve(1134,a,1116,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1134,a,1117,b)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1134,a,1118,b)].
% 7.23/7.43  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].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint).  [resolve(1135,a,1091,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__semiring(tc_nat).  [resolve(1135,a,1116,a)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1135,a,1117,b)].
% 7.23/7.43  Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1135,a,1118,b)].
% 7.23/7.43  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].
% 7.23/7.43  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1136,a,1091,a)].
% 7.23/7.43  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).  [resolve(1136,a,1116,a)].
% 7.23/7.43  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1136,a,1117,b)].
% 7.23/7.43  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1136,a,1118,b)].
% 7.23/7.43  1137 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom).  [assumption].
% 7.23/7.43  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1137,a,1117,b)].
% 7.23/7.43  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1137,a,1118,b)].
% 7.23/7.43  1138 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom).  [assumption].
% 7.23/7.43  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1138,a,1117,b)].
% 7.23/7.43  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1138,a,1118,b)].
% 7.23/7.43  1139 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom).  [assumption].
% 7.23/7.43  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)].
% 7.23/7.43  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)].
% 7.23/7.43  1142 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(81,b,69,b)].
% 7.23/7.43  1143 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(82,b,69,b)].
% 7.23/7.43  1144 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B.  [resolve(127,b,108,a)].
% 7.25/7.49  1145 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B.  [resolve(127,b,111,a)].
% 7.25/7.49  1146 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(127,b,117,a)].
% 7.25/7.49  1147 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A).  [resolve(127,b,118,a)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  1150 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(199,b,192,b)].
% 7.25/7.49  1151 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(200,b,192,b)].
% 7.25/7.49  1152 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(201,b,192,b)].
% 7.25/7.49  1153 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(202,b,192,b)].
% 7.25/7.49  1154 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(236,a,222,b)].
% 7.25/7.49  1155 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(237,a,222,b)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  1158 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0.  [resolve(298,b,280,a)].
% 7.25/7.49  1159 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0.  [resolve(298,b,282,a)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  1162 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(501,a,498,b)].
% 7.25/7.49  1163 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(508,a,498,b)].
% 7.25/7.49  1164 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(509,a,498,b)].
% 7.25/7.49  1165 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(513,a,498,b)].
% 7.25/7.49  1166 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(551,b,534,b)].
% 7.25/7.49  1167 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(585,a,565,b)].
% 7.25/7.49  1168 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(586,a,565,b)].
% 7.25/7.49  1169 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(589,b,565,b)].
% 7.25/7.49  1170 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(673,b,644,a)].
% 7.25/7.49  Derived: c_in(c_0,c_IntDef_ONats,tc_nat).  [resolve(1170,a,1116,a)].
% 7.25/7.49  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1170,a,1117,b)].
% 7.25/7.49  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1170,a,1118,b)].
% 7.25/7.49  1171 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(673,b,646,a)].
% 7.25/7.49  Derived: c_in(c_1,c_IntDef_ONats,tc_nat).  [resolve(1171,a,1116,a)].
% 7.25/7.49  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1171,a,1117,b)].
% 7.25/7.49  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1171,a,1118,b)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(1174,a,1116,a)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  1176 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(673,b,651,a)].
% 7.25/7.49  Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1.  [resolve(1176,a,1116,a)].
% 7.25/7.49  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A).  [resolve(1176,a,1117,b)].
% 7.25/7.49  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1176,a,1118,b)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.25/7.49  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)].
% 7.32/7.54  1179 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(673,b,654,a)].
% 7.32/7.54  Derived: -c_IntDef_Oiszero(c_1,tc_nat).  [resolve(1179,a,1116,a)].
% 7.32/7.54  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1179,a,1117,b)].
% 7.32/7.54  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1179,a,1118,b)].
% 7.32/7.54  1180 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(702,b,673,b)].
% 7.32/7.54  Derived: class_HOL_Oone(tc_nat).  [resolve(1180,b,1116,a)].
% 7.32/7.54  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1180,b,1117,b)].
% 7.32/7.54  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1180,b,1118,b)].
% 7.32/7.54  1181 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(794,a,708,a)].
% 7.32/7.54  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(1181,a,1116,a)].
% 7.32/7.54  1182 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A).  [resolve(794,a,715,a)].
% 7.32/7.54  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1182,a,1117,b)].
% 7.32/7.54  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1182,a,1118,b)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.54  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1192,a,1091,a)].
% 7.32/7.55  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(1192,a,1116,a)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1202,a,1091,a)].
% 7.32/7.55  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(1202,a,1116,a)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.55  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(1208,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(1209,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1211,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1212,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1214,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1215,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  1217 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(875,b,840,a)].
% 7.32/7.56  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(1217,a,1091,a)].
% 7.32/7.56  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(1217,a,1116,a)].
% 7.32/7.56  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1217,a,1117,b)].
% 7.32/7.56  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1217,a,1118,b)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1219,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(1220,a,1116,a)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  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)].
% 7.32/7.56  1222 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(875,b,845,a)].
% 7.32/7.56  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(1222,a,1091,a)].
% 7.32/7.56  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(1222,a,1116,a)].
% 7.32/7.56  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1222,a,1117,b)].
% 7.32/7.56  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1222,a,1118,b)].
% 7.32/7.56  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(1224,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(1225,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(1226,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(1227,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(1228,a,1091,a)].
% 7.32/7.57  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(1228,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(1229,a,1091,a)].
% 7.32/7.57  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(1229,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(1230,a,1091,a)].
% 7.32/7.57  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(1230,a,1116,a)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.32/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.57  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(1238,a,1091,a)].
% 7.39/7.60  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(1238,a,1116,a)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  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)].
% 7.39/7.60  1241 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1061,b,1046,a)].
% 7.39/7.60  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1241,a,1091,a)].
% 7.39/7.60  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(1241,a,1116,a)].
% 7.39/7.60  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1241,a,1117,b)].
% 7.39/7.60  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1241,a,1118,b)].
% 7.39/7.60  1242 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1084,b,1069,a)].
% 7.56/7.75  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1242,a,1091,a)].
% 7.56/7.75  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(1242,a,1116,a)].
% 7.56/7.75  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1242,a,1117,b)].
% 7.56/7.75  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1242,a,1118,b)].
% 7.56/7.75  1243 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom).  [assumption].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.75  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].
% 7.56/7.76  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].
% 7.56/7.76  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].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.76  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0.  [resolve(1243,a,1268,a)].
% 7.56/7.78  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].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.78  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.79  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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)].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.56/7.80  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].
% 7.63/7.81  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].
% 7.63/7.81  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].
% 7.63/7.81  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].
% 7.63/7.81  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].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint).  [resolve(1287,a,1243,a)].
% 7.63/7.81  Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1287,a,1269,b)].
% 7.63/7.81  Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1287,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1288,a,1243,a)].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1288,a,1269,b)].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1288,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(1289,a,1243,a)].
% 7.63/7.81  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1289,a,1269,b)].
% 7.63/7.81  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1289,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint).  [resolve(1290,a,1243,a)].
% 7.63/7.81  Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1290,a,1269,b)].
% 7.63/7.81  Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1290,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint).  [resolve(1291,a,1243,a)].
% 7.63/7.81  Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1291,a,1269,b)].
% 7.63/7.81  Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1291,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint).  [resolve(1292,a,1243,a)].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1292,a,1269,b)].
% 7.63/7.81  Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1292,a,1270,b)].
% 7.63/7.81  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].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint).  [resolve(1293,a,1243,a)].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1293,a,1269,b)].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1293,a,1270,b)].
% 7.63/7.85  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].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint).  [resolve(1294,a,1243,a)].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1294,a,1269,b)].
% 7.63/7.85  Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1294,a,1270,b)].
% 7.63/7.85  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].
% 7.63/7.85  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint).  [resolve(1295,a,1243,a)].
% 7.63/7.85  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1295,a,1269,b)].
% 7.63/7.85  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1295,a,1270,b)].
% 7.63/7.85  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].
% 7.63/7.85  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].
% 7.63/7.85  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)].
% 7.63/7.85  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)].
% 7.63/7.85  1300 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(30,b,9,a)].
% 7.63/7.85  1301 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(30,b,10,a)].
% 7.63/7.85  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)].
% 7.63/7.85  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)].
% 7.63/7.85  1304 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(165,a,151,b)].
% 7.63/7.85  1305 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(166,a,151,b)].
% 7.63/7.85  1306 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(236,a,221,b)].
% 7.63/7.85  1307 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(237,a,221,b)].
% 7.63/7.85  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)].
% 7.63/7.85  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)].
% 7.63/7.85  1310 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(297,b,280,a)].
% 7.63/7.85  1311 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(297,b,282,a)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  1314 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(317,a,297,b)].
% 7.63/7.86  1315 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(318,a,297,b)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  1321 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(344,a,336,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1321,b,1269,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1321,b,1270,b)].
% 7.63/7.86  1322 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(345,a,336,b)].
% 7.63/7.86  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1322,b,1269,b)].
% 7.63/7.86  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1322,b,1270,b)].
% 7.63/7.86  1323 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(356,b,336,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1323,b,1269,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1323,b,1270,b)].
% 7.63/7.86  1324 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(357,b,336,b)].
% 7.63/7.86  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1324,b,1269,b)].
% 7.63/7.86  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1324,b,1270,b)].
% 7.63/7.86  1325 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(358,b,336,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1325,b,1269,b)].
% 7.63/7.86  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1325,b,1270,b)].
% 7.63/7.86  1326 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(359,b,336,b)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.63/7.86  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  1329 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(362,a,336,b)].
% 7.69/7.93  1330 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(363,a,336,b)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  1333 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(786,a,708,a)].
% 7.69/7.93  1334 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(786,a,715,a)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.93  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.94  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)].
% 7.69/7.95  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)].
% 7.69/7.95  1369 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(874,b,840,a)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  1374 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(874,b,845,a)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.69/7.95  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)].
% 7.96/8.15  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)].
% 7.96/8.15  1393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1060,b,1046,a)].
% 7.96/8.15  1394 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1083,b,1069,a)].
% 7.96/8.15  1395 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom).  [assumption].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  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].
% 7.96/8.15  Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1396,a)].
% 7.96/8.15  Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint).  [resolve(1395,a,1397,a)].
% 7.96/8.15  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)].
% 7.96/8.15  Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1395,a,1399,a)].
% 7.96/8.15  Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0.  [resolve(1395,a,1400,a)].
% 7.96/8.15  Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1395,a,1401,a)].
% 7.96/8.15  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)].
% 7.96/8.15  Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1403,a)].
% 7.96/8.15  Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1395,a,1404,a)].
% 7.96/8.16  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)].
% 7.96/8.16  Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1395,a,1406,a)].
% 7.96/8.16  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A.  [resolve(1395,a,1407,a)].
% 7.96/8.16  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)].
% 7.96/8.16  Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1395,a,1409,a)].
% 7.96/8.16  Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1410,a)].
% 7.96/8.16  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].
% 7.96/8.16  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].
% 7.96/8.16  1413 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom).  [assumption].
% 7.96/8.16  1414 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom).  [assumption].
% 7.96/8.16  1415 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom).  [assumption].
% 7.96/8.16  1416 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom).  [assumption].
% 7.96/8.16  1417 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom).  [assumption].
% 7.96/8.16  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].
% 7.96/8.16  1419 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom).  [assumption].
% 7.96/8.16  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].
% 7.96/8.16  1421 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom).  [assumption].
% 7.96/8.16  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].
% 7.96/8.16  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].
% 7.96/8.16  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].
% 7.96/8.16  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].
% 7.96/8.16  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1425,b,1396,a)].
% 7.96/8.16  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1425,b,1397,a)].
% 7.96/8.16  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)].
% 7.96/8.16  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1425,b,1399,a)].
% 7.96/8.16  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1425,b,1400,a)].
% 7.96/8.16  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1425,b,1401,a)].
% 7.96/8.18  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)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1425,b,1404,a)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1425,b,1406,a)].
% 7.96/8.18  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)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1425,b,1409,a)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1425,b,1412,a)].
% 7.96/8.18  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].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1426,b,1396,a)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1426,b,1397,a)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1426,b,1399,a)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1426,b,1400,a)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1426,b,1401,a)].
% 7.96/8.18  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)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1426,b,1404,a)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1426,b,1406,a)].
% 7.96/8.18  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)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1426,b,1409,a)].
% 7.96/8.18  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)].
% 7.96/8.18  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].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1427,b,1396,a)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1427,b,1397,a)].
% 7.96/8.18  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)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1427,b,1399,a)].
% 7.96/8.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1427,b,1400,a)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1427,b,1401,a)].
% 8.17/8.38  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)].
% 8.17/8.38  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)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1427,b,1404,a)].
% 8.17/8.38  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)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1427,b,1406,a)].
% 8.17/8.38  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)].
% 8.17/8.38  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)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1427,b,1409,a)].
% 8.17/8.38  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)].
% 8.17/8.38  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)].
% 8.17/8.38  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)].
% 8.17/8.38  1430 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(50,b,47,a)].
% 8.17/8.38  1431 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A).  [resolve(50,b,48,a)].
