TSTP Solution File: ANA038-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA038-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 19:21:55 EDT 2022
% Result : Timeout 300.07s 300.19s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA038-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.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 05:35:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.57/1.80 ============================== Prover9 ===============================
% 1.57/1.80 Prover9 (32) version 2009-11A, November 2009.
% 1.57/1.80 Process 18261 was started by sandbox on n004.cluster.edu,
% 1.57/1.80 Fri Jul 8 05:35:53 2022
% 1.57/1.80 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18107_n004.cluster.edu".
% 1.57/1.80 ============================== end of head ===========================
% 1.57/1.80
% 1.57/1.80 ============================== INPUT =================================
% 1.57/1.80
% 1.57/1.80 % Reading from file /tmp/Prover9_18107_n004.cluster.edu
% 1.57/1.80
% 1.57/1.80 set(prolog_style_variables).
% 1.57/1.80 set(auto2).
% 1.57/1.80 % set(auto2) -> set(auto).
% 1.57/1.80 % set(auto) -> set(auto_inference).
% 1.57/1.80 % set(auto) -> set(auto_setup).
% 1.57/1.80 % set(auto_setup) -> set(predicate_elim).
% 1.57/1.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.57/1.80 % set(auto) -> set(auto_limits).
% 1.57/1.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.57/1.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.57/1.80 % set(auto) -> set(auto_denials).
% 1.57/1.80 % set(auto) -> set(auto_process).
% 1.57/1.80 % set(auto2) -> assign(new_constants, 1).
% 1.57/1.80 % set(auto2) -> assign(fold_denial_max, 3).
% 1.57/1.80 % set(auto2) -> assign(max_weight, "200.000").
% 1.57/1.80 % set(auto2) -> assign(max_hours, 1).
% 1.57/1.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.57/1.80 % set(auto2) -> assign(max_seconds, 0).
% 1.57/1.80 % set(auto2) -> assign(max_minutes, 5).
% 1.57/1.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.57/1.80 % set(auto2) -> set(sort_initial_sos).
% 1.57/1.80 % set(auto2) -> assign(sos_limit, -1).
% 1.57/1.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.57/1.80 % set(auto2) -> assign(max_megs, 400).
% 1.57/1.80 % set(auto2) -> assign(stats, some).
% 1.57/1.80 % set(auto2) -> clear(echo_input).
% 1.57/1.80 % set(auto2) -> set(quiet).
% 1.57/1.80 % set(auto2) -> clear(print_initial_clauses).
% 1.57/1.80 % set(auto2) -> clear(print_given).
% 1.57/1.80 assign(lrs_ticks,-1).
% 1.57/1.80 assign(sos_limit,10000).
% 1.57/1.80 assign(order,kbo).
% 1.57/1.80 set(lex_order_vars).
% 1.57/1.80 clear(print_given).
% 1.57/1.80
% 1.57/1.80 % formulas(sos). % not echoed (2802 formulas)
% 1.57/1.80
% 1.57/1.80 ============================== end of input ==========================
% 1.57/1.80
% 1.57/1.80 % From the command line: assign(max_seconds, 300).
% 1.57/1.80
% 1.57/1.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.57/1.80
% 1.57/1.80 % Formulas that are not ordinary clauses:
% 1.57/1.80
% 1.57/1.80 ============================== end of process non-clausal formulas ===
% 1.57/1.80
% 1.57/1.80 ============================== PROCESS INITIAL CLAUSES ===============
% 1.57/1.80
% 1.57/1.80 ============================== PREDICATE ELIMINATION =================
% 1.57/1.80 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].
% 1.57/1.80 2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom). [assumption].
% 1.57/1.80 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)].
% 1.57/1.80 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].
% 1.57/1.80 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)].
% 1.57/1.80 4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 1.57/1.80 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4,a,1,a)].
% 1.57/1.80 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4,a,3,a)].
% 1.57/1.80 5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 1.57/1.80 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(5,a,1,a)].
% 1.57/1.80 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(5,a,3,a)].
% 1.57/1.80 6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 1.57/1.80 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 1.57/1.80 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 1.57/1.80 7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 1.60/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(7,b,1,a)].
% 1.60/1.82 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(7,b,3,a)].
% 1.60/1.82 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].
% 1.60/1.82 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)].
% 1.60/1.82 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)].
% 1.60/1.82 9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(9,a,2,a)].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(9,a,4,a)].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(9,a,5,a)].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(9,a,7,b)].
% 1.60/1.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 1.60/1.82 10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 1.60/1.82 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(10,a,2,a)].
% 1.60/1.82 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(10,a,4,a)].
% 1.60/1.82 Derived: class_HOL_Oplus(tc_nat). [resolve(10,a,5,a)].
% 1.60/1.82 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 1.60/1.82 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(10,a,7,b)].
% 1.60/1.82 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 1.60/1.82 11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 1.60/1.82 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 1.60/1.82 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 1.60/1.82 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].
% 1.60/1.82 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)].
% 1.60/1.82 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)].
% 1.60/1.82 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].
% 1.60/1.82 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)].
% 1.60/1.82 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)].
% 1.60/1.82 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].
% 1.60/1.82 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)].
% 1.60/1.82 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)].
% 1.60/1.82 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 1.61/1.84 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 1.61/1.84 19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 1.61/1.84 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(19,b,1,a)].
% 1.61/1.84 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(19,b,3,a)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.84 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 1.61/1.84 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].
% 1.61/1.84 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)].
% 1.61/1.84 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)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 1.61/1.90 24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 1.61/1.90 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(24,b,1,a)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(24,b,3,a)].
% 1.61/1.90 25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 1.61/1.90 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 1.61/1.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 1.61/1.90 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].
% 1.61/1.90 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)].
% 1.61/1.90 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)].
% 1.61/1.90 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 1.69/1.93 37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 1.69/1.93 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 1.69/1.93 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 1.69/1.93 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].
% 1.69/1.93 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)].
% 1.69/1.93 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)].
% 1.69/1.93 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].
% 1.76/2.04 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)].
% 1.76/2.04 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)].
% 1.76/2.04 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].
% 1.76/2.04 42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom). [assumption].
% 1.76/2.04 43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 1.76/2.04 44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 1.76/2.04 45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 1.76/2.04 46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 1.76/2.04 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 1.76/2.04 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 1.76/2.04 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 1.76/2.04 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 1.76/2.04 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 1.76/2.04 47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 1.76/2.04 48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 1.76/2.04 49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 1.76/2.04 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 1.76/2.04 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 1.76/2.04 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].
% 1.76/2.04 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].
% 1.76/2.04 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].
% 1.76/2.04 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].
% 1.76/2.04 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].
% 1.76/2.04 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].
% 1.85/2.08 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 1.85/2.08 57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 1.85/2.08 62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 1.85/2.08 63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 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].
% 1.85/2.08 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 1.85/2.08 75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 1.87/2.09 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 1.87/2.09 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].
% 1.87/2.09 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 1.87/2.09 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].
% 1.87/2.09 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 1.87/2.09 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 1.87/2.09 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 1.87/2.09 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].
% 1.87/2.09 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)].
% 1.87/2.09 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)].
% 1.87/2.09 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(79,a,43,a)].
% 1.87/2.09 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(79,a,44,a)].
% 1.87/2.09 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 1.87/2.09 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(79,a,46,b)].
% 1.87/2.09 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)].
% 1.87/2.09 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)].
% 1.87/2.09 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(80,a,43,a)].
% 1.87/2.09 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(80,a,44,a)].
% 1.87/2.09 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 1.87/2.09 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(80,a,46,b)].
% 1.87/2.09 81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(81,b,42,a)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(81,b,43,a)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(81,b,44,a)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(81,b,46,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(81,b,54,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(81,b,57,b)].
% 1.87/2.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(81,b,59,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(81,b,62,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(81,b,66,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(81,b,67,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(81,b,73,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 2.01/2.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 2.01/2.23 82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(82,b,42,a)].
% 2.01/2.23 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(82,b,43,a)].
% 2.01/2.23 Derived: class_HOL_Oplus(tc_nat). [resolve(82,b,44,a)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(82,b,46,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(82,b,54,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(82,b,57,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(82,b,59,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(82,b,62,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(82,b,66,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(82,b,67,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(82,b,73,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 2.01/2.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 2.01/2.23 83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom). [assumption].
% 2.01/2.25 84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom). [assumption].
% 2.01/2.25 85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom). [assumption].
% 2.01/2.25 86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom). [assumption].
% 2.01/2.25 87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom). [assumption].
% 2.01/2.25 88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 2.01/2.25 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(83,a,84,a)].
% 2.01/2.25 Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(83,a,85,a)].
% 2.01/2.25 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(83,a,86,a)].
% 2.01/2.25 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(83,a,87,a)].
% 2.01/2.25 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 2.01/2.25 89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom). [assumption].
% 2.01/2.25 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(89,a,84,a)].
% 2.01/2.25 Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(89,a,85,a)].
% 2.01/2.25 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(89,a,86,a)].
% 2.01/2.25 Derived: class_HOL_Otimes(tc_nat). [resolve(89,a,87,a)].
% 2.01/2.25 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 2.01/2.25 90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 2.01/2.25 91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom). [assumption].
% 2.01/2.25 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(91,b,83,a)].
% 2.01/2.25 Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A). [resolve(91,b,89,a)].
% 2.01/2.25 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].
% 2.01/2.25 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].
% 2.01/2.25 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(93,b,83,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A). [resolve(93,b,89,a)].
% 2.01/2.25 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].
% 2.01/2.25 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].
% 2.01/2.25 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].
% 2.01/2.25 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].
% 2.01/2.25 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].
% 2.01/2.25 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 2.01/2.25 99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom). [assumption].
% 2.18/2.42 100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 2.18/2.42 101 -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].
% 2.18/2.42 102 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_20) # label(axiom). [assumption].
% 2.18/2.42 103 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 2.18/2.42 104 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 2.18/2.42 105 -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].
% 2.18/2.42 106 -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].
% 2.18/2.42 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(106,b,83,a)].
% 2.18/2.42 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A). [resolve(106,b,89,a)].
% 2.18/2.42 107 -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].
% 2.18/2.42 108 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 2.18/2.42 109 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom). [assumption].
% 2.18/2.42 110 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom). [assumption].
% 2.18/2.42 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(108,a,109,a)].
% 2.18/2.42 Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(108,a,110,a)].