% 8.17/8.38  1432 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1052,b,1046,a)].
% 8.17/8.38  1433 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1075,b,1069,a)].
% 8.17/8.38  1434 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint).  [resolve(1292,a,1243,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1434,a,1411,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(1434,a,1412,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1413,a)].
% 8.17/8.38  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1434,a,1414,a)].
% 8.17/8.38  Derived: class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(1434,a,1415,a)].
% 8.17/8.38  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1434,a,1416,a)].
% 8.17/8.38  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1434,a,1417,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(1434,a,1418,a)].
% 8.17/8.38  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(1434,a,1419,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(1434,a,1420,a)].
% 8.17/8.38  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(1434,a,1421,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1434,a,1422,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1423,a)].
% 8.17/8.38  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1424,a)].
% 8.17/8.38  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1434,a,1428,a)].
% 8.17/8.38  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1434,a,1429,a)].
% 8.17/8.38  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1434,a,1432,a)].
% 8.17/8.38  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1434,a,1433,a)].
% 8.17/8.38  1435 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1292,a,1269,b)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1435,a,1411,a)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1435,a,1412,a)].
% 8.17/8.38  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1435,a,1413,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1435,a,1414,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A).  [resolve(1435,a,1415,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1435,a,1416,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1435,a,1417,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A).  [resolve(1435,a,1421,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1435,a,1422,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1435,a,1423,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1435,a,1424,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1435,a,1432,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1435,a,1433,a)].
% 8.27/8.49  1436 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1292,a,1270,b)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1436,a,1411,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1436,a,1412,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1436,a,1413,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1436,a,1414,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A).  [resolve(1436,a,1415,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1436,a,1416,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1436,a,1417,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A).  [resolve(1436,a,1421,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1436,a,1422,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1436,a,1423,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1436,a,1424,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1436,a,1432,a)].
% 8.27/8.49  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1436,a,1433,a)].
% 8.27/8.49  1437 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom).  [assumption].
% 8.27/8.49  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].
% 8.27/8.49  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].
% 8.27/8.49  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].
% 8.27/8.49  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].
% 8.27/8.49  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].
% 8.33/8.50  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].
% 8.33/8.50  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].
% 8.33/8.50  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].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  1446 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom).  [assumption].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.50  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.51  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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)].
% 8.33/8.52  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].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1452,a,1447,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1452,a,1448,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1452,a,1449,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1452,a,1450,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1452,a,1451,b)].
% 8.33/8.52  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].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1453,a,1447,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1453,a,1448,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1453,a,1449,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1453,a,1450,b)].
% 8.33/8.52  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1453,a,1451,b)].
% 8.33/8.52  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].
% 8.33/8.52  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1454,a,1447,b)].
% 8.33/8.52  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1454,a,1448,b)].
% 8.33/8.53  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1454,a,1449,b)].
% 8.33/8.53  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1454,a,1451,b)].
% 8.33/8.53  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].
% 8.33/8.53  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1455,a,1447,b)].
% 8.33/8.53  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1455,a,1448,b)].
% 8.33/8.53  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1455,a,1449,b)].
% 8.33/8.53  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1455,a,1451,b)].
% 8.33/8.53  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].
% 8.33/8.53  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].
% 8.33/8.53  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].
% 8.33/8.53  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)].
% 8.33/8.53  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)].
% 8.33/8.53  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)].
% 8.33/8.53  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.54  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)].
% 8.33/8.55  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].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.55  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)].
% 8.33/8.57  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].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1463,b,1453,a)].
% 8.33/8.57  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1463,b,1454,a)].
% 8.33/8.57  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A).  [resolve(1463,b,1455,a)].
% 8.33/8.57  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)].
% 8.33/8.57  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1464,a,1447,b)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1465,a,1447,b)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  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)].
% 8.33/8.57  1466 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(81,b,55,b)].
% 8.33/8.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1466,b,1447,b)].
% 8.33/8.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1466,b,1448,b)].
% 8.33/8.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1466,b,1449,b)].
% 8.33/8.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1466,b,1450,b)].
% 8.33/8.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1466,b,1451,b)].
% 8.33/8.57  1467 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(82,b,55,b)].
% 8.72/8.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1467,b,1447,b)].
% 8.72/8.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1467,b,1448,b)].
% 8.72/8.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1467,b,1449,b)].
% 8.72/8.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1467,b,1450,b)].
% 8.72/8.89  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1467,b,1451,b)].
% 8.72/8.89  1468 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1130,a,1091,a)].
% 8.72/8.89  1469 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).  [resolve(1130,a,1116,a)].
% 8.72/8.89  Derived: class_Orderings_Oorder(tc_nat).  [resolve(1469,a,1454,a)].
% 8.72/8.89  Derived: class_Orderings_Oord(tc_nat).  [resolve(1469,a,1455,a)].
% 8.72/8.89  Derived: class_HOL_Oplus(tc_nat).  [resolve(1469,a,1457,a)].
% 8.72/8.89  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(1469,a,1464,a)].
% 8.72/8.89  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(1469,a,1465,a)].
% 8.72/8.89  1470 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1130,a,1117,b)].
% 8.72/8.89  1471 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1130,a,1118,b)].
% 8.72/8.89  1472 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1434,a,1422,a)].
% 8.72/8.89  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1472,a,1454,a)].
% 8.72/8.89  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1472,a,1455,a)].
% 8.72/8.89  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1472,a,1456,a)].
% 8.72/8.89  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1472,a,1457,a)].
% 8.72/8.89  1473 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1435,a,1422,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1473,b,1454,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1473,b,1455,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1473,b,1456,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1473,b,1457,a)].
% 8.72/8.89  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)].
% 8.72/8.89  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)].
% 8.72/8.89  1474 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1436,a,1422,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1474,b,1454,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1474,b,1455,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1474,b,1456,a)].
% 8.72/8.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1474,b,1457,a)].
% 8.72/8.89  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)].
% 8.72/8.89  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)].
% 8.72/8.89  1475 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom).  [assumption].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  1484 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom).  [assumption].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  1489 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom).  [assumption].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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].
% 8.72/8.89  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)].
% 8.72/8.89  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)].
% 8.72/8.89  Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1475,a,1478,a)].
% 8.72/8.89  Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(1475,a,1479,a)].
% 8.72/8.89  Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1475,a,1480,a)].
% 8.72/8.89  Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(1475,a,1481,a)].
% 8.72/8.89  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)].
% 8.72/8.90  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)].
% 8.72/8.90  Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1484,a)].
% 8.72/8.90  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1485,a)].
% 8.72/8.90  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A.  [resolve(1475,a,1486,a)].
% 8.72/8.90  Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1475,a,1487,a)].
% 8.72/8.90  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)].
% 8.72/8.90  Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1489,a)].
% 8.72/8.90  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1490,a)].
% 8.72/8.90  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A.  [resolve(1475,a,1491,a)].
% 8.72/8.90  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)].
% 8.72/8.90  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)].
% 8.72/8.90  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)].
% 8.72/8.90  Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1495,a)].
% 8.72/8.90  1496 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom).  [assumption].
% 8.72/8.90  1497 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom).  [assumption].
% 8.72/8.90  1498 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom).  [assumption].
% 8.72/8.90  1499 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom).  [assumption].
% 8.72/8.90  1500 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom).  [assumption].
% 8.72/8.90  1501 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom).  [assumption].
% 8.72/8.90  1502 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom).  [assumption].
% 8.72/8.90  1503 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom).  [assumption].
% 8.72/8.90  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].
% 8.72/8.90  1505 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom).  [assumption].
% 8.72/8.90  1506 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom).  [assumption].
% 8.72/8.90  1507 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom).  [assumption].
% 8.72/8.90  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].
% 8.72/8.90  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1508,b,1484,a)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1508,b,1487,a)].
% 8.76/8.91  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)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1508,b,1489,a)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1508,b,1495,a)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1508,b,1496,a)].
% 8.76/8.91  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1508,b,1497,a)].
% 8.76/8.91  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].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.91  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1509,b,1484,a)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1509,b,1487,a)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1509,b,1489,a)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1509,b,1495,a)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1509,b,1496,a)].
% 8.76/8.93  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1509,b,1497,a)].
% 8.76/8.93  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].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1510,b,1484,a)].
% 8.76/8.93  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)].
% 8.76/8.93  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)].
% 8.76/8.93  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1510,b,1487,a)].
% 8.78/8.94  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)].
% 8.78/8.94  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1510,b,1489,a)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1510,b,1495,a)].
% 8.78/8.94  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].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1511,b,1484,a)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1511,b,1487,a)].
% 8.78/8.94  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)].
% 8.78/8.94  Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1511,b,1489,a)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.78/8.94  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)].
% 8.94/9.16  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1511,b,1495,a)].
% 8.94/9.16  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].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1512,b,1484,a)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1512,b,1487,a)].
% 8.94/9.16  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)].
% 8.94/9.16  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1512,b,1489,a)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  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)].
% 8.94/9.16  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1512,b,1495,a)].
% 8.94/9.16  1513 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(11,b,1,a)].
% 8.94/9.16  1514 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(11,b,3,a)].
% 8.94/9.16  1515 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(81,b,49,b)].
% 8.94/9.16  1516 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(82,b,49,b)].
% 8.94/9.16  1517 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1051,b,1046,a)].
% 8.94/9.16  1518 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1074,b,1069,a)].
% 8.94/9.16  1519 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1288,a,1243,a)].
% 8.94/9.16  1520 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1288,a,1269,b)].
% 8.94/9.16  1521 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1288,a,1270,b)].
% 8.94/9.16  1522 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1434,a,1411,a)].
% 9.01/9.18  1523 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1435,a,1411,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1523,b,1497,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A).  [resolve(1523,b,1501,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(1523,b,1502,a)].
% 9.01/9.18  1524 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1436,a,1411,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1524,b,1497,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A).  [resolve(1524,b,1501,a)].
% 9.01/9.18  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(1524,b,1502,a)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  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)].
% 9.01/9.18  1533 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1452,a,1447,b)].
% 9.01/9.18  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1533,b,1475,a)].
% 9.01/9.18  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1533,b,1510,b)].
% 9.01/9.18  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1533,b,1511,b)].
% 9.01/9.18  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1533,b,1512,b)].
% 9.01/9.18  1534 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1453,a,1447,b)].
% 9.15/9.31  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1534,b,1475,a)].
% 9.15/9.31  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1534,b,1510,b)].
% 9.15/9.31  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1534,b,1511,b)].
% 9.15/9.31  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1534,b,1512,b)].
% 9.15/9.31  1535 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1454,a,1447,b)].
% 9.15/9.31  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1535,b,1510,b)].
% 9.15/9.31  1536 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1455,a,1447,b)].
% 9.15/9.31  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1536,b,1510,b)].
% 9.15/9.31  1537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1464,a,1447,b)].
% 9.15/9.31  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1537,c,1475,a)].
% 9.15/9.31  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)].
% 9.15/9.31  1538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1465,a,1447,b)].
% 9.15/9.31  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1538,c,1475,a)].
% 9.15/9.31  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)].
% 9.15/9.31  1539 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1466,b,1447,b)].
% 9.15/9.31  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1539,b,1510,b)].
% 9.15/9.31  1540 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1467,b,1447,b)].
% 9.15/9.31  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1540,b,1510,b)].
% 9.15/9.31  1541 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom).  [assumption].
% 9.15/9.31  1542 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom).  [assumption].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.31  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].
% 9.15/9.32  1552 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom).  [assumption].
% 9.15/9.32  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1541,a,1542,a)].
% 9.15/9.32  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1543,a)].
% 9.15/9.32  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1541,a,1544,a)].
% 9.15/9.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1545,a)].
% 9.15/9.32  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)].
% 9.15/9.32  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)].
% 9.15/9.32  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)].
% 9.15/9.32  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(1541,a,1549,a)].
% 9.15/9.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1550,a)].
% 9.15/9.32  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(1541,a,1551,a)].
% 9.15/9.32  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1541,a,1552,a)].
% 9.15/9.32  1553 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom).  [assumption].
% 9.15/9.32  Derived: -c_less(A,A,tc_nat).  [resolve(1553,a,1542,a)].
% 9.15/9.32  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1543,a)].
% 9.15/9.32  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1553,a,1544,a)].
% 9.15/9.32  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1545,a)].
% 9.15/9.32  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)].
% 9.15/9.32  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)].
% 9.15/9.32  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(1553,a,1548,a)].
% 9.15/9.32  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(1553,a,1549,a)].
% 9.15/9.32  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1550,a)].
% 9.15/9.32  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(1553,a,1551,a)].
% 9.15/9.32  Derived: c_lessequals(A,A,tc_nat).  [resolve(1553,a,1552,a)].
% 9.15/9.32  1554 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom).  [assumption].
% 9.15/9.32  Derived: -c_less(A,A,tc_set(B)).  [resolve(1554,a,1542,a)].
% 9.15/9.32  Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1543,a)].
% 9.15/9.32  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)).  [resolve(1554,a,1544,a)].
% 9.15/9.32  Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1545,a)].
% 9.15/9.32  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)].
% 9.15/9.32  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)].
% 9.15/9.33  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)].
% 9.15/9.33  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)].
% 9.15/9.33  Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1550,a)].
% 9.15/9.33  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)].
% 9.15/9.33  Derived: c_lessequals(A,A,tc_set(B)).  [resolve(1554,a,1552,a)].
% 9.15/9.33  1555 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom).  [assumption].
% 9.15/9.33  Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A).  [resolve(1555,b,1542,a)].
% 9.15/9.33  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1543,a)].
% 9.15/9.33  Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1544,a)].
% 9.15/9.33  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1555,b,1545,a)].
% 9.15/9.33  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)].
% 9.15/9.33  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)].
% 9.15/9.33  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)].
% 9.15/9.33  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)].
% 9.15/9.33  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1550,a)].
% 9.15/9.34  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)].
% 9.15/9.34  Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A).  [resolve(1555,b,1552,a)].
% 9.15/9.34  1556 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom).  [assumption].
% 9.15/9.34  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A).  [resolve(1556,b,1542,a)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.34  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)].
% 9.15/9.35  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A).  [resolve(1556,b,1552,a)].
% 9.15/9.35  1557 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom).  [assumption].
% 9.15/9.35  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A).  [resolve(1557,b,1542,a)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A).  [resolve(1557,b,1552,a)].
% 9.15/9.35  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].
% 9.15/9.35  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1558,b,1542,a)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.35  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)].
% 9.15/9.36  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1558,b,1552,a)].
% 9.15/9.36  1559 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom).  [assumption].
% 9.15/9.36  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A).  [resolve(1559,b,1542,a)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A).  [resolve(1559,b,1552,a)].
% 9.15/9.36  1560 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom).  [assumption].
% 9.15/9.36  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1560,b,1542,a)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  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)].
% 9.15/9.36  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1560,b,1552,a)].
% 9.15/9.37  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].
% 9.15/9.37  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1561,b,1542,a)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1561,b,1552,a)].
% 9.15/9.37  1562 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom).  [assumption].
% 9.15/9.37  Derived: class_Orderings_Oord(tc_set(A)).  [resolve(1562,a,1554,a)].
% 9.15/9.37  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1562,a,1560,b)].
% 9.15/9.37  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1562,a,1561,b)].
% 9.15/9.37  1563 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom).  [assumption].
% 9.15/9.37  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A).  [resolve(1563,b,1542,a)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.15/9.37  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)].
% 9.22/9.38  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)].
% 9.22/9.38  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A).  [resolve(1563,b,1552,a)].
% 9.22/9.38  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].
% 9.22/9.38  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A).  [resolve(1564,b,1542,a)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1564,b,1552,a)].
% 9.22/9.38  1565 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom).  [assumption].
% 9.22/9.38  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A).  [resolve(1565,b,1542,a)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.38  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)].
% 9.22/9.39  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)].
% 9.22/9.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A).  [resolve(1565,b,1552,a)].
% 9.22/9.39  1566 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom).  [assumption].
% 9.22/9.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A).  [resolve(1566,b,1542,a)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A).  [resolve(1566,b,1552,a)].
% 9.22/9.39  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].
% 9.22/9.39  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A).  [resolve(1567,b,1542,a)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.39  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)].
% 9.22/9.40  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1567,b,1552,a)].
% 9.22/9.40  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].
% 9.22/9.40  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A).  [resolve(1568,b,1542,a)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1568,b,1552,a)].
% 9.22/9.40  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].
% 9.22/9.40  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A).  [resolve(1569,b,1542,a)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.40  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)].
% 9.22/9.41  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A).  [resolve(1569,b,1552,a)].
% 9.22/9.41  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].
% 9.22/9.41  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A).  [resolve(1570,b,1542,a)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A).  [resolve(1570,b,1552,a)].
% 9.22/9.41  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].
% 9.22/9.41  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A).  [resolve(1571,b,1542,a)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  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)].
% 9.22/9.41  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1571,b,1552,a)].
% 9.22/9.42  1572 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom).  [assumption].
% 9.22/9.42  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A).  [resolve(1572,b,1542,a)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A).  [resolve(1572,b,1552,a)].
% 9.22/9.42  1573 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom).  [assumption].
% 9.22/9.42  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A).  [resolve(1573,b,1542,a)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  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)].
% 9.22/9.42  Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A).  [resolve(1573,b,1552,a)].
% 9.22/9.42  1574 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom).  [assumption].
% 9.22/9.42  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A).  [resolve(1574,b,1542,a)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1543,a)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1544,a)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1574,b,1545,a)].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1550,a)].
% 9.67/9.82  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)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A).  [resolve(1574,b,1552,a)].
% 9.67/9.82  1575 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(870,a,805,a)].
% 9.67/9.82  1576 class_Orderings_Oorder(tc_nat).  [resolve(870,a,864,a)].
% 9.67/9.82  1577 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(870,a,865,b)].
% 9.67/9.82  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A).  [resolve(1577,a,1562,a)].
% 9.67/9.82  1578 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A).  [resolve(877,b,870,a)].
% 9.67/9.82  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(1578,b,1562,a)].
% 9.67/9.82  1579 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A).  [resolve(1050,b,1049,a)].
% 9.67/9.82  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1579,b,1562,a)].
% 9.67/9.82  1580 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1056,b,1049,a)].
% 9.67/9.82  1581 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1137,a,1117,b)].
% 9.67/9.82  1582 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1137,a,1118,b)].
% 9.67/9.82  1583 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1434,a,1416,a)].
% 9.67/9.82  1584 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1435,a,1416,a)].
% 9.67/9.82  1585 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1436,a,1416,a)].
% 9.67/9.82  1586 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1454,a,1448,b)].
% 9.67/9.82  1587 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1454,a,1449,b)].
% 9.67/9.82  1588 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1454,a,1451,b)].
% 9.67/9.82  1589 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1463,b,1454,a)].
% 9.67/9.82  1590 class_Orderings_Oorder(tc_nat).  [resolve(1469,a,1454,a)].
% 9.67/9.82  1591 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1472,a,1454,a)].
% 9.67/9.82  1592 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1473,b,1454,a)].
% 9.67/9.82  1593 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1474,b,1454,a)].
% 9.67/9.82  1594 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1535,b,1510,b)].
% 9.67/9.82  1595 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom).  [assumption].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.82  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  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)].
% 9.67/9.84  1616 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom).  [assumption].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1596,a)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1616,a,1597,a)].
% 9.67/9.84  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)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1599,a)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1616,a,1600,a)].
% 9.67/9.84  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)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1602,a)].
% 9.67/9.84  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1616,a,1603,a)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1616,a,1604,a)].
% 9.67/9.84  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1616,a,1605,a)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1606,a)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1616,a,1607,a)].
% 9.67/9.84  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)].
% 9.67/9.84  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1609,a)].
% 9.67/9.85  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1616,a,1610,a)].
% 9.67/9.85  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)].
% 9.67/9.85  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1612,a)].
% 9.67/9.85  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1616,a,1613,a)].
% 9.67/9.85  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1616,a,1614,a)].
% 9.67/9.85  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1616,a,1615,a)].
% 9.67/9.85  1617 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom).  [assumption].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  1618 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom).  [assumption].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.85  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1602,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1618,b,1603,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1618,b,1604,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1618,b,1605,a)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1618,b,1612,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1618,b,1613,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1618,b,1614,a)].
% 9.67/9.86  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1618,b,1615,a)].
% 9.67/9.86  1619 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom).  [assumption].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.86  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  1620 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom).  [assumption].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.87  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.89  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)].
% 9.67/9.90  1622 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom).  [assumption].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  1623 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom).  [assumption].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.67/9.90  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.91  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.92  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  1626 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom).  [assumption].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.93  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  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)].
% 9.77/9.95  1628 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom).  [assumption].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  1629 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom).  [assumption].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.96  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.97  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.77/9.98  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/9.99  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.01  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  1635 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom).  [assumption].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.02  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  1636 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom).  [assumption].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.03  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  1637 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom).  [assumption].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 9.86/10.04  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)].
% 10.99/11.13  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)].
% 10.99/11.13  1638 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(869,a,805,a)].
% 10.99/11.13  1639 class_Orderings_Oord(tc_nat).  [resolve(869,a,864,a)].
% 10.99/11.13  1640 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(869,a,865,b)].
% 10.99/11.13  1641 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(877,b,869,a)].
% 10.99/11.13  1642 -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1050,b,1048,a)].
% 10.99/11.13  1643 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A).  [resolve(1056,b,1048,a)].
% 10.99/11.13  1644 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1138,a,1117,b)].
% 10.99/11.13  1645 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1138,a,1118,b)].
% 10.99/11.13  1646 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1434,a,1417,a)].
% 10.99/11.13  1647 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1435,a,1417,a)].
% 10.99/11.13  1648 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1436,a,1417,a)].
% 10.99/11.13  1649 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1455,a,1448,b)].
% 10.99/11.13  1650 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1455,a,1449,b)].
% 10.99/11.13  1651 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1455,a,1451,b)].
% 10.99/11.13  1652 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A).  [resolve(1463,b,1455,a)].
% 10.99/11.13  1653 class_Orderings_Oord(tc_nat).  [resolve(1469,a,1455,a)].
% 10.99/11.13  1654 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1472,a,1455,a)].
% 10.99/11.13  1655 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1473,b,1455,a)].
% 10.99/11.13  1656 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1474,b,1455,a)].
% 10.99/11.13  1657 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1536,b,1510,b)].
% 10.99/11.13  1658 class_Orderings_Oord(tc_set(A)).  [resolve(1562,a,1554,a)].
% 10.99/11.13  1659 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1562,a,1560,b)].
% 10.99/11.13  1660 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1562,a,1561,b)].
% 10.99/11.13  1661 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A).  [resolve(1577,a,1562,a)].
% 10.99/11.13  1662 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(1578,b,1562,a)].
% 10.99/11.13  1663 -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1579,b,1562,a)].
% 10.99/11.13  1664 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1050,b,1046,a)].
% 10.99/11.13  1665 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom).  [assumption].
% 10.99/11.13  1666 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom).  [assumption].
% 10.99/11.13  1667 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom).  [assumption].
% 10.99/11.13  1668 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom).  [assumption].
% 10.99/11.13  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].
% 10.99/11.13  1670 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom).  [assumption].
% 10.99/11.13  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].
% 10.99/11.13  1672 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom).  [assumption].
% 10.99/11.13  1673 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom).  [assumption].
% 11.09/11.25  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].
% 11.09/11.25  1675 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom).  [assumption].
% 11.09/11.25  1676 class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(866,a,805,a)].
% 11.09/11.25  1677 class_LOrder_Olorder(tc_nat).  [resolve(866,a,864,a)].
% 11.09/11.25  1678 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(866,a,865,b)].
% 11.09/11.25  1679 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A).  [resolve(877,b,866,a)].
% 11.09/11.25  1680 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1071,b,1069,a)].
% 11.09/11.25  1681 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1129,a,1117,b)].
% 11.09/11.25  1682 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1129,a,1118,b)].
% 11.09/11.25  1683 class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(1434,a,1415,a)].
% 11.09/11.25  1684 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A).  [resolve(1435,a,1415,a)].
% 11.09/11.25  1685 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A).  [resolve(1436,a,1415,a)].
% 11.09/11.25  1686 -class_LOrder_Olorder(A) | -c_less(B,B,A).  [resolve(1555,b,1542,a)].
% 11.09/11.25  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1686,a,1665,a)].
% 11.09/11.25  Derived: -c_less(A,A,tc_nat).  [resolve(1686,a,1666,a)].
% 11.09/11.25  1687 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1543,a)].
% 11.09/11.25  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1687,a,1665,a)].
% 11.09/11.25  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1687,a,1666,a)].
% 11.09/11.25  1688 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1544,a)].
% 11.09/11.25  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1688,a,1665,a)].
% 11.09/11.25  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1688,a,1666,a)].
% 11.09/11.25  1689 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1555,b,1545,a)].
% 11.09/11.25  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1689,a,1665,a)].
% 11.09/11.25  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1689,a,1666,a)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.09/11.25  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  1694 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1550,a)].
% 11.15/11.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1694,a,1665,a)].
% 11.15/11.29  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1694,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  1696 -class_LOrder_Olorder(A) | c_lessequals(B,B,A).  [resolve(1555,b,1552,a)].
% 11.15/11.29  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1696,a,1665,a)].
% 11.15/11.29  Derived: c_lessequals(A,A,tc_nat).  [resolve(1696,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1697,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1698,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1700,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1701,a,1666,a)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.29  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)].
% 11.15/11.30  1703 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1602,a)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1703,a,1666,a)].
% 11.15/11.30  1704 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1618,b,1603,a)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1704,a,1666,a)].
% 11.15/11.30  1705 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1618,b,1604,a)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1705,a,1666,a)].
% 11.15/11.30  1706 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1618,b,1605,a)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1706,a,1666,a)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1707,a,1666,a)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1708,a,1666,a)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1710,a,1666,a)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1711,a,1666,a)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.15/11.30  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)].
% 11.32/11.50  1713 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1618,b,1612,a)].
% 11.32/11.50  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)].