% 2.18/2.42 111 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 2.18/2.42 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(111,a,109,a)].
% 2.18/2.42 Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(111,a,110,a)].
% 2.18/2.42 112 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 2.18/2.42 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(112,a,108,a)].
% 2.18/2.42 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(112,a,111,a)].
% 2.18/2.42 113 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 2.18/2.42 Derived: c_times(c_1,A,tc_nat) = A. [resolve(113,a,108,a)].
% 2.18/2.42 Derived: c_times(A,c_1,tc_nat) = A. [resolve(113,a,111,a)].
% 2.18/2.42 114 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.18/2.42 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(114,b,108,a)].
% 2.18/2.42 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(114,b,111,a)].
% 2.18/2.42 115 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 2.18/2.42 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(115,b,108,a)].
% 2.18/2.42 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(115,b,111,a)].
% 2.18/2.42 116 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.21/2.45 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(116,a,109,a)].
% 2.21/2.45 Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(116,a,110,a)].
% 2.21/2.45 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(116,a,112,a)].
% 2.21/2.45 Derived: class_HOL_Oone(tc_nat). [resolve(116,a,113,a)].
% 2.21/2.45 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(116,a,114,b)].
% 2.21/2.45 Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(116,a,115,b)].
% 2.21/2.45 117 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 2.21/2.45 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(117,a,115,b)].
% 2.21/2.45 118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 2.21/2.45 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,115,b)].
% 2.21/2.45 119 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 2.21/2.45 Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B. [resolve(119,b,108,a)].
% 2.21/2.45 Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B. [resolve(119,b,111,a)].
% 2.21/2.45 120 -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].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B. [resolve(120,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B. [resolve(120,b,111,a)].
% 2.21/2.45 121 -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].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(121,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(121,b,111,a)].
% 2.21/2.45 122 -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].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(122,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(122,b,111,a)].
% 2.21/2.45 123 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B. [resolve(123,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B. [resolve(123,b,111,a)].
% 2.21/2.45 124 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(124,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(124,b,111,a)].
% 2.21/2.45 125 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B. [resolve(125,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B. [resolve(125,b,111,a)].
% 2.21/2.45 126 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B. [resolve(126,b,108,a)].
% 2.21/2.45 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B. [resolve(126,b,111,a)].
% 2.21/2.45 127 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(127,b,108,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(127,b,111,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(127,b,117,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(127,b,118,a)].
% 2.31/2.58 128 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(128,b,108,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(128,b,111,a)].
% 2.31/2.58 129 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(129,b,108,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(129,b,111,a)].
% 2.31/2.58 130 -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].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(130,b,108,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(130,b,111,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(130,b,116,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(130,b,117,a)].
% 2.31/2.58 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(130,b,118,a)].
% 2.31/2.58 131 -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].
% 2.31/2.58 132 class_Ring__and__Field_Osemiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_17) # label(axiom). [assumption].
% 2.31/2.58 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)].
% 2.31/2.58 133 -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].
% 2.31/2.58 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)].
% 2.31/2.58 134 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.31/2.58 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(134,a,131,b)].
% 2.31/2.58 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(134,a,133,b)].
% 2.38/2.61 135 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 136 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 137 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 138 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 139 -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].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 140 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 2.38/2.61 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)].
% 2.38/2.61 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)].
% 2.38/2.61 141 -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].
% 2.38/2.61 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)].
% 2.38/2.62 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)].
% 2.38/2.62 142 -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].
% 2.38/2.62 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)].
% 2.38/2.62 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)].
% 2.38/2.62 143 -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].
% 2.38/2.62 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)].
% 2.38/2.62 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)].
% 2.38/2.62 144 -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].
% 2.38/2.62 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)].
% 2.38/2.62 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)].
% 2.38/2.62 145 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.38/2.62 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)].
% 2.38/2.62 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)].
% 2.38/2.62 146 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.38/2.62 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)].
% 2.38/2.62 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)].
% 2.38/2.62 147 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 2.38/2.62 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)].
% 2.38/2.64 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)].
% 2.38/2.64 148 -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].
% 2.38/2.64 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)].
% 2.38/2.64 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)].
% 2.38/2.64 149 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 2.38/2.64 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)].
% 2.38/2.64 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)].
% 2.38/2.64 150 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 2.38/2.64 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)].
% 2.38/2.64 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)].
% 2.38/2.64 151 -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].
% 2.38/2.64 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)].
% 2.38/2.64 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)].
% 2.38/2.64 152 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 2.38/2.64 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)].
% 2.38/2.64 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)].
% 2.38/2.64 153 -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].
% 2.38/2.64 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)].
% 2.38/2.66 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)].
% 2.38/2.66 154 -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].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 155 -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].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 156 -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].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 157 -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].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 158 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 159 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 160 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 161 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 2.38/2.66 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)].
% 2.38/2.66 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)].
% 2.38/2.66 162 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(162,a,132,a)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(162,a,137,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(162,a,138,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(162,a,139,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(162,a,140,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(162,a,141,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(162,a,142,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(162,a,143,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(162,a,145,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(162,a,146,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(162,a,147,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(162,a,148,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(162,a,149,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(162,a,150,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(162,a,152,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(162,a,153,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(162,a,155,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(162,a,156,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(162,a,157,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(162,a,159,b)].
% 2.38/2.66 163 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(163,a,132,a)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(163,a,140,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(163,a,141,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(163,a,143,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(163,a,157,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(163,a,159,b)].
% 2.38/2.66 164 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.38/2.66 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,132,a)].
% 2.38/2.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,140,b)].
% 2.38/2.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,141,b)].
% 2.38/2.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,143,b)].
% 2.38/2.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,157,b)].
% 2.38/2.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,159,b)].
% 2.38/2.66 165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(165,a,132,a)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(165,a,138,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,140,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,141,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(165,a,142,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,143,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(165,a,145,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(165,a,146,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(165,a,147,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(165,a,148,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(165,a,149,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(165,a,150,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(165,a,151,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(165,a,153,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(165,a,154,b)].
% 2.38/2.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(165,a,155,b)].
% 2.45/2.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,157,b)].
% 2.45/2.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(165,a,158,b)].
% 2.45/2.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,159,b)].
% 2.45/2.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(165,a,160,b)].
% 2.45/2.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(165,a,161,b)].
% 2.45/2.67 166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.45/2.67 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(166,a,132,a)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(166,a,138,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,140,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,141,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(166,a,142,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,143,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(166,a,145,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(166,a,146,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(166,a,147,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(166,a,148,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(166,a,149,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(166,a,150,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(166,a,151,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(166,a,153,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(166,a,154,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(166,a,155,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,157,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(166,a,158,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,159,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(166,a,160,b)].
% 2.45/2.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(166,a,161,b)].
% 2.45/2.67 167 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.45/2.67 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)].
% 2.45/2.67 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)].
% 2.45/2.67 168 -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].
% 2.45/2.67 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)].
% 2.45/2.67 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)].
% 2.46/2.67 169 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.46/2.67 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)].
% 2.46/2.67 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)].
% 2.46/2.67 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(169,b,164,a)].
% 2.46/2.67 170 -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].
% 2.46/2.67 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)].
% 2.46/2.67 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)].
% 2.46/2.67 171 -class_Ring__and__Field_Osemiring(A) | c_times(B,c_plus(C,D,A),A) = c_plus(c_times(B,C,A),c_times(B,D,A),A) # label(cls_Ring__and__Field_Oring__distrib__1_0) # label(axiom). [assumption].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(171,a,132,a)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(171,a,134,a)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(171,a,135,a)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(171,a,136,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(171,a,137,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(171,a,138,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(171,a,139,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(171,a,140,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(171,a,141,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(171,a,142,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(171,a,143,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(171,a,144,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(171,a,145,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(171,a,146,b)].
% 2.46/2.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(171,a,147,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(171,a,148,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(171,a,149,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(171,a,150,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(171,a,151,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(171,a,152,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(171,a,153,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(171,a,154,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(171,a,155,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(171,a,156,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(171,a,157,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(171,a,158,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(171,a,159,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(171,a,160,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(171,a,161,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0(D). [resolve(171,a,167,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0__cancel(D). [resolve(171,a,168,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1(D). [resolve(171,a,169,b)].
% 2.46/2.68 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1__cancel(D). [resolve(171,a,170,b)].
% 2.46/2.68 172 -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),D,A) = c_plus(c_times(B,D,A),c_times(C,D,A),A) # label(cls_Ring__and__Field_Oring__distrib__2_0) # label(axiom). [assumption].
% 2.46/2.68 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(172,a,132,a)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(172,a,134,a)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(172,a,135,a)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(172,a,136,b)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(172,a,137,b)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(172,a,138,b)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(172,a,139,b)].
% 2.46/2.68 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(172,a,140,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(172,a,141,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(172,a,142,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(172,a,143,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(172,a,144,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(172,a,145,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(172,a,146,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(172,a,147,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(172,a,148,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(172,a,149,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(172,a,150,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(172,a,151,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(172,a,152,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(172,a,153,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(172,a,154,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(172,a,155,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(172,a,156,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(172,a,157,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(172,a,158,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(172,a,159,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(172,a,160,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(172,a,161,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0(C). [resolve(172,a,167,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(172,a,168,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1(C). [resolve(172,a,169,b)].
% 2.53/2.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(172,a,170,b)].
% 2.53/2.83 173 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.53/2.83 174 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].
% 2.62/2.89 175 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.62/2.89 176 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.62/2.89 177 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.62/2.89 178 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.62/2.89 179 -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].
% 2.62/2.89 180 -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].
% 2.62/2.89 181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.62/2.89 182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.62/2.89 183 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.62/2.89 184 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.62/2.89 185 -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].
% 2.62/2.89 186 -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].
% 2.62/2.89 187 -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].
% 2.62/2.89 188 -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].
% 2.62/2.89 189 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.62/2.89 190 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.62/2.89 191 -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].
% 2.62/2.89 192 -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].
% 2.62/2.89 193 -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].
% 2.62/2.89 194 -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].
% 2.62/2.89 195 -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].
% 2.62/2.89 196 -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].
% 2.62/2.89 197 -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].
% 2.62/2.89 198 -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)].
% 2.68/2.90 199 -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)].
% 2.68/2.90 200 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(162,a,140,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(200,b,174,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(200,b,175,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(200,b,176,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(200,b,177,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(200,b,178,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,b,179,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(200,b,180,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(200,b,188,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(200,b,195,b)].