% 11.32/11.50  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1713,a,1666,a)].
% 11.32/11.50  1714 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1618,b,1613,a)].
% 11.32/11.50  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)].
% 11.32/11.50  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1714,a,1666,a)].
% 11.32/11.50  1715 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1618,b,1614,a)].
% 11.32/11.50  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)].
% 11.32/11.50  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1715,a,1666,a)].
% 11.32/11.50  1716 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1618,b,1615,a)].
% 11.32/11.50  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)].
% 11.32/11.50  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1716,a,1666,a)].
% 11.32/11.50  1717 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom).  [assumption].
% 11.32/11.50  1718 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom).  [assumption].
% 11.32/11.50  1719 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom).  [assumption].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  1724 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom).  [assumption].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.32/11.50  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].
% 11.62/11.75  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].
% 11.62/11.75  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].
% 11.62/11.75  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].
% 11.62/11.75  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].
% 11.62/11.75  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].
% 11.62/11.75  1737 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1136,a,1091,a)].
% 11.62/11.75  1738 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).  [resolve(1136,a,1116,a)].
% 11.62/11.75  1739 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1136,a,1117,b)].
% 11.62/11.75  1740 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1136,a,1118,b)].
% 11.62/11.75  1741 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1424,a)].
% 11.62/11.75  1742 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1435,a,1424,a)].
% 11.62/11.75  1743 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1436,a,1424,a)].
% 11.62/11.75  1744 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1453,a,1448,b)].
% 11.62/11.75  1745 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1453,a,1449,b)].
% 11.62/11.75  1746 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1453,a,1450,b)].
% 11.62/11.75  1747 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1453,a,1451,b)].
% 11.62/11.75  1748 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1463,b,1453,a)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1748,b,1717,a)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(1748,b,1724,a)].
% 11.62/11.75  1749 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1534,b,1475,a)].
% 11.62/11.75  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1749,a,1717,a)].
% 11.62/11.75  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1749,a,1724,a)].
% 11.62/11.75  1750 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1534,b,1510,b)].
% 11.62/11.75  1751 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1534,b,1511,b)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1751,a,1717,a)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1751,a,1724,a)].
% 11.62/11.75  1752 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1534,b,1512,b)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1752,a,1717,a)].
% 11.62/11.75  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1752,a,1724,a)].
% 11.62/11.75  1753 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1560,b,1542,a)].
% 11.62/11.76  Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1753,a,1720,b)].
% 11.62/11.76  Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1753,a,1721,b)].
% 11.62/11.76  Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1753,a,1722,b)].
% 11.62/11.76  Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1753,a,1723,b)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.76  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.77  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)].
% 11.62/11.82  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)].
% 11.62/11.82  1763 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1560,b,1552,a)].
% 11.62/11.82  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1763,a,1720,b)].
% 11.62/11.82  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1763,a,1721,b)].
% 11.62/11.82  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1763,a,1722,b)].
% 11.62/11.82  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1763,a,1723,b)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.82  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.62/11.83  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.72/11.84  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)].
% 11.92/12.11  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)].
% 11.92/12.11  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)].
% 11.92/12.11  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].
% 11.92/12.11  1785 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom).  [assumption].
% 11.92/12.11  1786 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom).  [assumption].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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].
% 11.92/12.11  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)].
% 11.92/12.11  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)].
% 11.92/12.11  1800 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(18,b,9,a)].
% 11.92/12.11  1801 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(18,b,10,a)].
% 11.92/12.11  1802 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(749,b,708,a)].
% 11.92/12.11  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1802,a,1793,b)].
% 11.92/12.11  1803 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(749,b,715,a)].
% 11.92/12.11  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1803,a,1793,b)].
% 12.15/12.30  1804 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1131,a,1091,a)].
% 12.15/12.30  1805 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1131,a,1116,a)].
% 12.15/12.30  1806 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1131,a,1117,b)].
% 12.15/12.30  1807 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1131,a,1118,b)].
% 12.15/12.30  1808 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1423,a)].
% 12.15/12.30  1809 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1435,a,1423,a)].
% 12.15/12.30  1810 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1436,a,1423,a)].
% 12.15/12.30  1811 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1452,a,1448,b)].
% 12.15/12.30  1812 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1452,a,1449,b)].
% 12.15/12.30  1813 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1452,a,1450,b)].
% 12.15/12.30  1814 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1452,a,1451,b)].
% 12.15/12.30  1815 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1533,b,1475,a)].
% 12.15/12.30  1816 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1533,b,1510,b)].
% 12.15/12.30  1817 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1533,b,1511,b)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  1818 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1533,b,1512,b)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  1819 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1561,b,1542,a)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.15/12.30  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)].
% 12.38/12.55  1829 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1561,b,1552,a)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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)].
% 12.38/12.55  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].
% 12.38/12.55  1851 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom).  [assumption].
% 12.38/12.55  1852 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom).  [assumption].
% 12.38/12.55  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].
% 12.50/12.63  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].
% 12.50/12.63  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].
% 12.50/12.63  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].
% 12.50/12.63  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].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  1860 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(81,b,53,b)].
% 12.50/12.63  1861 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(82,b,53,b)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.63  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.64  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)].
% 12.50/12.65  1896 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(865,b,840,a)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  1901 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(865,b,845,a)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.50/12.65  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)].
% 12.66/12.79  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)].
% 12.66/12.79  1920 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1055,b,1046,a)].
% 12.66/12.79  1921 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1078,b,1069,a)].
% 12.66/12.79  1922 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1128,a,1091,a)].
% 12.66/12.79  1923 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1128,a,1116,a)].
% 12.66/12.79  1924 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1128,a,1117,b)].
% 12.66/12.79  1925 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1128,a,1118,b)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  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)].
% 12.66/12.79  1936 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1466,b,1450,b)].
% 12.66/12.86  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(1936,b,1852,a)].
% 12.66/12.86  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1936,b,1857,b)].
% 12.66/12.86  1937 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1467,b,1450,b)].
% 12.66/12.86  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1937,b,1857,b)].
% 12.66/12.86  1938 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1558,b,1542,a)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  1948 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1558,b,1552,a)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.66/12.86  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  1969 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1753,a,1722,b)].
% 12.79/12.92  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1969,b,1851,a)].
% 12.79/12.92  Derived: -c_less(A,A,tc_nat).  [resolve(1969,b,1852,a)].
% 12.79/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1969,b,1854,b)].
% 12.79/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1969,b,1855,b)].
% 12.79/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1969,b,1856,b)].
% 12.79/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1969,b,1857,b)].
% 12.79/12.92  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)].
% 12.79/12.92  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1970,c,1851,a)].
% 12.79/12.92  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1970,c,1852,a)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1971,b,1851,a)].
% 12.79/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1971,b,1852,a)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.79/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1972,c,1851,a)].
% 12.80/12.92  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1972,c,1852,a)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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_Oordered__comm__semiring__strict(B).  [resolve(1973,c,1854,b)].
% 12.80/12.92  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_Oordered__field(B).  [resolve(1973,c,1855,b)].
% 12.80/12.92  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_Oordered__idom(B).  [resolve(1973,c,1856,b)].
% 12.80/12.92  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_Oordered__semiring__strict(B).  [resolve(1973,c,1857,b)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.92  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_Oordered__comm__semiring__strict(C).  [resolve(1974,c,1854,b)].
% 12.80/12.92  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_Oordered__field(C).  [resolve(1974,c,1855,b)].
% 12.80/12.92  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_Oordered__idom(C).  [resolve(1974,c,1856,b)].
% 12.80/12.92  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_Oordered__semiring__strict(C).  [resolve(1974,c,1857,b)].
% 12.80/12.92  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)].
% 12.80/12.92  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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_Oordered__comm__semiring__strict(B).  [resolve(1975,c,1854,b)].
% 12.80/12.93  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_Oordered__field(B).  [resolve(1975,c,1855,b)].
% 12.80/12.93  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_Oordered__idom(B).  [resolve(1975,c,1856,b)].
% 12.80/12.93  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_Oordered__semiring__strict(B).  [resolve(1975,c,1857,b)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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_Oordered__comm__semiring__strict(C).  [resolve(1976,c,1854,b)].
% 12.80/12.93  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_Oordered__field(C).  [resolve(1976,c,1855,b)].
% 12.80/12.93  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_Oordered__idom(C).  [resolve(1976,c,1856,b)].
% 12.80/12.93  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_Oordered__semiring__strict(C).  [resolve(1976,c,1857,b)].
% 12.80/12.93  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)].
% 12.80/12.93  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1977,c,1851,a)].
% 12.80/12.93  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1977,c,1852,a)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  1979 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1763,a,1722,b)].
% 12.80/12.93  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1979,b,1851,a)].
% 12.80/12.93  Derived: c_lessequals(A,A,tc_nat).  [resolve(1979,b,1852,a)].
% 12.80/12.93  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1979,b,1854,b)].
% 12.80/12.93  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1979,b,1855,b)].
% 12.80/12.93  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1979,b,1856,b)].
% 12.80/12.93  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1979,b,1857,b)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1980,c,1852,a)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1981,c,1852,a)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.93  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1983,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1984,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1986,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1987,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1988,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1989,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1990,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1991,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1993,c,1852,a)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.94  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1994,c,1852,a)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1996,c,1852,a)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1997,c,1852,a)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.80/12.95  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1998,c,1852,a)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1999,c,1852,a)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  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)].
% 12.99/13.11  2000 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom).  [assumption].
% 12.99/13.11  2001 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom).  [assumption].
% 12.99/13.11  2002 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom).  [assumption].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.11  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].
% 12.99/13.13  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].
% 12.99/13.13  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].
% 12.99/13.13  2013 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom).  [assumption].
% 12.99/13.13  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].
% 12.99/13.13  2015 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom).  [assumption].
% 12.99/13.13  2016 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom).  [assumption].
% 12.99/13.13  2017 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom).  [assumption].
% 12.99/13.13  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)].
% 12.99/13.13  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)].
% 12.99/13.13  2020 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(163,a,159,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2020,b,2011,b)].
% 12.99/13.13  2021 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(164,a,159,b)].
% 12.99/13.13  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2021,b,2011,b)].
% 12.99/13.13  2022 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(165,a,159,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2022,b,2004,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2022,b,2007,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2022,b,2008,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2022,b,2009,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2022,b,2011,b)].
% 12.99/13.13  2023 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(166,a,159,b)].
% 12.99/13.13  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2023,b,2004,b)].
% 12.99/13.13  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2023,b,2007,b)].
% 12.99/13.13  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2023,b,2008,b)].
% 12.99/13.13  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2023,b,2009,b)].
% 12.99/13.13  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2023,b,2011,b)].
% 12.99/13.13  2024 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(236,a,229,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2024,b,2004,b)].
% 12.99/13.13  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2024,b,2007,b)].
% 12.99/13.14  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2024,b,2008,b)].
% 12.99/13.14  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2024,b,2009,b)].
% 12.99/13.14  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2024,b,2011,b)].
% 12.99/13.14  2025 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(237,a,229,b)].
% 12.99/13.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2025,b,2004,b)].
% 12.99/13.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2025,b,2007,b)].
% 12.99/13.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2025,b,2008,b)].
% 12.99/13.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2025,b,2009,b)].
% 12.99/13.14  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2025,b,2011,b)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 12.99/13.14  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)].
% 13.20/13.36  2028 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint).  [resolve(1135,a,1091,a)].
% 13.20/13.36  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2028,a,2000,a)].
% 13.20/13.36  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2028,a,2013,a)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  2029 class_Ring__and__Field_Opordered__semiring(tc_nat).  [resolve(1135,a,1116,a)].
% 13.20/13.36  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2029,a,2000,a)].
% 13.20/13.36  Derived: class_HOL_Otimes(tc_nat).  [resolve(2029,a,2013,a)].
% 13.20/13.36  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2029,a,2014,a)].
% 13.20/13.36  Derived: class_HOL_Ozero(tc_nat).  [resolve(2029,a,2017,a)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  2030 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1135,a,1117,b)].
% 13.20/13.36  2031 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1135,a,1118,b)].
% 13.20/13.36  2032 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A).  [resolve(1573,b,1542,a)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2032,a,2003,b)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2032,a,2008,b)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2032,a,2009,b)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2032,a,2010,b)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2032,a,2011,b)].
% 13.20/13.36  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2032,a,2012,b)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.36  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.37  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.20/13.38  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  2042 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A).  [resolve(1573,b,1552,a)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2042,a,2003,b)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2042,a,2008,b)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2042,a,2009,b)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2042,a,2010,b)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2042,a,2011,b)].
% 13.28/13.43  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2042,a,2012,b)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.43  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.44  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.28/13.45  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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)].
% 13.51/13.68  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].
% 13.51/13.70  2064 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom).  [assumption].
% 13.51/13.70  2065 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom).  [assumption].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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].
% 13.51/13.70  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)].
% 13.51/13.70  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)].
% 13.51/13.70  2080 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A).  [resolve(34,b,10,a)].
% 13.51/13.70  2081 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(81,b,72,b)].
% 13.51/13.70  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)].
% 13.51/13.70  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)].