% 2.68/2.90 201 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(163,a,140,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(201,b,174,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(201,b,175,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(201,b,176,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(201,b,177,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(201,b,178,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,b,179,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(201,b,180,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(201,b,186,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(201,b,188,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(201,b,189,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(201,b,190,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(201,b,191,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(201,b,192,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(201,b,193,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(201,b,194,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(201,b,195,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(201,b,196,b)].
% 2.68/2.90 202 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,140,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 2.68/2.90 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 2.68/2.90 Derived: class_HOL_Oplus(tc_nat). [resolve(202,b,176,a)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(202,b,186,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(202,b,189,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(202,b,190,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(202,b,191,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(202,b,192,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(202,b,193,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(202,b,194,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 2.68/2.90 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(202,b,196,b)].
% 2.68/2.90 203 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,140,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(203,b,174,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(203,b,175,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(203,b,176,a)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(203,b,178,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(203,b,180,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 2.68/2.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(203,b,196,b)].
% 2.68/2.90 204 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,140,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(204,b,174,a)].
% 2.68/2.90 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(204,b,175,a)].
% 2.68/2.90 Derived: class_HOL_Otimes(tc_nat). [resolve(204,b,176,a)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(204,b,178,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(204,b,180,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 2.68/2.90 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(204,b,196,b)].
% 2.68/2.90 205 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(171,a,140,b)].
% 2.68/2.90 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(205,b,174,a)].
% 2.68/2.90 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(205,b,175,a)].
% 2.68/2.90 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(205,b,176,a)].
% 2.83/3.08 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(205,b,177,b)].
% 2.83/3.08 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(205,b,178,b)].
% 2.83/3.08 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(205,b,179,b)].
% 2.83/3.08 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(205,b,180,b)].
% 2.83/3.08 206 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(172,a,140,b)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(206,b,174,a)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(206,b,175,a)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(206,b,176,a)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(206,b,177,b)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(206,b,178,b)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(206,b,179,b)].
% 2.83/3.08 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(206,b,180,b)].
% 2.83/3.08 207 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 2.83/3.08 208 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].
% 2.83/3.08 209 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 2.83/3.08 210 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 2.83/3.08 211 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 2.83/3.08 212 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 2.83/3.08 213 -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].
% 2.83/3.08 214 -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].
% 2.83/3.08 215 -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].
% 2.83/3.08 216 -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].
% 2.83/3.08 217 -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].
% 2.83/3.08 218 -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].
% 2.83/3.08 219 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 2.83/3.08 220 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 2.83/3.08 221 -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].
% 2.83/3.09 222 -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].
% 2.83/3.09 223 -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].
% 2.83/3.09 224 -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].
% 2.83/3.09 225 -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].
% 2.83/3.09 226 -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].
% 2.83/3.09 227 -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].
% 2.83/3.09 228 -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].
% 2.83/3.09 229 -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].
% 2.83/3.09 230 -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].
% 2.83/3.09 231 -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].
% 2.83/3.09 232 -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].
% 2.83/3.09 233 -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].
% 2.83/3.09 234 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 2.83/3.09 235 -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].
% 2.83/3.09 236 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 2.83/3.09 237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 2.83/3.09 238 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 2.83/3.09 239 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 2.83/3.09 240 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(240,a,208,a)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(240,a,209,a)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(240,a,210,a)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(240,a,212,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(240,a,214,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(240,a,219,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(240,a,223,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(240,a,224,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(240,a,230,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 2.83/3.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 2.83/3.09 241 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 2.83/3.09 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(241,a,208,a)].
% 2.83/3.09 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(241,a,209,a)].
% 2.83/3.09 Derived: class_HOL_Ozero(tc_nat). [resolve(241,a,210,a)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(241,a,212,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(241,a,214,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(241,a,219,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 2.83/3.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(241,a,223,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(241,a,224,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(241,a,230,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 2.83/3.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 2.83/3.14 242 -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].
% 2.83/3.14 243 -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].
% 2.83/3.14 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 2.83/3.14 244 -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].
% 2.83/3.14 245 -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)].
% 2.83/3.14 246 -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)].
% 2.83/3.14 247 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0(D). [resolve(171,a,167,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(247,b,215,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(247,b,216,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(247,b,217,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(247,b,218,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(247,b,219,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(247,b,220,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(247,b,221,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(247,b,222,b)].
% 2.83/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(247,b,223,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(247,b,224,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(247,b,225,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(247,b,226,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(247,b,227,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(247,b,228,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(247,b,229,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(247,b,230,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(247,b,231,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(247,b,232,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(247,b,233,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(247,b,234,b)].
% 2.92/3.14 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(247,b,235,b)].
% 2.92/3.14 248 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0(C). [resolve(172,a,167,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(248,b,215,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(248,b,216,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(248,b,217,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(248,b,218,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(248,b,219,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(248,b,220,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(248,b,221,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(248,b,222,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(248,b,223,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(248,b,224,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(248,b,225,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(248,b,226,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(248,b,227,b)].
% 2.92/3.14 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(248,b,228,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(248,b,229,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(248,b,230,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(248,b,231,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(248,b,232,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(248,b,233,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(248,b,234,b)].
% 3.05/3.27 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(248,b,235,b)].
% 3.05/3.27 249 -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].
% 3.05/3.27 250 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].
% 3.05/3.27 251 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.05/3.27 252 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.05/3.27 253 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.05/3.27 254 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.05/3.27 255 -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].
% 3.05/3.27 256 -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].
% 3.05/3.27 257 -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].
% 3.05/3.27 258 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.05/3.27 259 -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].
% 3.05/3.27 260 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.05/3.27 261 -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].
% 3.05/3.27 262 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.05/3.27 263 -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].
% 3.05/3.27 264 -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].
% 3.05/3.27 265 -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].
% 3.05/3.27 266 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.05/3.27 267 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.10/3.35 268 -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].
% 3.10/3.35 269 -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].
% 3.10/3.35 270 -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].
% 3.10/3.35 271 -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].
% 3.10/3.35 272 -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].
% 3.10/3.35 273 -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].
% 3.10/3.35 274 -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].
% 3.10/3.35 275 -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)].
% 3.10/3.35 276 -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)].
% 3.10/3.35 277 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(162,a,141,b)].
% 3.10/3.35 278 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(163,a,141,b)].
% 3.10/3.35 279 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,141,b)].
% 3.10/3.35 280 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,141,b)].
% 3.10/3.35 281 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,141,b)].
% 3.10/3.35 282 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(171,a,141,b)].
% 3.10/3.35 283 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(172,a,141,b)].
% 3.10/3.35 284 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(284,b,250,a)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(284,b,251,a)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(284,b,252,a)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(284,b,253,b)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(284,b,254,b)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,b,255,b)].
% 3.10/3.35 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(284,b,256,b)].
% 3.10/3.35 285 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 3.10/3.35 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(285,b,250,a)].
% 3.10/3.35 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(285,b,251,a)].
% 3.10/3.35 Derived: class_HOL_Ozero(tc_nat). [resolve(285,b,252,a)].
% 3.10/3.35 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(285,b,253,b)].
% 3.10/3.35 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(285,b,254,b)].
% 3.23/3.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,b,255,b)].
% 3.23/3.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(285,b,256,b)].
% 3.23/3.47 286 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(247,b,215,b)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(286,b,250,a)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(286,b,251,a)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(286,b,252,a)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(286,b,253,b)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(286,b,254,b)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(286,b,255,b)].
% 3.23/3.47 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(286,b,256,b)].
% 3.23/3.47 287 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(248,b,215,b)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(287,b,250,a)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(287,b,251,a)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(287,b,252,a)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(287,b,253,b)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(287,b,254,b)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(287,b,255,b)].
% 3.23/3.47 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(287,b,256,b)].
% 3.23/3.47 288 -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].
% 3.23/3.47 289 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].
% 3.23/3.47 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(288,a,289,a)].
% 3.23/3.47 290 -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].
% 3.23/3.47 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(290,a,289,a)].
% 3.23/3.47 291 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 3.23/3.47 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(291,a,288,a)].
% 3.23/3.47 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(291,a,290,a)].
% 3.23/3.47 292 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 3.23/3.47 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(292,a,288,a)].
% 3.23/3.47 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(292,a,290,a)].
% 3.23/3.47 293 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 3.23/3.47 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,288,a)].
% 3.27/3.50 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,290,a)].
% 3.27/3.50 294 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 3.27/3.50 Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0. [resolve(294,b,288,a)].
% 3.27/3.50 Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0. [resolve(294,b,290,a)].
% 3.27/3.50 295 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,290,a)].
% 3.27/3.50 296 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,290,a)].
% 3.27/3.50 297 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,290,a)].
% 3.27/3.50 298 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,290,a)].
% 3.27/3.50 299 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,290,a)].
% 3.27/3.50 300 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,290,a)].
% 3.27/3.50 301 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,290,a)].
% 3.27/3.50 302 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,290,a)].
% 3.27/3.50 303 -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].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,288,a)].
% 3.27/3.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,290,a)].
% 3.27/3.50 304 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,290,a)].
% 3.27/3.52 305 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,290,a)].
% 3.27/3.52 306 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,290,a)].
% 3.27/3.52 307 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,290,a)].
% 3.27/3.52 308 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,290,a)].
% 3.27/3.52 309 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,290,a)].
% 3.27/3.52 310 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,290,a)].
% 3.27/3.52 311 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,290,a)].
% 3.27/3.52 312 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(312,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(312,b,290,a)].
% 3.27/3.52 313 -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].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(313,b,288,a)].
% 3.27/3.52 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(313,b,290,a)].
% 3.27/3.52 314 -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].
% 3.27/3.52 315 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 3.33/3.55 316 -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].
% 3.33/3.55 317 -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].
% 3.33/3.55 318 -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].
% 3.33/3.55 319 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 3.33/3.55 320 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 3.33/3.55 321 -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].
% 3.33/3.55 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(321,b,288,a)].
% 3.33/3.55 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(321,b,290,a)].
% 3.33/3.55 322 -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)].
% 3.33/3.55 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(322,a,289,a)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(322,a,294,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(322,a,295,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(322,a,296,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(322,a,297,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(322,a,298,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(322,a,299,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(322,a,300,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(322,a,301,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(322,a,302,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(322,a,303,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(322,a,304,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(322,a,305,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(322,a,306,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(322,a,307,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(322,a,308,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(322,a,309,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(322,a,310,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(322,a,311,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(322,a,312,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(322,a,313,b)].