% 13.51/13.70  2084 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(165,a,155,b)].
% 13.51/13.70  2085 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(166,a,155,b)].
% 13.51/13.70  2086 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(236,a,225,b)].
% 13.81/13.94  2087 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(237,a,225,b)].
% 13.81/13.94  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)].
% 13.81/13.94  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)].
% 13.81/13.94  2090 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(301,b,280,a)].
% 13.81/13.94  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2090,a,2067,b)].
% 13.81/13.94  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2090,a,2070,b)].
% 13.81/13.94  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2090,a,2071,b)].
% 13.81/13.94  2091 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(301,b,282,a)].
% 13.81/13.94  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2091,a,2067,b)].
% 13.81/13.94  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2091,a,2070,b)].
% 13.81/13.94  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2091,a,2071,b)].
% 13.81/13.94  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)].
% 13.81/13.94  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)].
% 13.81/13.94  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)].
% 13.81/13.94  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)].
% 13.81/13.94  2094 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(318,a,301,b)].
% 13.81/13.94  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2094,b,2071,b)].
% 13.81/13.94  2095 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(764,a,708,a)].
% 13.81/13.94  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2095,a,2071,b)].
% 13.81/13.94  2096 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint).  [resolve(1133,a,1091,a)].
% 13.81/13.94  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(2096,a,2090,a)].
% 13.81/13.94  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(2096,a,2091,a)].
% 13.81/13.94  2097 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).  [resolve(1133,a,1116,a)].
% 13.81/13.94  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(2097,a,2090,a)].
% 13.81/13.94  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(2097,a,2091,a)].
% 13.81/13.94  2098 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1133,a,1117,b)].
% 13.81/13.94  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0.  [resolve(2098,a,2090,a)].
% 13.81/13.94  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0.  [resolve(2098,a,2091,a)].
% 13.81/13.94  2099 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1133,a,1118,b)].
% 13.81/13.94  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0.  [resolve(2099,a,2090,a)].
% 13.81/13.94  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0.  [resolve(2099,a,2091,a)].
% 13.81/13.94  2100 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A).  [resolve(1569,b,1542,a)].
% 13.81/13.94  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)].
% 13.81/13.94  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  2110 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A).  [resolve(1569,b,1552,a)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.81/14.01  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)].
% 13.90/14.08  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)].
% 13.90/14.08  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)].
% 13.90/14.08  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)].
% 13.90/14.08  2131 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2022,b,2009,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2131,b,2066,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2131,b,2067,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2131,b,2068,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2131,b,2069,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2131,b,2070,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2131,b,2071,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2131,b,2077,b)].
% 13.90/14.08  2132 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2023,b,2009,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2132,b,2066,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2132,b,2067,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2132,b,2068,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2132,b,2069,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2132,b,2070,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2132,b,2071,b)].
% 13.90/14.08  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2132,b,2077,b)].
% 13.90/14.08  2133 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2024,b,2009,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2133,b,2064,a)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2133,b,2066,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2133,b,2067,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2133,b,2068,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2133,b,2069,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2133,b,2070,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2133,b,2071,b)].
% 13.90/14.08  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2133,b,2077,b)].
% 13.90/14.08  2134 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2025,b,2009,b)].
% 13.90/14.08  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2134,b,2064,a)].
% 13.90/14.08  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2134,b,2066,b)].
% 13.90/14.08  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2134,b,2067,b)].
% 13.90/14.08  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2134,b,2068,b)].
% 13.90/14.08  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2134,b,2069,b)].
% 13.98/14.09  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2134,b,2070,b)].
% 13.98/14.09  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2134,b,2071,b)].
% 13.98/14.09  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2134,b,2077,b)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  2137 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2032,a,2009,b)].
% 13.98/14.09  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2137,b,2064,a)].
% 13.98/14.09  Derived: -c_less(A,A,tc_nat).  [resolve(2137,b,2065,a)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2137,b,2066,b)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2137,b,2067,b)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2137,b,2068,b)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2137,b,2069,b)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2137,b,2070,b)].
% 13.98/14.09  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2137,b,2071,b)].
% 13.98/14.09  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)].
% 13.98/14.09  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2138,c,2064,a)].
% 13.98/14.09  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2138,c,2065,a)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2139,b,2064,a)].
% 13.98/14.09  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2139,b,2065,a)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.09  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)].
% 13.98/14.10  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2140,c,2064,a)].
% 13.98/14.10  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2140,c,2065,a)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.10  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)].
% 13.98/14.11  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2145,c,2064,a)].
% 13.98/14.11  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2145,c,2065,a)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  2147 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2042,a,2009,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2147,b,2064,a)].
% 13.98/14.11  Derived: c_lessequals(A,A,tc_nat).  [resolve(2147,b,2065,a)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2147,b,2066,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2147,b,2067,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2147,b,2068,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2147,b,2069,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2147,b,2070,b)].
% 13.98/14.11  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2147,b,2071,b)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2148,c,2065,a)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2149,c,2065,a)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.11  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)].
% 13.98/14.12  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)].
% 13.98/14.12  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2151,c,2065,a)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2152,c,2065,a)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2154,c,2065,a)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2155,c,2065,a)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2156,c,2065,a)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.12  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2157,c,2065,a)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2158,c,2065,a)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2159,c,2065,a)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2161,c,2065,a)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2162,c,2065,a)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.13  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2164,c,2065,a)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2165,c,2065,a)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 13.98/14.14  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2166,c,2065,a)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2167,c,2065,a)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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)].
% 14.21/14.34  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].
% 14.21/14.34  2169 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom).  [assumption].
% 14.21/14.34  2170 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom).  [assumption].
% 14.21/14.34  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].
% 14.21/14.34  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].
% 14.21/14.34  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].
% 14.21/14.34  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].
% 14.21/14.34  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].
% 14.27/14.43  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].
% 14.27/14.43  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].
% 14.27/14.43  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].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  2181 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(81,b,70,b)].
% 14.27/14.43  2182 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(82,b,70,b)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  2185 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(165,a,153,b)].
% 14.27/14.43  2186 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(166,a,153,b)].
% 14.27/14.43  2187 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(236,a,223,b)].
% 14.27/14.43  2188 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(237,a,223,b)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  2191 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(299,b,280,a)].
% 14.27/14.43  2192 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(299,b,282,a)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  2195 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(763,a,708,a)].
% 14.27/14.43  2196 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(763,a,715,a)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.43  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.44  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.27/14.45  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  2231 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(876,b,840,a)].
% 14.36/14.46  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2231,a,2171,b)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  2236 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(876,b,845,a)].
% 14.36/14.46  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2236,a,2171,b)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.46  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.36/14.47  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  2255 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1062,b,1046,a)].
% 14.43/14.59  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2255,a,2171,b)].
% 14.43/14.59  2256 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1085,b,1069,a)].
% 14.43/14.59  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2256,a,2171,b)].
% 14.43/14.59  2257 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint).  [resolve(1127,a,1091,a)].
% 14.43/14.59  2258 class_Ring__and__Field_Oordered__semiring__strict(tc_nat).  [resolve(1127,a,1116,a)].
% 14.43/14.59  2259 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1127,a,1117,b)].
% 14.43/14.59  2260 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1127,a,1118,b)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.43/14.59  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  2269 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A).  [resolve(1567,b,1542,a)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.51/14.64  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  2279 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1567,b,1552,a)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.74  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(2300,c,2169,a)].
% 14.58/14.74  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(2300,c,2170,a)].
% 14.58/14.74  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)].
% 14.58/14.74  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(2301,c,2169,a)].
% 14.58/14.76  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(2301,c,2170,a)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  2302 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1936,b,1857,b)].
% 14.58/14.76  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(2302,b,2169,a)].
% 14.58/14.76  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(2302,b,2170,a)].
% 14.58/14.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2302,b,2171,b)].
% 14.58/14.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2302,b,2172,b)].
% 14.58/14.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2302,b,2173,b)].
% 14.58/14.76  2303 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1937,b,1857,b)].
% 14.58/14.76  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(2303,b,2169,a)].
% 14.58/14.76  Derived: class_HOL_Oplus(tc_nat).  [resolve(2303,b,2170,a)].
% 14.58/14.76  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2303,b,2171,b)].
% 14.58/14.76  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2303,b,2172,b)].
% 14.58/14.76  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2303,b,2173,b)].
% 14.58/14.76  2304 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1969,b,1857,b)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  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)].
% 14.58/14.76  2314 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1979,b,1857,b)].
% 14.58/14.76  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  2335 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2022,b,2007,b)].
% 14.71/14.83  2336 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2023,b,2007,b)].
% 14.71/14.83  2337 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2024,b,2007,b)].
% 14.71/14.83  2338 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2025,b,2007,b)].
% 14.71/14.83  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)].
% 14.71/14.83  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)].
% 14.71/14.83  2341 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2090,a,2070,b)].
% 14.75/14.84  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2341,b,2171,b)].
% 14.75/14.84  2342 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2091,a,2070,b)].
% 14.75/14.84  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2342,b,2171,b)].
% 14.75/14.84  2343 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2131,b,2070,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2343,b,2169,a)].
% 14.75/14.84  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2343,b,2170,a)].
% 14.75/14.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2343,b,2171,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2343,b,2172,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2343,b,2173,b)].
% 14.75/14.84  2344 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2132,b,2070,b)].
% 14.75/14.84  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2344,b,2169,a)].
% 14.75/14.84  Derived: class_HOL_Otimes(tc_nat).  [resolve(2344,b,2170,a)].
% 14.75/14.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2344,b,2171,b)].
% 14.75/14.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2344,b,2172,b)].
% 14.75/14.84  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2344,b,2173,b)].
% 14.75/14.84  2345 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2133,b,2070,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2345,b,2169,a)].
% 14.75/14.84  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2345,b,2170,a)].
% 14.75/14.84  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2345,b,2171,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2345,b,2172,b)].
% 14.75/14.84  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2345,b,2173,b)].
% 14.75/14.84  2346 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2134,b,2070,b)].
% 14.75/14.84  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2346,b,2169,a)].
% 14.75/14.84  Derived: class_HOL_Ozero(tc_nat).  [resolve(2346,b,2170,a)].
% 14.75/14.84  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2346,b,2171,b)].
% 14.75/14.84  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2346,b,2172,b)].
% 14.75/14.84  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2346,b,2173,b)].
% 14.75/14.84  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)].
% 14.75/14.84  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)].
% 14.75/14.84  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)].
% 14.75/14.84  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)].
% 14.75/14.84  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  2349 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2137,b,2070,b)].
% 14.75/14.85  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2349,b,2169,a)].
% 14.75/14.85  Derived: -c_less(A,A,tc_nat).  [resolve(2349,b,2170,a)].
% 14.75/14.85  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2349,b,2171,b)].
% 14.75/14.85  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2349,b,2172,b)].
% 14.75/14.85  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2349,b,2173,b)].
% 14.75/14.85  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)].
% 14.75/14.85  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2350,c,2169,a)].
% 14.75/14.85  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2350,c,2170,a)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.85  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2351,b,2169,a)].
% 14.75/14.85  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2351,b,2170,a)].
% 14.75/14.85  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)].
% 14.75/14.85  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2352,c,2169,a)].
% 14.75/14.86  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2352,c,2170,a)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.86  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2357,c,2169,a)].
% 14.75/14.87  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2357,c,2170,a)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  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)].
% 14.75/14.87  2359 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2147,b,2070,b)].
% 14.75/14.87  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2359,b,2169,a)].
% 14.75/14.87  Derived: c_lessequals(A,A,tc_nat).  [resolve(2359,b,2170,a)].
% 14.75/14.87  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2359,b,2171,b)].
% 14.75/14.87  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2359,b,2172,b)].
% 14.75/14.87  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2359,b,2173,b)].
% 14.75/14.87  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)].
% 14.75/14.88  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)].
% 14.75/14.88  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2360,c,2170,a)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2361,c,2170,a)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2363,c,2170,a)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  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)].
% 14.75/14.88  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2364,c,2170,a)].
% 14.75/14.88  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2366,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2367,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2368,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2369,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2370,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2371,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  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)].
% 14.75/14.89  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2373,c,2170,a)].
% 14.75/14.89  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2374,c,2170,a)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2376,c,2170,a)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2377,c,2170,a)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 14.75/14.90  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)].
% 15.01/15.11  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2378,c,2170,a)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2379,c,2170,a)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.01/15.11  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].
% 15.01/15.11  2381 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom).  [assumption].
% 15.01/15.11  2382 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom).  [assumption].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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].
% 15.01/15.11  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)].
% 15.01/15.11  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)].
% 15.28/15.38  2395 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(163,a,157,b)].
% 15.28/15.38  2396 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(164,a,157,b)].
% 15.28/15.38  2397 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(165,a,157,b)].
% 15.28/15.38  2398 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(166,a,157,b)].
% 15.28/15.38  2399 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(236,a,227,b)].
% 15.28/15.38  2400 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(237,a,227,b)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  2403 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint).  [resolve(1134,a,1091,a)].
% 15.28/15.38  2404 class_Ring__and__Field_Opordered__comm__semiring(tc_nat).  [resolve(1134,a,1116,a)].
% 15.28/15.38  2405 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1134,a,1117,b)].
% 15.28/15.38  2406 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1134,a,1118,b)].
% 15.28/15.38  2407 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A).  [resolve(1571,b,1542,a)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  2417 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1571,b,1552,a)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.28/15.38  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  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)].
% 15.35/15.45  2438 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2020,b,2011,b)].
% 15.35/15.45  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2438,b,2387,b)].
% 15.35/15.45  2439 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2021,b,2011,b)].
% 15.35/15.45  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2439,b,2387,b)].
% 15.35/15.45  2440 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2022,b,2011,b)].
% 15.35/15.45  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2440,b,2387,b)].
% 15.35/15.45  2441 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2023,b,2011,b)].
% 15.35/15.45  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2441,b,2387,b)].
% 15.35/15.45  2442 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2024,b,2011,b)].
% 15.35/15.45  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2442,b,2387,b)].
% 15.35/15.45  2443 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2025,b,2011,b)].
% 15.35/15.45  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2443,b,2387,b)].
% 15.35/15.45  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  2446 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2032,a,2011,b)].
% 15.35/15.47  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2446,b,2387,b)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.47  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)].
% 15.35/15.49  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_Opordered__comm__ring(B).  [resolve(2455,b,2387,b)].
% 15.35/15.49  2456 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2042,a,2011,b)].
% 15.35/15.49  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2456,b,2387,b)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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_Opordered__comm__ring(C).  [resolve(2459,d,2387,b)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.35/15.49  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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)].
% 15.66/15.74  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].
% 15.66/15.74  2478 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom).  [assumption].
% 15.66/15.74  2479 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom).  [assumption].
% 15.66/15.74  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].
% 15.66/15.74  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].
% 15.66/15.74  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].
% 15.66/15.74  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].
% 15.66/15.74  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].
% 15.81/15.97  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].
% 15.81/15.97  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].
% 15.81/15.97  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].
% 15.81/15.97  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)].
% 15.81/15.97  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)].
% 15.81/15.97  2490 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(33,b,9,a)].
% 15.81/15.97  2491 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A).  [resolve(33,b,10,a)].
% 15.81/15.97  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)].
% 15.81/15.97  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)].
% 15.81/15.97  2494 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(165,a,154,b)].
% 15.81/15.97  2495 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(166,a,154,b)].
% 15.81/15.97  2496 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(199,b,193,b)].
% 15.81/15.97  2497 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(200,b,193,b)].
% 15.81/15.97  2498 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(236,a,224,b)].
% 15.81/15.97  2499 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(237,a,224,b)].
% 15.81/15.97  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)].
% 15.81/15.97  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)].
% 15.81/15.97  2502 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(300,b,280,a)].
% 15.81/15.97  2503 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(300,b,282,a)].
% 15.81/15.97  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)].
% 15.81/15.97  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)].
% 15.81/15.97  2506 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint).  [resolve(1132,a,1091,a)].
% 15.81/15.97  2507 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat).  [resolve(1132,a,1116,a)].
% 15.81/15.97  2508 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1132,a,1117,b)].
% 15.81/15.97  2509 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1132,a,1118,b)].
% 15.81/15.97  2510 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A).  [resolve(1568,b,1542,a)].
% 15.81/15.97  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  2520 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1568,b,1552,a)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.93/16.02  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  2541 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2022,b,2008,b)].
% 15.94/16.09  2542 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2023,b,2008,b)].
% 15.94/16.09  2543 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2024,b,2008,b)].
% 15.94/16.09  2544 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2025,b,2008,b)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  2547 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2032,a,2008,b)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 15.94/16.09  2557 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2042,a,2008,b)].
% 15.94/16.09  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)].
% 15.94/16.09  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  2578 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2090,a,2071,b)].
% 16.02/16.12  2579 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2091,a,2071,b)].
% 16.02/16.12  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)].
% 16.02/16.12  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)].
% 16.02/16.12  2582 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2094,b,2071,b)].
% 16.02/16.12  2583 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2095,a,2071,b)].
% 16.02/16.12  2584 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2131,b,2071,b)].
% 16.02/16.12  2585 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2132,b,2071,b)].
% 16.02/16.12  2586 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2133,b,2071,b)].
% 16.02/16.16  2587 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2134,b,2071,b)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  2590 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2137,b,2071,b)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  2600 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2147,b,2071,b)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.02/16.16  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  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].
% 16.24/16.38  2622 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom).  [assumption].
% 16.24/16.38  2623 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom).  [assumption].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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].
% 16.24/16.38  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)].
% 16.24/16.38  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)].
% 16.24/16.38  2633 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(27,b,10,a)].
% 16.24/16.38  2634 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(81,b,65,b)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  2637 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(165,a,148,b)].
% 16.34/16.44  2638 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(166,a,148,b)].
% 16.34/16.44  2639 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(199,b,189,b)].
% 16.34/16.44  2640 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(200,b,189,b)].
% 16.34/16.44  2641 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(236,a,218,b)].
% 16.34/16.44  2642 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(237,a,218,b)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  2645 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(294,b,280,a)].
% 16.34/16.44  2646 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(294,b,282,a)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.44  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  2683 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(871,b,840,a)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  2688 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(871,b,845,a)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.34/16.45  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  2707 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1057,b,1046,a)].
% 16.52/16.60  2708 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1080,b,1069,a)].
% 16.52/16.60  2709 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint).  [resolve(1126,a,1091,a)].
% 16.52/16.60  2710 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).  [resolve(1126,a,1116,a)].
% 16.52/16.60  2711 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1126,a,1117,b)].
% 16.52/16.60  2712 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1126,a,1118,b)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  2721 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A).  [resolve(1564,b,1542,a)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.52/16.60  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  2731 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1564,b,1552,a)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.64  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)].
% 16.53/16.70  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)].
% 16.53/16.70  2752 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1802,a,1793,b)].
% 16.53/16.70  2753 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1803,a,1793,b)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  2756 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1969,b,1854,b)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  2766 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1979,b,1854,b)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.53/16.70  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  2787 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2022,b,2004,b)].
% 16.62/16.74  2788 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2023,b,2004,b)].
% 16.62/16.74  2789 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2024,b,2004,b)].
% 16.62/16.74  2790 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2025,b,2004,b)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  2793 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2090,a,2067,b)].
% 16.62/16.74  2794 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2091,a,2067,b)].
% 16.62/16.74  2795 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2131,b,2067,b)].
% 16.62/16.74  2796 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2132,b,2067,b)].
% 16.62/16.74  2797 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2133,b,2067,b)].
% 16.62/16.74  2798 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2134,b,2067,b)].
% 16.62/16.74  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)].
% 16.62/16.74  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)].
% 16.62/16.74  2801 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2137,b,2067,b)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  2811 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2147,b,2067,b)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.77  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.78  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2841,b,2622,a)].
% 16.62/16.79  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(2841,b,2623,a)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.62/16.79  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2851,b,2622,a)].
% 16.73/16.80  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(2851,b,2623,a)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(2857,c,2623,a)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(2858,c,2623,a)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.80  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2860,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2861,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2863,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2864,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  2866 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2231,a,2171,b)].
% 16.73/16.81  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(2866,b,2622,a)].
% 16.73/16.81  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(2866,b,2623,a)].
% 16.73/16.81  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2866,b,2629,b)].
% 16.73/16.81  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2866,b,2630,b)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2868,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(2869,c,2623,a)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  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)].
% 16.73/16.81  2871 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2236,a,2171,b)].
% 16.73/16.81  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(2871,b,2622,a)].
% 16.73/16.82  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(2871,b,2623,a)].
% 16.73/16.82  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2871,b,2629,b)].
% 16.73/16.82  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2871,b,2630,b)].
% 16.73/16.82  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)].
% 16.73/16.82  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(2872,b,2622,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(2873,b,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(2874,b,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(2875,b,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(2876,b,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(2877,c,2622,a)].
% 16.73/16.82  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(2877,c,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(2878,c,2622,a)].
% 16.73/16.82  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(2878,c,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(2879,c,2622,a)].
% 16.73/16.82  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(2879,c,2623,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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(2880,c,2622,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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(2881,c,2622,a)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.82  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2882,c,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2883,d,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2884,d,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2885,c,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2886,d,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(2887,c,2622,a)].
% 16.73/16.83  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(2887,c,2623,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2888,c,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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(2889,c,2622,a)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.83  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)].
% 16.73/16.84  2890 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2255,a,2171,b)].
% 16.73/16.84  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(2890,b,2622,a)].
% 16.73/16.84  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(2890,b,2623,a)].
% 16.73/16.84  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2890,b,2629,b)].
% 16.73/16.84  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2890,b,2630,b)].
% 16.73/16.84  2891 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2256,a,2171,b)].
% 16.73/16.84  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(2891,b,2622,a)].
% 16.73/16.84  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(2891,b,2623,a)].
% 16.73/16.84  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2891,b,2629,b)].
% 16.73/16.84  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2891,b,2630,b)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.84  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)].
% 16.73/16.85  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(2899,c,2622,a)].
% 16.73/16.85  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)].
% 16.73/16.85  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)].
% 16.73/16.85  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(2900,c,2622,a)].
% 16.73/16.85  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(2900,c,2623,a)].
% 16.73/16.85  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)].
% 16.73/16.85  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(2901,c,2622,a)].
% 16.73/16.85  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(2901,c,2623,a)].
% 16.73/16.85  2902 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2302,b,2171,b)].
% 16.73/16.85  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(2902,b,2622,a)].
% 16.73/16.85  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(2902,b,2623,a)].
% 16.73/16.85  2903 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2303,b,2171,b)].
% 16.73/16.85  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(2903,b,2622,a)].
% 16.73/16.85  Derived: class_HOL_Oplus(tc_nat).  [resolve(2903,b,2623,a)].
% 16.73/16.85  2904 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2341,b,2171,b)].
% 16.73/16.85  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(2904,b,2622,a)].
% 16.73/16.85  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(2904,b,2623,a)].
% 16.73/16.85  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(2904,b,2629,b)].
% 16.73/16.85  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2904,b,2630,b)].
% 16.73/16.85  2905 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2342,b,2171,b)].
% 16.73/16.85  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(2905,b,2622,a)].
% 16.73/16.85  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(2905,b,2623,a)].
% 16.73/16.85  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(2905,b,2629,b)].
% 16.73/16.85  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2905,b,2630,b)].
% 16.73/16.85  2906 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2343,b,2171,b)].
% 16.73/16.85  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2906,b,2622,a)].
% 16.73/16.85  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2906,b,2623,a)].
% 16.73/16.85  2907 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2344,b,2171,b)].
% 16.73/16.85  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2907,b,2622,a)].
% 16.73/16.85  Derived: class_HOL_Otimes(tc_nat).  [resolve(2907,b,2623,a)].
% 16.73/16.85  2908 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2345,b,2171,b)].
% 16.73/16.85  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2908,b,2622,a)].
% 16.73/16.85  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2908,b,2623,a)].
% 16.73/16.85  2909 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2346,b,2171,b)].
% 16.73/16.85  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2909,b,2622,a)].
% 16.73/16.85  Derived: class_HOL_Ozero(tc_nat).  [resolve(2909,b,2623,a)].
% 16.73/16.85  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)].
% 16.73/16.85  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  2912 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2349,b,2171,b)].
% 16.73/16.86  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2912,b,2622,a)].
% 16.73/16.86  Derived: -c_less(A,A,tc_nat).  [resolve(2912,b,2623,a)].
% 16.73/16.86  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)].
% 16.73/16.86  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2913,c,2622,a)].
% 16.73/16.86  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2913,c,2623,a)].
% 16.73/16.86  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)].
% 16.73/16.86  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2914,b,2622,a)].
% 16.73/16.86  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2914,b,2623,a)].
% 16.73/16.86  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)].
% 16.73/16.86  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2915,c,2622,a)].
% 16.73/16.86  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2915,c,2623,a)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.86  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)].
% 16.73/16.87  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(2918,c,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2920,c,2622,a)].
% 16.73/16.87  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2920,c,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  2922 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2359,b,2171,b)].
% 16.73/16.87  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2922,b,2622,a)].
% 16.73/16.87  Derived: c_lessequals(A,A,tc_nat).  [resolve(2922,b,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2923,c,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2924,c,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.87  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2926,c,2623,a)].
% 16.73/16.87  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)].
% 16.73/16.87  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2927,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2929,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2930,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2931,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2932,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2933,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2934,c,2623,a)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  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)].
% 16.73/16.88  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2936,c,2623,a)].
% 16.73/16.88  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)].
% 17.24/17.31  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)].
% 17.24/17.31  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2937,c,2623,a)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2939,c,2623,a)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2940,c,2623,a)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2941,c,2623,a)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2942,c,2623,a)].
% 17.24/17.31  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].
% 17.24/17.31  2944 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom).  [assumption].
% 17.24/17.31  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].
% 17.24/17.31  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].
% 17.24/17.31  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].
% 17.24/17.31  2948 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint).  [resolve(1287,a,1243,a)].