% 3.33/3.55 323 -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)].
% 3.33/3.55 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(323,a,289,a)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(323,a,294,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(323,a,295,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(323,a,296,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(323,a,297,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(323,a,298,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(323,a,299,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(323,a,300,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(323,a,301,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(323,a,302,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(323,a,303,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(323,a,304,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(323,a,305,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(323,a,306,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(323,a,307,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(323,a,308,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(323,a,309,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(323,a,310,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(323,a,311,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(323,a,312,b)].
% 3.33/3.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(323,a,313,b)].
% 3.33/3.55 324 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 3.33/3.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,305,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,311,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(324,a,312,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,313,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(324,a,321,b)].
% 3.33/3.55 325 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 3.33/3.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(325,a,305,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(325,a,311,b)].
% 3.33/3.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(325,a,313,b)].
% 3.33/3.55 326 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 3.33/3.55 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(326,a,305,b)].
% 3.33/3.55 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(326,a,309,b)].
% 3.46/3.71 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(326,a,311,b)].
% 3.46/3.71 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(326,a,313,b)].
% 3.46/3.71 327 -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)].
% 3.46/3.71 328 -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)].
% 3.46/3.71 329 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0__cancel(D). [resolve(171,a,168,b)].
% 3.46/3.71 330 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(172,a,168,b)].
% 3.46/3.71 331 -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].
% 3.46/3.71 332 class_Ring__and__Field_Oring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_22) # label(axiom). [assumption].
% 3.46/3.71 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(331,b,332,a)].
% 3.46/3.71 333 -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].
% 3.46/3.71 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(333,b,332,a)].
% 3.46/3.71 334 -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].
% 3.46/3.71 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(334,a,332,a)].
% 3.46/3.71 335 -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].
% 3.46/3.71 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(335,a,332,a)].
% 3.46/3.71 336 -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].
% 3.46/3.71 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(336,a,332,a)].
% 3.46/3.71 337 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 3.46/3.71 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(337,a,331,b)].
% 3.46/3.71 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(337,a,333,b)].
% 3.46/3.73 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(337,a,334,a)].
% 3.46/3.73 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(337,a,335,a)].
% 3.46/3.73 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(337,a,336,a)].
% 3.46/3.73 338 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 3.46/3.73 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(338,b,331,b)].
% 3.46/3.73 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(338,b,333,b)].
% 3.46/3.73 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,334,a)].
% 3.46/3.73 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,335,a)].
% 3.46/3.73 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,336,a)].
% 3.46/3.73 339 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 3.46/3.73 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(339,b,331,b)].
% 3.46/3.73 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(339,b,333,b)].
% 3.46/3.73 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(339,b,334,a)].
% 3.46/3.73 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(339,b,335,a)].
% 3.46/3.73 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(339,b,336,a)].
% 3.46/3.73 340 -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].
% 3.46/3.73 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(340,b,331,b)].
% 3.46/3.73 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(340,b,333,b)].
% 3.46/3.73 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(340,b,334,a)].
% 3.46/3.73 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(340,b,335,a)].
% 3.46/3.73 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(340,b,336,a)].
% 3.46/3.73 341 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 3.46/3.73 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(341,b,331,b)].
% 3.54/3.74 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(341,b,333,b)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(341,b,334,a)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(341,b,335,a)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(341,b,336,a)].
% 3.54/3.74 342 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 3.54/3.74 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(342,b,331,b)].
% 3.54/3.74 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(342,b,333,b)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(342,b,334,a)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,335,a)].
% 3.54/3.74 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,336,a)].
% 3.54/3.74 343 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 3.54/3.74 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(343,b,331,b)].
% 3.54/3.74 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(343,b,333,b)].
% 3.54/3.74 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(343,b,334,a)].
% 3.54/3.74 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(343,b,335,a)].
% 3.54/3.74 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(343,b,336,a)].
% 3.54/3.74 344 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 3.54/3.74 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(344,b,331,b)].
% 3.54/3.74 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(344,b,333,b)].
% 3.54/3.74 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(344,b,334,a)].
% 3.54/3.74 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(344,b,335,a)].
% 3.54/3.74 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(344,b,336,a)].
% 3.54/3.74 345 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 3.54/3.74 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(345,b,331,b)].
% 3.54/3.76 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(345,b,333,b)].
% 3.54/3.76 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(345,b,334,a)].
% 3.54/3.76 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(345,b,335,a)].
% 3.54/3.76 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(345,b,336,a)].
% 3.54/3.76 346 -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].
% 3.54/3.76 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(346,b,331,b)].
% 3.54/3.76 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(346,b,333,b)].
% 3.54/3.76 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(346,b,334,a)].
% 3.54/3.76 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(346,b,335,a)].
% 3.54/3.76 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(346,b,336,a)].
% 3.54/3.76 347 -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].
% 3.54/3.76 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(347,b,331,b)].
% 3.54/3.76 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(347,b,333,b)].
% 3.54/3.76 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(347,b,334,a)].
% 3.54/3.76 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(347,b,335,a)].
% 3.54/3.76 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(347,b,336,a)].
% 3.54/3.76 348 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 3.54/3.76 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(348,b,331,b)].
% 3.54/3.76 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(348,b,333,b)].
% 3.54/3.76 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(348,b,334,a)].
% 3.54/3.76 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(348,b,335,a)].
% 3.54/3.76 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(348,b,336,a)].
% 3.54/3.77 349 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 3.54/3.77 350 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 3.54/3.77 351 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 3.54/3.77 352 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 3.54/3.77 353 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 3.54/3.77 354 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(354,a,332,a)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(354,a,337,a)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(354,a,338,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(354,a,339,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(354,a,340,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(354,a,341,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,a,342,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,a,343,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(354,a,344,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(354,a,345,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,a,346,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(354,a,347,b)].
% 3.54/3.77 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,a,348,b)].
% 3.54/3.77 355 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom). [assumption].
% 3.54/3.77 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(355,a,332,a)].
% 3.54/3.77 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(355,a,337,a)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(355,a,338,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(355,a,339,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(355,a,340,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(355,a,341,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(355,a,342,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(355,a,343,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(355,a,344,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(355,a,345,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(355,a,346,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(355,a,347,b)].
% 3.54/3.77 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(355,a,348,b)].
% 3.54/3.77 356 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 3.54/3.77 357 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 3.54/3.77 358 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 3.58/3.81 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(358,b,331,b)].
% 3.58/3.81 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(358,b,333,b)].
% 3.58/3.81 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(358,b,334,a)].
% 3.58/3.81 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(358,b,335,a)].
% 3.58/3.81 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(358,b,336,a)].
% 3.58/3.81 359 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 3.58/3.81 360 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 3.58/3.81 361 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 3.58/3.81 362 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,343,b)].
% 3.58/3.81 363 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 3.58/3.81 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,343,b)].
% 3.58/3.81 364 -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)].
% 3.58/3.81 365 -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)].
% 3.58/3.81 366 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(165,a,160,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(366,b,341,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(366,b,342,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,b,343,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(366,b,344,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(366,b,345,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,b,346,b)].
% 3.58/3.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,b,348,b)].
% 3.58/3.81 367 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(166,a,160,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(367,b,341,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(367,b,342,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,b,343,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(367,b,344,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(367,b,345,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,b,346,b)].
% 3.58/3.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,b,348,b)].
% 3.58/3.81 368 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(171,a,160,b)].
% 3.58/3.81 369 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(172,a,160,b)].
% 3.58/3.82 370 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(370,b,341,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(370,b,342,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(370,b,343,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(370,b,344,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(370,b,345,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(370,b,346,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(370,b,347,b)].
% 3.58/3.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(370,b,348,b)].
% 3.58/3.82 371 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(371,b,341,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(371,b,342,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(371,b,343,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(371,b,344,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(371,b,345,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(371,b,346,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(371,b,347,b)].
% 3.58/3.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(371,b,348,b)].
% 3.58/3.82 372 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(247,b,234,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(372,b,341,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(372,b,342,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(372,b,343,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(372,b,344,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(372,b,345,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(372,b,346,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(372,b,347,b)].
% 3.58/3.82 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(372,b,348,b)].
% 3.58/3.82 373 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(248,b,234,b)].
% 3.58/3.82 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(373,b,341,b)].
% 3.58/3.82 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(373,b,342,b)].
% 3.58/3.82 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(373,b,343,b)].
% 3.58/3.82 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(373,b,344,b)].
% 3.58/3.82 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(373,b,345,b)].
% 3.58/3.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(373,b,346,b)].
% 3.58/3.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(373,b,347,b)].
% 3.58/3.83 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(373,b,348,b)].
% 3.58/3.83 374 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(312,b,288,a)].
% 3.58/3.83 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(374,a,332,a)].
% 3.58/3.83 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(374,a,337,a)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(374,a,338,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(374,a,339,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(374,a,340,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(374,a,341,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(374,a,342,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(374,a,343,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(374,a,344,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(374,a,345,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(374,a,346,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(374,a,347,b)].
% 3.58/3.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(374,a,348,b)].
% 3.58/3.83 375 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(312,b,290,a)].
% 3.58/3.83 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(375,a,332,a)].
% 3.58/3.83 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(375,a,337,a)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(375,a,338,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(375,a,339,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(375,a,340,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(375,a,341,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(375,a,342,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(375,a,343,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(375,a,344,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(375,a,345,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(375,a,346,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(375,a,347,b)].
% 3.58/3.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(375,a,348,b)].
% 3.58/3.83 376 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(322,a,312,b)].
% 3.58/3.83 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(376,c,332,a)].
% 3.58/3.83 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(376,c,337,a)].
% 3.58/3.83 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(376,c,338,b)].
% 3.58/3.83 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(376,c,339,b)].
% 3.58/3.83 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(376,c,340,b)].
% 3.58/3.83 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(376,c,341,b)].
% 3.58/3.83 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(376,c,342,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(376,c,343,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(376,c,344,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(376,c,345,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(376,c,346,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(376,c,347,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(376,c,348,b)].
% 3.58/3.84 377 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(323,a,312,b)].
% 3.58/3.84 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(377,c,332,a)].