% 17.24/17.31  2949 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1287,a,1269,b)].
% 17.24/17.31  2950 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1287,a,1270,b)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.24/17.31  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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)].
% 17.57/17.65  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].
% 17.57/17.65  2972 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom).  [assumption].
% 17.57/17.65  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].
% 17.57/17.65  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].
% 17.57/17.65  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].
% 17.57/17.65  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].
% 17.57/17.65  2977 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom).  [assumption].
% 17.57/17.65  2978 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom).  [assumption].
% 17.57/17.65  2979 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom).  [assumption].
% 17.57/17.65  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].
% 17.57/17.68  2981 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom).  [assumption].
% 17.57/17.68  2982 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom).  [assumption].
% 17.57/17.68  2983 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom).  [assumption].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  2986 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(36,b,9,a)].
% 17.57/17.68  2987 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(36,b,10,a)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  2990 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(165,a,158,b)].
% 17.57/17.68  2991 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(166,a,158,b)].
% 17.57/17.68  2992 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(236,a,228,b)].
% 17.57/17.68  2993 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(237,a,228,b)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  2996 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(303,b,280,a)].
% 17.57/17.68  2997 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(303,b,282,a)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  3000 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(317,a,303,b)].
% 17.57/17.68  3001 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(318,a,303,b)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.57/17.68  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  3007 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(344,a,338,b)].
% 17.71/17.81  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3007,b,2973,b)].
% 17.71/17.81  3008 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(345,a,338,b)].
% 17.71/17.81  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3008,b,2973,b)].
% 17.71/17.81  3009 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(356,b,338,b)].
% 17.71/17.81  3010 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(357,b,338,b)].
% 17.71/17.81  3011 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(358,b,338,b)].
% 17.71/17.81  3012 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(359,b,338,b)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  3015 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(362,a,338,b)].
% 17.71/17.81  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3015,b,2973,b)].
% 17.71/17.81  3016 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(363,a,338,b)].
% 17.71/17.81  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3016,b,2973,b)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  3019 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(788,a,708,a)].
% 17.71/17.81  3020 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(788,a,715,a)].
% 17.71/17.81  3021 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint).  [resolve(1291,a,1243,a)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  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)].
% 17.71/17.81  3022 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1291,a,1269,b)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  3023 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1291,a,1270,b)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.71/17.84  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)].
% 17.82/17.92  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)].
% 17.82/17.92  3032 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A).  [resolve(1572,b,1542,a)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  3042 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A).  [resolve(1572,b,1552,a)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.82/17.92  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  3063 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1748,b,1717,a)].
% 17.87/17.98  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3063,a,2973,b)].
% 17.87/17.98  3064 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(1748,b,1724,a)].
% 17.87/17.98  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3064,a,2973,b)].
% 17.87/17.98  3065 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2032,a,2012,b)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  3075 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2042,a,2012,b)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 17.87/17.98  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  3096 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2131,b,2077,b)].
% 18.17/18.25  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3096,b,2973,b)].
% 18.17/18.25  3097 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2132,b,2077,b)].
% 18.17/18.25  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3097,b,2973,b)].
% 18.17/18.25  3098 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2133,b,2077,b)].
% 18.17/18.25  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3098,b,2973,b)].
% 18.17/18.25  3099 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2134,b,2077,b)].
% 18.17/18.25  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3099,b,2973,b)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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)].
% 18.17/18.25  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].
% 18.17/18.25  3103 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom).  [assumption].
% 18.17/18.25  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].
% 18.33/18.41  3105 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom).  [assumption].
% 18.33/18.41  3106 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom).  [assumption].
% 18.33/18.41  3107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom).  [assumption].
% 18.33/18.41  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].
% 18.33/18.41  3109 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom).  [assumption].
% 18.33/18.41  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].
% 18.33/18.41  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].
% 18.33/18.41  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].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  3115 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(81,b,52,b)].
% 18.33/18.41  3116 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(82,b,52,b)].
% 18.33/18.41  3117 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1054,b,1046,a)].
% 18.33/18.41  3118 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1077,b,1069,a)].
% 18.33/18.41  3119 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint).  [resolve(1293,a,1243,a)].
% 18.33/18.41  3120 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1293,a,1269,b)].
% 18.33/18.41  3121 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1293,a,1270,b)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  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)].
% 18.33/18.41  3132 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1466,b,1449,b)].
% 18.33/18.41  3133 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1467,b,1449,b)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3136,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(3137,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3138,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(3139,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  3142 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1509,b,1484,a)].
% 18.33/18.43  Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(3142,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0.  [resolve(3143,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A.  [resolve(3144,a,3103,a)].
% 18.33/18.43  3145 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1509,b,1487,a)].
% 18.33/18.43  Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3145,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  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)].
% 18.33/18.43  3147 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1509,b,1489,a)].
% 18.33/18.43  Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(3147,a,3103,a)].
% 18.33/18.43  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)].
% 18.33/18.43  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0.  [resolve(3148,a,3103,a)].
% 18.33/18.43  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)].
% 18.39/18.47  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A.  [resolve(3149,a,3103,a)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  3153 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1509,b,1495,a)].
% 18.39/18.47  Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3153,a,3103,a)].
% 18.39/18.47  3154 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1509,b,1496,a)].
% 18.39/18.47  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(3154,a,3103,a)].
% 18.39/18.47  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3154,a,3110,b)].
% 18.39/18.47  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3154,a,3111,b)].
% 18.39/18.47  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3154,a,3112,b)].
% 18.39/18.47  3155 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1509,b,1497,a)].
% 18.39/18.47  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(3155,a,3103,a)].
% 18.39/18.47  3156 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A).  [resolve(1557,b,1542,a)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.39/18.47  3166 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A).  [resolve(1557,b,1552,a)].
% 18.39/18.47  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)].
% 18.39/18.47  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  3187 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1753,a,1721,b)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.44/18.50  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  3197 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1763,a,1721,b)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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)].
% 18.72/18.81  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].
% 18.72/18.81  3219 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom).  [assumption].
% 18.72/18.81  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].
% 18.86/18.97  3221 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom).  [assumption].
% 18.86/18.97  3222 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom).  [assumption].
% 18.86/18.97  3223 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom).  [assumption].
% 18.86/18.97  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].
% 18.86/18.97  3225 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom).  [assumption].
% 18.86/18.97  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].
% 18.86/18.97  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].
% 18.86/18.97  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].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  3231 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(81,b,51,b)].
% 18.86/18.97  3232 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(82,b,51,b)].
% 18.86/18.97  3233 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1053,b,1046,a)].
% 18.86/18.97  3234 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1076,b,1069,a)].
% 18.86/18.97  3235 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint).  [resolve(1294,a,1243,a)].
% 18.86/18.97  3236 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1294,a,1269,b)].
% 18.86/18.97  3237 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1294,a,1270,b)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  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)].
% 18.86/18.97  3248 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1466,b,1448,b)].
% 18.86/18.97  3249 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1467,b,1448,b)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  3258 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1508,b,1484,a)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  3261 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1508,b,1487,a)].
% 18.92/19.00  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)].
% 18.92/19.00  3263 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1508,b,1489,a)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  3269 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1508,b,1495,a)].
% 18.92/19.00  3270 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1508,b,1496,a)].
% 18.92/19.00  3271 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1508,b,1497,a)].
% 18.92/19.00  3272 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A).  [resolve(1556,b,1542,a)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.00  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  3282 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A).  [resolve(1556,b,1552,a)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  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)].
% 18.92/19.05  3303 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1753,a,1720,b)].
% 18.92/19.05  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  3313 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1763,a,1720,b)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.00/19.06  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)].
% 19.24/19.36  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)].
% 19.24/19.36  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)].
% 19.24/19.36  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)].
% 19.24/19.36  3334 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom).  [assumption].
% 19.24/19.36  3335 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom).  [assumption].
% 19.24/19.36  3336 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom).  [assumption].
% 19.24/19.36  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].
% 19.24/19.36  3338 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom).  [assumption].
% 19.24/19.36  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].
% 19.24/19.36  3340 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom).  [assumption].
% 19.24/19.36  3341 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom).  [assumption].
% 19.24/19.36  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].
% 19.24/19.36  3343 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom).  [assumption].
% 19.24/19.36  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].
% 19.24/19.36  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].
% 19.24/19.36  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)].
% 19.24/19.36  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)].
% 19.24/19.36  3348 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(81,b,64,b)].
% 19.24/19.36  3349 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(82,b,64,b)].
% 19.24/19.36  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)].
% 19.24/19.36  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)].
% 19.24/19.36  3352 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(165,a,147,b)].
% 19.24/19.36  3353 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(166,a,147,b)].
% 19.24/19.36  3354 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(236,a,217,b)].
% 19.24/19.36  3355 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(237,a,217,b)].
% 19.24/19.36  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)].
% 19.24/19.36  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)].
% 19.37/19.49  3358 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(293,b,280,a)].
% 19.37/19.49  3359 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(293,b,282,a)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  3367 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(344,a,333,b)].
% 19.37/19.49  3368 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(345,a,333,b)].
% 19.37/19.49  3369 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(352,b,333,b)].
% 19.37/19.49  3370 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(353,b,333,b)].
% 19.37/19.49  3371 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(356,b,333,b)].
% 19.37/19.49  3372 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(357,b,333,b)].
% 19.37/19.49  3373 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(358,b,333,b)].
% 19.37/19.49  3374 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(359,b,333,b)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  3377 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(362,a,333,b)].
% 19.37/19.49  3378 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(363,a,333,b)].
% 19.37/19.49  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)].
% 19.37/19.49  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)].
% 19.37/19.49  3381 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(783,a,708,a)].
% 19.37/19.49  3382 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A).  [resolve(783,a,715,a)].
% 19.37/19.49  3383 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1056,b,1046,a)].
% 19.37/19.49  3384 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1079,b,1069,a)].
% 19.37/19.49  3385 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint).  [resolve(1290,a,1243,a)].
% 19.37/19.49  3386 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1290,a,1269,b)].
% 19.37/19.49  3387 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1290,a,1270,b)].
% 19.37/19.49  3388 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1425,b,1396,a)].
% 19.45/19.51  Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0.  [resolve(3388,a,3335,a)].
% 19.45/19.51  3389 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1425,b,1397,a)].
% 19.45/19.51  Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint).  [resolve(3389,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  3391 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1425,b,1399,a)].
% 19.45/19.51  Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3391,a,3335,a)].
% 19.45/19.51  3392 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1425,b,1400,a)].
% 19.45/19.51  Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0.  [resolve(3392,a,3335,a)].
% 19.45/19.51  3393 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1425,b,1401,a)].
% 19.45/19.51  Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3393,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(3395,a,3335,a)].
% 19.45/19.51  3396 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1425,b,1404,a)].
% 19.45/19.51  Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3396,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  3398 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1425,b,1406,a)].
% 19.45/19.51  Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3398,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A.  [resolve(3399,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  3401 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1425,b,1409,a)].
% 19.45/19.51  Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3401,a,3335,a)].
% 19.45/19.51  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)].
% 19.45/19.51  Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0.  [resolve(3402,a,3335,a)].
% 19.45/19.51  3403 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1425,b,1412,a)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.51  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  3420 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1510,b,1484,a)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  3423 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1510,b,1487,a)].
% 19.45/19.54  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)].
% 19.45/19.54  3425 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1510,b,1489,a)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  3431 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1510,b,1495,a)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.54  3434 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1539,b,1510,b)].
% 19.45/19.54  3435 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1540,b,1510,b)].
% 19.45/19.54  3436 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A).  [resolve(1563,b,1542,a)].
% 19.45/19.54  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)].
% 19.45/19.54  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  3446 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A).  [resolve(1563,b,1552,a)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.45/19.56  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)].
% 19.52/19.61  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)].
% 19.52/19.61  3467 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2032,a,2003,b)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  3477 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2042,a,2003,b)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.61  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  3498 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2131,b,2066,b)].
% 19.52/19.63  3499 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2132,b,2066,b)].
% 19.52/19.63  3500 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2133,b,2066,b)].
% 19.52/19.63  3501 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2134,b,2066,b)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  3504 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2137,b,2066,b)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  3514 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2147,b,2066,b)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.52/19.63  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  3540 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3007,b,2973,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3540,b,3344,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3540,b,3345,b)].
% 19.67/19.74  3541 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3008,b,2973,b)].
% 19.67/19.74  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(3541,b,3335,a)].
% 19.67/19.74  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3541,b,3344,b)].
% 19.67/19.74  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3541,b,3345,b)].
% 19.67/19.74  3542 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3015,b,2973,b)].
% 19.67/19.74  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(3542,b,3335,a)].
% 19.67/19.74  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(3542,b,3344,b)].
% 19.67/19.74  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(3542,b,3345,b)].
% 19.67/19.74  3543 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3016,b,2973,b)].
% 19.67/19.74  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(3543,b,3335,a)].
% 19.67/19.74  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(3543,b,3344,b)].
% 19.67/19.74  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(3543,b,3345,b)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  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)].
% 19.67/19.74  3552 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3063,a,2973,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(3552,b,3335,a)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3552,b,3344,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3552,b,3345,b)].