% 3.58/3.84 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(377,c,337,a)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(377,c,338,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(377,c,339,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(377,c,340,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(377,c,341,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(377,c,342,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(377,c,343,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(377,c,344,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(377,c,345,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(377,c,346,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(377,c,347,b)].
% 3.58/3.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(377,c,348,b)].
% 3.58/3.84 378 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(324,a,312,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(378,b,332,a)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(378,b,337,a)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(378,b,338,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(378,b,339,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(378,b,340,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(378,b,341,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(378,b,342,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(378,b,343,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(378,b,344,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(378,b,345,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(378,b,346,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(378,b,347,b)].
% 3.58/3.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(378,b,348,b)].
% 3.82/4.03 379 -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].
% 3.82/4.03 380 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].
% 3.82/4.03 381 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 3.82/4.03 382 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 3.82/4.03 383 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 3.82/4.03 384 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 3.82/4.03 385 -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].
% 3.82/4.03 386 -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].
% 3.82/4.03 387 -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].
% 3.82/4.03 388 -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].
% 3.82/4.03 389 -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].
% 3.82/4.03 390 -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].
% 3.82/4.03 391 -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].
% 3.82/4.03 392 -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].
% 3.82/4.03 393 -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].
% 3.82/4.03 394 -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].
% 3.82/4.03 395 -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].
% 3.82/4.03 396 -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].
% 3.82/4.03 397 -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].
% 3.82/4.03 398 -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].
% 3.82/4.03 399 -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].
% 3.82/4.03 400 -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)].
% 3.82/4.03 401 -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)].
% 3.82/4.03 402 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 3.82/4.03 403 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 3.87/4.08 404 -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)].
% 3.87/4.08 405 -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)].
% 3.87/4.08 406 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(162,a,142,b)].
% 3.87/4.08 407 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(165,a,142,b)].
% 3.87/4.08 408 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(166,a,142,b)].
% 3.87/4.08 409 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(171,a,142,b)].
% 3.87/4.08 410 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(172,a,142,b)].
% 3.87/4.08 411 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(201,b,186,b)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(411,b,380,a)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(411,b,381,a)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(411,b,382,a)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(411,b,383,b)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(411,b,384,b)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(411,b,385,b)].
% 3.87/4.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(411,b,386,b)].
% 3.87/4.08 412 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(202,b,186,b)].
% 3.87/4.08 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(412,b,380,a)].
% 3.87/4.08 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(412,b,381,a)].
% 3.87/4.08 Derived: class_HOL_Oplus(tc_nat). [resolve(412,b,382,a)].
% 3.87/4.08 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(412,b,383,b)].
% 3.87/4.08 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(412,b,384,b)].
% 3.87/4.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(412,b,385,b)].
% 3.87/4.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(412,b,386,b)].
% 3.87/4.08 413 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 3.87/4.08 414 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 3.87/4.08 415 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(247,b,216,b)].
% 3.87/4.08 416 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(248,b,216,b)].
% 3.87/4.08 417 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,288,a)].
% 3.87/4.08 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(417,a,382,a)].
% 3.87/4.08 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(417,a,384,b)].
% 3.87/4.08 418 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,290,a)].
% 3.87/4.08 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(418,a,382,a)].
% 3.87/4.08 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(418,a,384,b)].
% 3.87/4.08 419 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(322,a,297,b)].
% 3.87/4.08 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(419,c,382,a)].
% 3.87/4.08 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(419,c,384,b)].
% 4.06/4.26 420 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(323,a,297,b)].
% 4.06/4.26 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(420,c,382,a)].
% 4.06/4.26 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(420,c,384,b)].
% 4.06/4.26 421 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom). [assumption].
% 4.06/4.26 422 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].
% 4.06/4.26 423 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 4.06/4.26 424 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 4.06/4.26 425 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 4.06/4.26 426 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 4.06/4.26 427 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom). [assumption].
% 4.06/4.26 428 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 4.06/4.26 429 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 4.06/4.26 430 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 4.06/4.26 431 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 4.06/4.26 432 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 4.06/4.26 433 -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].
% 4.06/4.26 434 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 4.06/4.26 435 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 4.06/4.26 436 -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].
% 4.06/4.26 437 -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].
% 4.06/4.26 438 -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].
% 4.06/4.26 439 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(20,b,1,a)].
% 4.06/4.26 440 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(20,b,3,a)].
% 4.06/4.26 441 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 4.06/4.26 442 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 4.06/4.26 443 -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)].
% 4.06/4.26 444 -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)].
% 4.06/4.26 445 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(162,a,138,b)].
% 4.06/4.29 446 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(165,a,138,b)].
% 4.06/4.29 447 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(166,a,138,b)].
% 4.06/4.29 448 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(171,a,138,b)].
% 4.06/4.29 449 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(172,a,138,b)].
% 4.06/4.29 450 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,b,179,b)].
% 4.06/4.29 451 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,b,179,b)].
% 4.06/4.29 452 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 4.06/4.29 453 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 4.06/4.29 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(453,b,422,a)].
% 4.06/4.29 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(453,b,423,a)].
% 4.06/4.29 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 4.06/4.29 454 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 4.06/4.29 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(454,b,422,a)].
% 4.06/4.29 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(454,b,423,a)].
% 4.06/4.29 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(454,b,424,b)].
% 4.06/4.29 455 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(205,b,179,b)].
% 4.06/4.29 456 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(206,b,179,b)].
% 4.06/4.29 457 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 4.06/4.29 458 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 4.06/4.29 459 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,b,255,b)].
% 4.06/4.29 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(459,b,422,a)].
% 4.06/4.29 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(459,b,423,a)].
% 4.06/4.29 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(459,b,424,b)].
% 4.06/4.29 460 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,b,255,b)].
% 4.06/4.29 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(460,b,422,a)].
% 4.06/4.29 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(460,b,423,a)].
% 4.06/4.29 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(460,b,424,b)].
% 4.06/4.29 461 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(286,b,255,b)].
% 4.06/4.29 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(461,b,422,a)].
% 4.06/4.29 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(461,b,423,a)].
% 4.06/4.29 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(461,b,424,b)].
% 4.06/4.29 462 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(287,b,255,b)].
% 4.06/4.29 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(462,b,422,a)].
% 4.06/4.29 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(462,b,423,a)].
% 4.06/4.29 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(462,b,424,b)].
% 4.06/4.30 463 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,288,a)].
% 4.06/4.30 464 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,290,a)].
% 4.06/4.30 465 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(322,a,295,b)].
% 4.06/4.30 466 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(323,a,295,b)].
% 4.06/4.30 467 -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(339,b,331,b)].
% 4.06/4.30 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(467,a,422,a)].
% 4.06/4.30 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(467,a,423,a)].
% 4.06/4.30 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(467,a,424,b)].
% 4.06/4.30 468 -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(339,b,333,b)].
% 4.06/4.30 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(468,a,422,a)].
% 4.06/4.30 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(468,a,423,a)].
% 4.06/4.30 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(468,a,424,b)].
% 4.06/4.30 469 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(339,b,334,a)].
% 4.06/4.30 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(469,a,422,a)].
% 4.06/4.30 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(469,a,423,a)].
% 4.06/4.30 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(469,a,424,b)].
% 4.06/4.30 470 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,335,a)].
% 4.06/4.30 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(470,a,422,a)].
% 4.06/4.30 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(470,a,423,a)].
% 4.06/4.30 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(470,a,424,b)].
% 4.06/4.30 471 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,336,a)].
% 4.06/4.32 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(471,a,422,a)].
% 4.06/4.32 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(471,a,423,a)].
% 4.06/4.32 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(471,a,424,b)].
% 4.06/4.32 472 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(354,a,339,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(472,b,422,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(472,b,423,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(472,b,424,b)].
% 4.06/4.32 473 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(355,a,339,b)].
% 4.06/4.32 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(473,b,422,a)].
% 4.06/4.32 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(473,b,423,a)].
% 4.06/4.32 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(473,b,424,b)].
% 4.06/4.32 474 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(374,a,339,b)].
% 4.06/4.32 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(474,b,422,a)].
% 4.06/4.32 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(474,b,423,a)].
% 4.06/4.32 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(474,b,424,b)].
% 4.06/4.32 475 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(375,a,339,b)].
% 4.06/4.32 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(475,b,422,a)].
% 4.06/4.32 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(475,b,423,a)].
% 4.06/4.32 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(475,b,424,b)].
% 4.06/4.32 476 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(376,c,339,b)].
% 4.06/4.32 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(476,c,422,a)].
% 4.06/4.32 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(476,c,423,a)].
% 4.06/4.32 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(476,c,424,b)].
% 4.06/4.32 477 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(377,c,339,b)].
% 4.06/4.32 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(477,c,422,a)].
% 4.06/4.32 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(477,c,423,a)].
% 4.06/4.32 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(477,c,424,b)].
% 4.06/4.32 478 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(378,b,339,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(478,b,422,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(478,b,423,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(478,b,424,b)].
% 4.06/4.32 479 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(411,b,385,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(479,b,422,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(479,b,423,a)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(479,b,424,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(479,b,434,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(479,b,435,b)].
% 4.06/4.32 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(479,b,436,b)].
% 4.25/4.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(479,b,437,b)].
% 4.25/4.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(479,b,438,b)].
% 4.25/4.46 480 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(412,b,385,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(480,b,422,a)].
% 4.25/4.46 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(480,b,423,a)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,424,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(480,b,434,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(480,b,435,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(480,b,436,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(480,b,437,b)].
% 4.25/4.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(480,b,438,b)].
% 4.25/4.46 481 -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].
% 4.25/4.46 482 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].
% 4.25/4.46 Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(481,a,482,a)].
% 4.25/4.46 483 -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].
% 4.25/4.46 Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(483,a,482,a)].
% 4.25/4.46 484 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 4.25/4.46 Derived: c_0 != c_1. [resolve(484,a,481,a)].
% 4.25/4.46 Derived: c_1 != c_0. [resolve(484,a,483,a)].
% 4.25/4.46 485 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 4.25/4.46 486 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 4.25/4.46 487 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 4.25/4.46 488 -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].
% 4.25/4.46 489 -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].
% 4.25/4.46 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(489,a,482,a)].
% 4.25/4.46 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(489,a,487,b)].
% 4.25/4.46 490 -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].
% 4.25/4.46 491 -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].
% 4.25/4.46 492 -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].
% 4.25/4.46 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(492,b,489,a)].
% 4.25/4.46 493 -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].
% 4.25/4.46 494 -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].
% 4.25/4.46 495 -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].
% 4.25/4.46 496 -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].
% 4.47/4.70 497 -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].
% 4.47/4.70 498 -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].
% 4.47/4.70 499 -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].
% 4.47/4.70 500 -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].
% 4.47/4.70 501 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 4.47/4.70 502 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].
% 4.47/4.70 503 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 4.47/4.70 504 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 4.47/4.70 505 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 4.47/4.70 506 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 4.47/4.70 507 -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].
% 4.47/4.70 508 -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].
% 4.47/4.70 509 -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].
% 4.47/4.70 510 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 4.47/4.70 511 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 4.47/4.70 512 -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].
% 4.47/4.70 513 -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].
% 4.47/4.70 514 -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].
% 4.47/4.70 515 -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].
% 4.47/4.70 516 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom). [assumption].
% 4.47/4.70 517 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(517,a,507,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(517,a,508,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(517,a,510,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(517,a,511,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(517,a,512,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(517,a,513,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(517,a,514,b)].
% 4.47/4.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(517,a,515,b)].
% 4.47/4.73 518 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 4.47/4.73 519 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 4.47/4.73 520 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 4.47/4.73 521 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 4.47/4.73 522 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 4.47/4.73 523 -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].
% 4.47/4.73 524 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(129,b,108,a)].
% 4.47/4.73 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(524,a,502,a)].
% 4.47/4.73 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(524,a,503,a)].
% 4.47/4.73 Derived: c_times(c_1,A,tc_nat) = A. [resolve(524,a,504,a)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(524,a,505,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(524,a,506,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(524,a,507,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(524,a,508,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(524,a,509,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(524,a,510,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(524,a,511,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(524,a,512,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(524,a,513,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(524,a,514,b)].
% 4.47/4.73 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(524,a,515,b)].
% 4.47/4.73 525 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(129,b,111,a)].
% 4.47/4.73 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(525,a,502,a)].
% 4.47/4.73 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(525,a,503,a)].
% 4.47/4.73 Derived: c_times(A,c_1,tc_nat) = A. [resolve(525,a,504,a)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(525,a,505,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(525,a,506,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(525,a,507,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(525,a,508,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(525,a,509,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(525,a,510,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(525,a,511,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(525,a,512,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(525,a,513,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(525,a,514,b)].
% 4.47/4.73 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(525,a,515,b)].
% 4.47/4.73 526 -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)].
% 4.65/4.91 527 -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)].
% 4.65/4.91 528 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(169,b,164,a)].
% 4.65/4.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,a,508,b)].
% 4.65/4.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(528,a,523,b)].
% 4.65/4.91 529 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1(D). [resolve(171,a,169,b)].
% 4.65/4.91 530 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1(C). [resolve(172,a,169,b)].
% 4.65/4.91 531 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 4.65/4.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(531,a,508,b)].
% 4.65/4.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(531,a,509,b)].
% 4.65/4.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(531,a,514,b)].
% 4.65/4.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(531,a,515,b)].
% 4.65/4.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(531,a,523,b)].
% 4.65/4.91 532 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 4.65/4.91 533 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].
% 4.65/4.91 534 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 4.65/4.91 535 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 4.65/4.91 536 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 4.65/4.91 537 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 4.65/4.91 538 -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].
% 4.65/4.91 539 -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].
% 4.65/4.91 540 -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].
% 4.65/4.91 541 -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].
% 4.65/4.91 542 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_13) # label(axiom). [assumption].
% 4.65/4.91 543 -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].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(543,a,533,a)].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(543,a,534,a)].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(543,a,535,a)].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(543,a,536,b)].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(543,a,537,b)].
% 4.65/4.91 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(543,a,538,b)].
% 4.65/4.91 544 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 4.79/5.03 545 -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].
% 4.79/5.03 546 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 4.79/5.03 547 -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].
% 4.79/5.03 548 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 4.79/5.03 549 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 4.79/5.03 550 -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].
% 4.79/5.03 551 -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].
% 4.79/5.03 552 -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].
% 4.79/5.03 553 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(121,b,108,a)].
% 4.79/5.03 554 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(121,b,111,a)].
% 4.79/5.03 555 -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)].
% 4.79/5.03 556 -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)].
% 4.79/5.03 557 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(162,a,143,b)].
% 4.79/5.03 558 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(163,a,143,b)].
% 4.79/5.03 559 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,143,b)].
% 4.79/5.03 560 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,143,b)].
% 4.79/5.03 561 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,143,b)].
% 4.79/5.03 562 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(171,a,143,b)].
% 4.79/5.03 563 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(172,a,143,b)].
% 4.79/5.03 564 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 4.79/5.03 565 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 4.79/5.03 566 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(247,b,217,b)].
% 4.79/5.03 567 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(248,b,217,b)].
% 4.79/5.03 568 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(517,a,508,b)].
% 4.79/5.03 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(568,b,533,a)].
% 4.79/5.03 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(568,b,534,a)].
% 4.79/5.03 Derived: class_HOL_Oone(tc_nat). [resolve(568,b,535,a)].
% 4.79/5.03 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(568,b,536,b)].
% 4.79/5.03 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(568,b,537,b)].
% 4.79/5.03 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(568,b,538,b)].
% 4.79/5.03 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(568,b,547,b)].
% 4.93/5.16 569 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(524,a,508,b)].
% 4.93/5.16 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(569,b,533,a)].
% 4.93/5.16 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(569,b,534,a)].
% 4.93/5.16 Derived: c_times(c_1,A,tc_nat) = A. [resolve(569,b,535,a)].
% 4.93/5.16 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(569,b,536,b)].
% 4.93/5.16 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(569,b,537,b)].
% 4.93/5.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(569,b,538,b)].
% 4.93/5.16 570 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(525,a,508,b)].
% 4.93/5.16 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(570,b,533,a)].
% 4.93/5.16 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(570,b,534,a)].
% 4.93/5.16 Derived: c_times(A,c_1,tc_nat) = A. [resolve(570,b,535,a)].
% 4.93/5.16 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(570,b,536,b)].
% 4.93/5.16 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(570,b,537,b)].
% 4.93/5.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(570,b,538,b)].
% 4.93/5.16 571 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,a,508,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(571,b,533,a)].
% 4.93/5.16 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(571,b,534,a)].
% 4.93/5.16 Derived: class_HOL_Oplus(tc_nat). [resolve(571,b,535,a)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(571,b,536,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(571,b,537,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(571,b,538,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(571,b,547,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(571,b,548,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(571,b,549,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(571,b,550,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(571,b,551,b)].
% 4.93/5.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(571,b,552,b)].
% 4.93/5.16 572 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(531,a,508,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(572,b,533,a)].
% 4.93/5.16 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(572,b,534,a)].
% 4.93/5.16 Derived: class_HOL_Ozero(tc_nat). [resolve(572,b,535,a)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(572,b,536,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(572,b,537,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(572,b,538,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(572,b,548,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(572,b,549,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(572,b,550,b)].
% 4.93/5.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(572,b,551,b)].
% 4.93/5.16 573 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 4.93/5.16 574 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].
% 4.93/5.16 575 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 4.93/5.16 576 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 4.93/5.16 577 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 4.93/5.20 578 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 4.93/5.20 579 -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].
% 4.93/5.20 580 -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].
% 4.93/5.20 581 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 4.93/5.20 582 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 4.93/5.20 583 -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].
% 4.93/5.20 584 -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].
% 4.93/5.20 585 -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].
% 4.93/5.20 586 -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].
% 4.93/5.20 587 -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].
% 4.93/5.20 588 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 4.93/5.20 589 -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].
% 4.93/5.20 590 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 4.93/5.20 591 -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].
% 4.93/5.20 592 -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].
% 4.93/5.20 593 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_8) # label(axiom). [assumption].
% 4.93/5.20 594 -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)].
% 4.93/5.20 595 -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)].
% 4.93/5.20 596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 4.93/5.20 597 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 4.93/5.20 598 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(130,b,108,a)].
% 4.93/5.20 599 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(130,b,111,a)].
% 4.93/5.20 600 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(130,b,116,a)].
% 4.93/5.20 601 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(130,b,117,a)].
% 4.93/5.20 602 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(130,b,118,a)].
% 4.93/5.20 603 -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)].
% 4.93/5.20 604 -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)].
% 5.20/5.40 605 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1__cancel(D). [resolve(171,a,170,b)].
% 5.20/5.40 606 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(172,a,170,b)].
% 5.20/5.40 607 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(321,b,288,a)].
% 5.20/5.40 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(607,a,580,b)].
% 5.20/5.40 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(607,a,585,b)].
% 5.20/5.40 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(607,a,586,b)].
% 5.20/5.40 608 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(321,b,290,a)].
% 5.20/5.40 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(608,a,580,b)].
% 5.20/5.40 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(608,a,585,b)].
% 5.20/5.40 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(608,a,586,b)].
% 5.20/5.40 609 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(324,a,321,b)].
% 5.20/5.40 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(609,b,576,a)].
% 5.20/5.40 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(609,b,578,b)].
% 5.20/5.40 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(609,b,580,b)].
% 5.20/5.40 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(609,b,585,b)].
% 5.20/5.40 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(609,b,586,b)].
% 5.20/5.40 610 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(528,a,523,b)].
% 5.20/5.40 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(610,b,586,b)].
% 5.20/5.40 611 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(531,a,523,b)].
% 5.20/5.40 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(611,b,580,b)].
% 5.20/5.40 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(611,b,585,b)].
% 5.20/5.40 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(611,b,586,b)].
% 5.20/5.40 612 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 5.20/5.40 613 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].
% 5.20/5.40 614 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 5.20/5.40 615 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 5.20/5.40 616 -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].
% 5.20/5.40 617 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 5.20/5.40 618 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 5.20/5.40 619 -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].
% 5.20/5.40 620 -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].
% 5.20/5.40 621 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 5.24/5.47 622 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 5.24/5.47 623 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 5.24/5.47 624 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom). [assumption].
% 5.24/5.47 625 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 5.24/5.47 626 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 5.24/5.47 627 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom). [assumption].
% 5.24/5.47 628 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 5.24/5.47 629 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 5.24/5.47 630 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(38,b,1,a)].
% 5.24/5.47 631 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(38,b,3,a)].