% 19.67/19.74  3553 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3064,a,2973,b)].
% 19.67/19.74  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(3553,b,3335,a)].
% 19.67/19.74  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3553,b,3344,b)].
% 19.67/19.74  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3553,b,3345,b)].
% 19.67/19.74  3554 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3096,b,2973,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(3554,b,3335,a)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3554,b,3344,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3554,b,3345,b)].
% 19.67/19.74  3555 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3097,b,2973,b)].
% 19.67/19.74  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(3555,b,3335,a)].
% 19.67/19.74  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3555,b,3344,b)].
% 19.67/19.74  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3555,b,3345,b)].
% 19.67/19.74  3556 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3098,b,2973,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(3556,b,3335,a)].
% 19.67/19.74  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3556,b,3344,b)].
% 19.67/19.74  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3556,b,3345,b)].
% 19.67/19.74  3557 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3099,b,2973,b)].
% 19.67/19.75  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(3557,b,3335,a)].
% 19.67/19.75  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3557,b,3344,b)].
% 19.67/19.75  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3557,b,3345,b)].
% 19.67/19.75  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)].
% 19.67/19.75  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)].
% 19.67/19.75  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)].
% 20.23/20.33  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_Oordered__idom(A).  [resolve(3558,c,3345,b)].
% 20.23/20.33  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)].
% 20.23/20.33  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(3559,c,3335,a)].
% 20.23/20.33  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_Oordered__field(A).  [resolve(3559,c,3344,b)].
% 20.23/20.33  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_Oordered__idom(A).  [resolve(3559,c,3345,b)].
% 20.23/20.33  3560 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3154,a,3110,b)].
% 20.23/20.33  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(3560,b,3335,a)].
% 20.23/20.33  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].
% 20.23/20.33  3562 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom).  [assumption].
% 20.23/20.33  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].
% 20.23/20.33  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].
% 20.23/20.33  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].
% 20.23/20.33  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].
% 20.23/20.33  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].
% 20.23/20.33  3568 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint).  [resolve(1295,a,1243,a)].
% 20.23/20.33  3569 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1295,a,1269,b)].
% 20.23/20.33  3570 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1295,a,1270,b)].
% 20.23/20.33  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].
% 20.23/20.33  3572 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom).  [assumption].
% 20.23/20.33  3573 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom).  [assumption].
% 20.23/20.33  Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3571,a,3573,b)].
% 20.23/20.33  3574 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom).  [assumption].
% 20.23/20.33  3575 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom).  [assumption].
% 20.23/20.33  3576 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom).  [assumption].
% 20.23/20.35  3577 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom).  [assumption].
% 20.23/20.35  3578 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom).  [assumption].
% 20.23/20.35  3579 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom).  [assumption].
% 20.23/20.35  3580 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom).  [assumption].
% 20.23/20.35  3581 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom).  [assumption].
% 20.23/20.35  3582 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom).  [assumption].
% 20.23/20.35  3583 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom).  [assumption].
% 20.23/20.35  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3583,a,3573,b)].
% 20.23/20.35  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].
% 20.23/20.35  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].
% 20.23/20.35  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(3585,b,3571,a)].
% 20.23/20.35  3586 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(25,b,1,a)].
% 20.23/20.35  3587 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(25,b,3,a)].
% 20.23/20.35  3588 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(81,b,63,b)].
% 20.23/20.35  3589 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(82,b,63,b)].
% 20.23/20.35  3590 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B.  [resolve(124,b,108,a)].
% 20.23/20.35  3591 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B.  [resolve(124,b,111,a)].
% 20.23/20.35  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)].
% 20.23/20.35  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)].
% 20.23/20.35  3594 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(165,a,146,b)].
% 20.23/20.35  3595 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(166,a,146,b)].
% 20.23/20.35  3596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(199,b,188,b)].
% 20.23/20.35  3597 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(200,b,188,b)].
% 20.23/20.35  3598 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(236,a,216,b)].
% 20.23/20.35  3599 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(237,a,216,b)].
% 20.23/20.35  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)].
% 20.23/20.35  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)].
% 20.23/20.35  3602 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0.  [resolve(292,b,280,a)].
% 20.23/20.35  3603 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0.  [resolve(292,b,282,a)].
% 20.23/20.35  3604 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(314,a,292,b)].
% 20.23/20.35  3605 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(315,a,292,b)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  3611 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(344,a,332,b)].
% 20.23/20.37  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3611,b,3573,b)].
% 20.23/20.37  3612 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(345,a,332,b)].
% 20.23/20.37  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3612,b,3573,b)].
% 20.23/20.37  3613 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(356,b,332,b)].
% 20.23/20.37  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3613,b,3573,b)].
% 20.23/20.37  3614 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(357,b,332,b)].
% 20.23/20.37  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3614,b,3573,b)].
% 20.23/20.37  3615 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(358,b,332,b)].
% 20.23/20.37  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3615,b,3573,b)].
% 20.23/20.37  3616 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(359,b,332,b)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  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)].
% 20.23/20.37  3619 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(362,a,332,b)].
% 20.23/20.37  3620 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(363,a,332,b)].
% 20.23/20.37  3621 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(364,c,332,b)].
% 20.23/20.37  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(3621,c,3573,b)].
% 20.23/20.37  3622 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(365,c,332,b)].
% 20.23/20.37  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(3622,c,3573,b)].
% 20.23/20.37  3623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(463,b,421,b)].
% 20.23/20.37  3624 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(464,b,421,b)].
% 20.23/20.37  3625 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(501,a,495,b)].
% 20.23/20.37  3626 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(508,a,495,b)].
% 20.23/20.37  3627 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(509,a,495,b)].
% 20.23/20.37  3628 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(551,b,531,b)].
% 20.23/20.37  3629 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(552,b,531,b)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  3635 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(635,b,596,b)].
% 20.23/20.38  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3635,b,3573,b)].
% 20.23/20.38  3636 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(636,b,596,b)].
% 20.23/20.38  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(3636,b,3573,b)].
% 20.23/20.38  3637 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(637,b,596,b)].
% 20.23/20.38  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(3637,b,3573,b)].
% 20.23/20.38  3638 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(639,b,596,b)].
% 20.23/20.38  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(3638,b,3573,b)].
% 20.23/20.38  3639 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(640,b,596,b)].
% 20.23/20.38  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(3639,b,3573,b)].
% 20.23/20.38  3640 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(642,b,596,b)].
% 20.23/20.38  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3640,b,3573,b)].
% 20.23/20.38  3641 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(643,b,596,b)].
% 20.23/20.38  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3641,b,3573,b)].
% 20.23/20.38  3642 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(670,b,644,a)].
% 20.23/20.38  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3642,a,3573,b)].
% 20.23/20.38  3643 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(670,b,646,a)].
% 20.23/20.38  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3643,a,3573,b)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 20.23/20.38  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)].
% 22.15/22.22  3646 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(670,b,649,a)].
% 22.15/22.22  Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3646,a,3573,b)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  3648 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(670,b,651,a)].
% 22.15/22.22  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A).  [resolve(3648,a,3573,b)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  3651 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(670,b,654,a)].
% 22.15/22.22  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3651,a,3573,b)].
% 22.15/22.22  3652 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(800,a,708,a)].
% 22.15/22.22  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3652,a,3573,b)].
% 22.15/22.22  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)].
% 22.15/22.22  3654 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom).  [assumption].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  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)].
% 22.15/22.22  3663 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,815,a)].
% 22.15/22.22  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  3673 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,825,a)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.15/22.23  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)].
% 22.17/22.24  3688 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(877,b,840,a)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  3693 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(877,b,845,a)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  3699 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(877,b,851,a)].
% 22.17/22.24  3700 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(877,b,852,a)].
% 22.17/22.24  3701 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(877,b,853,a)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  3709 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(877,b,861,a)].
% 22.17/22.24  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)].
% 22.17/22.24  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)].
% 22.17/22.24  3712 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1063,b,1046,a)].
% 22.26/22.34  3713 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1086,b,1069,a)].
% 22.26/22.34  3714 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A).  [resolve(1574,b,1542,a)].
% 22.26/22.34  3715 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1543,a)].
% 22.26/22.34  3716 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1544,a)].
% 22.26/22.34  3717 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1574,b,1545,a)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  3722 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1550,a)].
% 22.26/22.34  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)].
% 22.26/22.34  3724 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A).  [resolve(1574,b,1552,a)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 22.26/22.34  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)].
% 24.06/24.20  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)].
% 24.06/24.20  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)].
% 24.06/24.20  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)].
% 24.06/24.20  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)].
% 24.06/24.20  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)].
% 24.06/24.20  
% 24.06/24.20  ============================== end predicate elimination =============
% 24.06/24.20  
% 24.06/24.20  Auto_denials:  (non-Horn, no changes).
% 24.06/24.20  
% 24.06/24.20  Term ordering decisions:
% 24.06/24.20  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. 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. 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. 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. 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_g=1. v_x=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.
% 26.84/26.89  
% 26.84/26.89  ============================== end of process initial clauses ========
% 26.84/26.89  
% 26.84/26.89  ============================== CLAUSES FOR SEARCH ====================
% 26.84/26.89  
% 26.84/26.89  ============================== end of clauses for search =============
% 26.84/26.89  
% 26.84/26.89  ============================== SEARCH ================================
% 26.84/26.89  
% 26.84/26.89  % Starting search at 22.67 seconds.
% 26.84/26.89  
% 26.84/26.89  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 23.12 sec).
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=41.000, iters=3452
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=39.000, iters=3358
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=37.000, iters=3394
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=36.000, iters=3362
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=35.000, iters=3382
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=34.000, iters=3353
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=33.000, iters=3431
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=31.000, iters=3358
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=29.000, iters=3352
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=28.000, iters=3333
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=27.000, iters=3348
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=26.000, iters=3333
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=25.000, iters=3372
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=24.000, iters=3365
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=23.000, iters=3341
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=22.000, iters=3423
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=21.000, iters=3333
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=20.000, iters=3334
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=19.000, iters=3388
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=18.000, iters=3417
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=17.000, iters=3355
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=16.000, iters=3351
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=15.000, iters=3333
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=14.000, iters=3363
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=13.000, iters=3382
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=12.000, iters=3460
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=11.000, iters=3498
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=10.000, iters=3478
% 26.84/26.89  
% 26.84/26.89  Low Water (keep): wt=9.000, iters=3387
% 26.84/26.89  
% 26.84/26.89  ============================== PROOF =================================
% 26.84/26.89  % SZS status Unsatisfiable
% 26.84/26.89  % SZS output start Refutation
% 26.84/26.89  
% 26.84/26.89  % Proof 1 at 25.31 (+ 0.07) seconds.
% 26.84/26.89  % Length of proof is 10.
% 26.84/26.89  % Level of proof is 3.
% 26.84/26.89  % Maximum clause weight is 11.000.
% 26.84/26.89  % Given clauses 3253.
% 26.84/26.89  
% 26.84/26.89  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].
% 26.84/26.89  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].
% 26.84/26.89  5074 -class_Ring__and__Field_Oordered__idom(A) | B = c_times(c_1,B,A) # label(cls_Ring__and__Field_Omult__cancel__right1_2) # label(axiom).  [assumption].
% 26.84/26.89  5075 -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B.  [copy(5074),flip(b)].
% 26.84/26.89  5601 -c_lessequals(c_0,c_times(A,c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b) # label(cls_conjecture_0) # label(negated_conjecture).  [assumption].
% 26.84/26.89  5602 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture).  [assumption].
% 26.84/26.89  6771 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1427,b,1401,a)].
% 26.84/26.89  11549 c_times(c_1,A,t_b) = A.  [resolve(5602,a,5075,a)].
% 26.84/26.89  12664 c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b).  [resolve(6771,a,5602,a)].
% 26.84/26.89  18322 $F.  [para(11549(a,1),5601(a,2)),unit_del(a,12664)].
% 26.84/26.89  
% 26.84/26.89  % SZS output end Refutation
% 26.84/26.89  ============================== end of proof ==========================
% 26.84/26.89  
% 26.84/26.89  ============================== STATISTICS ============================
% 26.84/26.89  
% 26.84/26.89  Given=3253. Generated=40009. Kept=13494. proofs=1.
% 26.84/26.89  Usable=3222. Sos=9581. Demods=1368. Limbo=0, Disabled=9024. Hints=0.
% 26.84/26.89  Megabytes=70.49.
% 26.84/26.89  User_CPU=25.31, System_CPU=0.07, Wall_clock=26.
% 26.84/26.89  
% 26.84/26.89  ============================== end of statistics =====================
% 26.84/26.89  
% 26.84/26.89  ============================== end of search =========================
% 26.84/26.89  
% 26.84/26.89  THEOREM PROVED
% 26.84/26.89  % SZS status Unsatisfiable
% 26.84/26.89  
% 26.84/26.89  Exiting with 1 proof.
% 26.84/26.89  
% 26.84/26.89  Process 23542 exit (max_proofs) Fri Jul  8 02:46:36 2022
% 26.84/26.89  Prover9 interrupted
%------------------------------------------------------------------------------