% 5.24/5.47 632 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 5.24/5.47 633 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 5.24/5.47 634 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 5.24/5.47 635 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(128,b,108,a)].
% 5.24/5.47 636 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(128,b,111,a)].
% 5.24/5.47 637 -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)].
% 5.24/5.47 638 -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)].
% 5.24/5.47 639 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(165,a,161,b)].
% 5.24/5.47 640 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(166,a,161,b)].
% 5.24/5.47 641 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(171,a,161,b)].
% 5.24/5.47 642 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(172,a,161,b)].
% 5.24/5.47 643 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 5.24/5.47 644 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 5.24/5.47 645 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(247,b,235,b)].
% 5.24/5.47 646 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(248,b,235,b)].
% 5.24/5.47 647 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(313,b,288,a)].
% 5.24/5.47 648 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(313,b,290,a)].
% 5.24/5.47 649 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(322,a,313,b)].
% 5.24/5.47 650 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(323,a,313,b)].
% 5.24/5.47 651 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,313,b)].
% 5.24/5.47 652 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(325,a,313,b)].
% 5.24/5.47 653 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(326,a,313,b)].
% 5.24/5.47 654 -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(358,b,331,b)].
% 5.24/5.47 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(654,a,616,b)].
% 5.24/5.47 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(654,a,617,b)].
% 5.24/5.47 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(654,a,618,b)].
% 5.24/5.47 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(654,a,619,b)].
% 5.24/5.47 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(654,a,620,b)].
% 5.24/5.47 655 -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(358,b,333,b)].
% 5.24/5.47 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(655,a,616,b)].
% 5.24/5.47 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(655,a,617,b)].
% 5.24/5.47 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(655,a,618,b)].
% 5.24/5.47 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(655,a,619,b)].
% 5.24/5.47 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(655,a,620,b)].
% 5.24/5.47 656 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(358,b,334,a)].
% 5.24/5.47 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(656,a,616,b)].
% 5.24/5.47 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(656,a,617,b)].
% 5.24/5.47 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(656,a,618,b)].
% 5.24/5.47 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(656,a,619,b)].
% 5.24/5.47 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(656,a,620,b)].
% 5.24/5.47 657 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,335,a)].
% 5.24/5.47 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(657,a,616,b)].
% 5.24/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(657,a,617,b)].
% 5.24/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(657,a,618,b)].
% 5.24/5.50 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(657,a,619,b)].
% 5.24/5.50 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(657,a,620,b)].
% 5.24/5.50 658 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,336,a)].
% 5.24/5.50 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(658,a,616,b)].
% 5.24/5.50 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(658,a,617,b)].
% 5.24/5.50 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(658,a,618,b)].
% 5.24/5.50 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(658,a,619,b)].
% 5.24/5.50 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(658,a,620,b)].
% 5.24/5.50 659 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(517,a,515,b)].
% 5.24/5.50 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(659,b,617,b)].
% 5.24/5.50 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(659,b,618,b)].
% 5.24/5.50 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(659,b,619,b)].
% 5.24/5.50 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(659,b,620,b)].
% 5.24/5.50 660 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(524,a,515,b)].
% 5.24/5.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(660,b,617,b)].
% 5.24/5.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(660,b,618,b)].
% 5.24/5.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(660,b,619,b)].
% 5.24/5.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(660,b,620,b)].
% 5.24/5.50 661 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(525,a,515,b)].
% 5.24/5.50 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(661,b,617,b)].
% 5.24/5.50 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(661,b,618,b)].
% 5.24/5.50 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(661,b,619,b)].
% 5.24/5.50 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(661,b,620,b)].
% 5.24/5.50 662 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(531,a,515,b)].
% 5.24/5.50 663 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(607,a,586,b)].
% 5.24/5.50 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(663,b,613,a)].
% 5.24/5.50 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(663,b,614,a)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(663,b,615,b)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(663,b,616,b)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(663,b,617,b)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(663,b,618,b)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(663,b,619,b)].
% 5.24/5.50 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(663,b,620,b)].
% 5.24/5.50 664 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(608,a,586,b)].
% 5.24/5.50 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(664,b,613,a)].
% 5.24/5.50 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(664,b,614,a)].
% 5.24/5.50 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(664,b,615,b)].
% 5.24/5.50 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(664,b,616,b)].
% 5.24/5.50 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(664,b,617,b)].
% 5.24/5.50 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(664,b,618,b)].
% 5.33/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(664,b,619,b)].
% 5.33/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(664,b,620,b)].
% 5.33/5.56 665 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(609,b,586,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(665,b,613,a)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(665,b,614,a)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(665,b,615,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(665,b,616,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(665,b,617,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(665,b,618,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(665,b,619,b)].
% 5.33/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(665,b,620,b)].
% 5.33/5.56 666 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(610,b,586,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(666,b,613,a)].
% 5.33/5.56 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(666,b,614,a)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(666,b,615,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(666,b,616,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(666,b,617,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(666,b,618,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(666,b,619,b)].
% 5.33/5.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(666,b,620,b)].
% 5.33/5.56 667 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(611,b,586,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(667,b,613,a)].
% 5.33/5.56 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(667,b,614,a)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(667,b,615,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(667,b,616,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(667,b,617,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(667,b,618,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(667,b,619,b)].
% 5.33/5.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(667,b,620,b)].
% 5.33/5.56 668 -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].
% 5.33/5.56 669 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].
% 5.33/5.56 Derived: c_in(c_0,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(668,a,669,a)].
% 5.33/5.56 670 -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].
% 5.33/5.56 Derived: c_in(c_1,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(670,a,669,a)].
% 5.33/5.56 671 -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].
% 5.33/5.56 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(671,a,669,a)].
% 5.33/5.56 672 -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].
% 5.41/5.61 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(672,a,669,a)].
% 5.41/5.61 673 -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].
% 5.41/5.61 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(673,a,669,a)].
% 5.41/5.61 674 -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].
% 5.41/5.61 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(674,a,669,a)].
% 5.41/5.61 675 -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].
% 5.41/5.61 Derived: c_NatArith_Oof__nat(c_1,tc_fun(A,B)) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(675,a,669,a)].
% 5.41/5.61 676 -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].
% 5.41/5.61 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(676,a,669,a)].
% 5.41/5.61 677 -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].
% 5.41/5.61 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(677,a,669,a)].
% 5.41/5.61 678 -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].
% 5.41/5.61 Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(678,a,669,a)].
% 5.41/5.61 679 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 5.41/5.61 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,668,a)].
% 5.41/5.61 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,670,a)].
% 5.41/5.61 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(679,a,671,a)].
% 5.41/5.61 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(679,a,672,a)].
% 5.41/5.61 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,673,a)].
% 5.41/5.61 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(679,a,674,a)].
% 5.41/5.61 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(679,a,675,a)].
% 5.41/5.61 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(679,a,676,a)].
% 5.41/5.61 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(679,a,677,a)].
% 5.41/5.61 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(679,a,678,a)].
% 5.41/5.61 680 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 5.41/5.63 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(680,a,668,a)].
% 5.41/5.63 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(680,a,670,a)].
% 5.41/5.63 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(680,a,671,a)].
% 5.41/5.63 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(680,a,672,a)].
% 5.41/5.63 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(680,a,673,a)].
% 5.41/5.63 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(680,a,674,a)].
% 5.41/5.63 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(680,a,675,a)].
% 5.41/5.63 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(680,a,676,a)].
% 5.41/5.63 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(680,a,677,a)].
% 5.41/5.63 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(680,a,678,a)].
% 5.41/5.63 681 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 5.41/5.63 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(681,b,668,a)].
% 5.41/5.63 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(681,b,670,a)].
% 5.41/5.63 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(681,b,671,a)].
% 5.41/5.63 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(681,b,672,a)].
% 5.41/5.63 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(681,b,673,a)].
% 5.41/5.63 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(681,b,674,a)].
% 5.41/5.63 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(681,b,675,a)].
% 5.41/5.63 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(681,b,676,a)].
% 5.41/5.63 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(681,b,677,a)].
% 5.41/5.63 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(681,b,678,a)].
% 5.41/5.63 682 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 5.41/5.63 Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(682,b,668,a)].
% 5.41/5.63 Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(682,b,670,a)].
% 5.41/5.63 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(682,b,671,a)].
% 5.41/5.63 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(682,b,672,a)].
% 5.41/5.63 Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(682,b,673,a)].
% 5.41/5.63 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(682,b,674,a)].
% 5.41/5.63 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(682,b,675,a)].
% 5.41/5.63 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(682,b,676,a)].
% 5.41/5.63 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(682,b,677,a)].
% 5.41/5.63 Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A). [resolve(682,b,678,a)].
% 5.41/5.63 683 -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].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(683,b,668,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(683,b,670,a)].
% 5.41/5.64 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(683,b,671,a)].
% 5.41/5.64 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(683,b,672,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(683,b,673,a)].
% 5.41/5.64 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(683,b,674,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(683,b,675,a)].
% 5.41/5.64 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(683,b,676,a)].
% 5.41/5.64 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(683,b,677,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A). [resolve(683,b,678,a)].
% 5.41/5.64 684 -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].
% 5.41/5.64 685 -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].
% 5.41/5.64 686 -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].
% 5.41/5.64 687 -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].
% 5.41/5.64 688 -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].
% 5.41/5.64 689 -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].
% 5.41/5.64 690 -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].
% 5.41/5.64 691 -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].
% 5.41/5.64 692 -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].
% 5.41/5.64 693 -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].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(693,b,668,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(693,b,670,a)].
% 5.41/5.64 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(693,b,671,a)].
% 5.41/5.64 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(693,b,672,a)].
% 5.41/5.64 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(693,b,673,a)].
% 5.41/5.64 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(693,b,674,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(693,b,675,a)].
% 5.41/5.65 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(693,b,676,a)].
% 5.41/5.65 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(693,b,677,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A). [resolve(693,b,678,a)].
% 5.41/5.65 694 -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].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(694,b,668,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(694,b,670,a)].
% 5.41/5.65 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(694,b,671,a)].
% 5.41/5.65 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(694,b,672,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(694,b,673,a)].
% 5.41/5.65 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(694,b,674,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(694,b,675,a)].
% 5.41/5.65 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(694,b,676,a)].
% 5.41/5.65 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(694,b,677,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(694,b,678,a)].
% 5.41/5.65 695 -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].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(695,b,668,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(695,b,670,a)].
% 5.41/5.65 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(695,b,671,a)].
% 5.41/5.65 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(695,b,672,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(695,b,673,a)].
% 5.41/5.65 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(695,b,674,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(695,b,675,a)].
% 5.41/5.65 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(695,b,676,a)].
% 5.41/5.65 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(695,b,677,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A). [resolve(695,b,678,a)].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(695,b,691,a)].
% 5.41/5.65 696 -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].
% 5.41/5.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(696,b,668,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(696,b,670,a)].
% 5.49/5.69 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(696,b,671,a)].
% 5.49/5.69 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(696,b,672,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(696,b,673,a)].
% 5.49/5.69 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(696,b,674,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(696,b,675,a)].
% 5.49/5.69 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(696,b,676,a)].
% 5.49/5.69 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(696,b,677,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(696,b,678,a)].
% 5.49/5.69 697 -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].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(697,b,668,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(697,b,670,a)].
% 5.49/5.69 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(697,b,671,a)].
% 5.49/5.69 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(697,b,672,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(697,b,673,a)].
% 5.49/5.69 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(697,b,674,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(697,b,675,a)].
% 5.49/5.69 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(697,b,676,a)].
% 5.49/5.69 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(697,b,677,a)].
% 5.49/5.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(697,b,678,a)].
% 5.49/5.69 698 -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)].
% 5.49/5.69 699 -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)].
% 5.49/5.69 700 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 5.49/5.69 701 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 5.49/5.69 702 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 5.49/5.69 703 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 5.49/5.69 704 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 5.49/5.69 705 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(122,b,108,a)].
% 5.49/5.69 706 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(122,b,111,a)].
% 5.49/5.69 707 -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)].
% 5.49/5.75 708 -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)].
% 5.49/5.75 709 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(171,a,144,b)].
% 5.49/5.75 710 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(172,a,144,b)].
% 5.49/5.75 711 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(200,b,188,b)].
% 5.49/5.75 712 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(201,b,188,b)].
% 5.49/5.75 713 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 5.49/5.75 714 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 5.49/5.75 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(714,b,680,a)].
% 5.49/5.75 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(714,b,682,b)].
% 5.49/5.75 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(714,b,683,b)].
% 5.49/5.75 715 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 5.49/5.75 Derived: class_HOL_Otimes(tc_nat). [resolve(715,b,680,a)].
% 5.49/5.75 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(715,b,682,b)].
% 5.49/5.75 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(715,b,683,b)].
% 5.49/5.75 716 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 5.49/5.75 717 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 5.49/5.75 718 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(247,b,218,b)].
% 5.49/5.75 719 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(248,b,218,b)].
% 5.49/5.75 720 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,288,a)].
% 5.49/5.75 721 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,290,a)].
% 5.49/5.75 722 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(322,a,298,b)].
% 5.49/5.75 723 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(323,a,298,b)].
% 5.49/5.75 724 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(492,b,489,a)].
% 5.49/5.75 725 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(524,a,509,b)].
% 5.49/5.75 726 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(525,a,509,b)].
% 5.49/5.75 727 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(531,a,509,b)].
% 5.49/5.75 728 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(568,b,547,b)].
% 5.49/5.75 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(728,b,669,a)].
% 5.49/5.75 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(728,b,679,a)].
% 5.49/5.75 Derived: class_HOL_Oone(tc_nat). [resolve(728,b,680,a)].
% 5.49/5.75 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,681,b)].
% 5.49/5.75 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(728,b,682,b)].
% 5.49/5.75 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(728,b,683,b)].
% 5.49/5.75 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(728,b,697,b)].
% 5.49/5.75 729 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(571,b,547,b)].
% 5.64/5.88 Derived: class_HOL_Oplus(tc_nat). [resolve(729,b,680,a)].
% 5.64/5.88 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(729,b,682,b)].
% 5.64/5.88 730 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(607,a,580,b)].
% 5.64/5.88 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(730,b,680,a)].
% 5.64/5.88 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(730,b,682,b)].
% 5.64/5.88 731 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(608,a,580,b)].
% 5.64/5.88 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(731,b,680,a)].
% 5.64/5.88 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(731,b,682,b)].
% 5.64/5.88 732 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(609,b,580,b)].
% 5.64/5.88 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(732,b,680,a)].
% 5.64/5.88 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(732,b,682,b)].
% 5.64/5.88 733 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(611,b,580,b)].
% 5.64/5.88 Derived: class_HOL_Ozero(tc_nat). [resolve(733,b,680,a)].
% 5.64/5.88 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(733,b,682,b)].
% 5.64/5.88 734 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom). [assumption].
% 5.64/5.88 735 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom). [assumption].
% 5.64/5.88 736 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom). [assumption].
% 5.64/5.88 737 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom). [assumption].
% 5.64/5.88 738 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom). [assumption].
% 5.64/5.88 739 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 5.64/5.88 740 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom). [assumption].
% 5.64/5.88 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(734,a,735,a)].
% 5.64/5.88 Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(734,a,736,a)].
% 5.64/5.88 741 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom). [assumption].
% 5.64/5.88 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(741,a,735,a)].
% 5.64/5.88 Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(741,a,736,a)].
% 5.64/5.88 742 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 5.64/5.88 743 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 5.64/5.88 744 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 5.64/5.88 745 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 5.64/5.88 746 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 5.64/5.88 747 -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].
% 5.64/5.88 748 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom). [assumption].
% 5.64/5.91 749 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 5.64/5.91 750 -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].
% 5.64/5.91 751 -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].
% 5.64/5.91 752 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom). [assumption].
% 5.64/5.91 753 -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].
% 5.64/5.91 754 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom). [assumption].
% 5.64/5.91 755 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 5.64/5.91 756 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 5.64/5.91 757 -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].
% 5.64/5.91 758 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_27) # label(axiom). [assumption].
% 5.64/5.91 759 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 5.64/5.91 760 -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].
% 5.64/5.91 761 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 5.64/5.91 762 -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].
% 5.64/5.91 763 -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].
% 5.64/5.91 764 -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].
% 5.64/5.91 765 -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].
% 5.64/5.91 766 -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].
% 5.64/5.91 767 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 5.64/5.91 768 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 5.64/5.91 769 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 5.64/5.91 770 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 5.64/5.91 771 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 5.64/5.91 772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 5.74/5.95 773 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 5.74/5.95 774 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 5.74/5.95 775 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 5.74/5.95 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(775,b,734,a)].
% 5.74/5.95 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(775,b,741,a)].
% 5.74/5.95 776 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 5.74/5.95 777 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 5.74/5.95 778 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 5.74/5.95 779 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(162,a,132,a)].
% 5.74/5.95 780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(162,a,137,b)].
% 5.74/5.95 781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(162,a,139,b)].
% 5.74/5.95 782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(162,a,145,b)].
% 5.74/5.95 783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(162,a,146,b)].
% 5.74/5.95 784 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(162,a,147,b)].
% 5.74/5.95 785 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(162,a,148,b)].
% 5.74/5.95 786 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(162,a,149,b)].
% 5.74/5.95 787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(162,a,150,b)].
% 5.74/5.95 788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(162,a,152,b)].
% 5.74/5.95 789 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(162,a,153,b)].
% 5.74/5.95 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(789,a,734,a)].
% 5.74/5.95 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(789,a,741,a)].
% 5.74/5.95 790 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(162,a,155,b)].
% 5.74/5.95 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(790,a,734,a)].
% 5.74/5.95 791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(162,a,156,b)].
% 5.74/5.95 792 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(162,a,157,b)].
% 5.74/5.95 793 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(162,a,159,b)].
% 5.74/5.95 794 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(200,b,174,a)].
% 5.74/5.95 795 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(200,b,175,a)].
% 5.74/5.95 796 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(200,b,176,a)].
% 5.74/5.95 797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(200,b,177,b)].
% 5.74/5.95 798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(200,b,178,b)].
% 5.74/5.95 799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(200,b,180,b)].
% 5.74/5.95 800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(200,b,195,b)].
% 5.74/5.95 801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,305,b)].
% 5.74/5.95 802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,311,b)].
% 5.74/5.99 803 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(378,b,332,a)].
% 5.74/5.99 804 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(378,b,337,a)].
% 5.74/5.99 805 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(378,b,338,b)].
% 5.74/5.99 806 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(378,b,340,b)].
% 5.74/5.99 807 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(378,b,341,b)].
% 5.74/5.99 808 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(378,b,342,b)].
% 5.74/5.99 809 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(378,b,343,b)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,734,a)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(809,a,741,a)].
% 5.74/5.99 810 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(378,b,344,b)].
% 5.74/5.99 811 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(378,b,345,b)].
% 5.74/5.99 812 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(378,b,346,b)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(812,a,734,a)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(812,a,741,a)].
% 5.74/5.99 813 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(378,b,347,b)].
% 5.74/5.99 814 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(378,b,348,b)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,734,a)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(814,a,741,a)].
% 5.74/5.99 815 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(478,b,422,a)].
% 5.74/5.99 816 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(478,b,423,a)].
% 5.74/5.99 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(478,b,424,b)].
% 5.74/5.99 818 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(609,b,576,a)].
% 5.74/5.99 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(818,a,734,a)].
% 5.74/5.99 819 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(609,b,578,b)].
% 5.74/5.99 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(819,a,734,a)].
% 5.74/5.99 820 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(609,b,585,b)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(820,a,734,a)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(820,a,741,a)].
% 5.74/5.99 821 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(665,b,613,a)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)). [resolve(821,a,734,a)].
% 5.74/5.99 822 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(665,b,614,a)].
% 5.74/5.99 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(822,a,734,a)].
% 5.74/5.99 823 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(665,b,615,b)].
% 5.74/5.99 Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(823,a,734,a)].
% 5.74/5.99 824 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(665,b,616,b)].
% 5.74/5.99 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(824,a,734,a)].
% 5.74/5.99 825 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(665,b,617,b)].
% 5.89/6.10 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(825,a,734,a)].
% 5.89/6.10 826 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(665,b,618,b)].
% 5.89/6.10 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(826,a,734,a)].
% 5.89/6.10 827 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(665,b,619,b)].
% 5.89/6.10 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(827,a,734,a)].
% 5.89/6.10 828 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(665,b,620,b)].
% 5.89/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(828,a,734,a)].
% 5.89/6.10 829 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(732,b,680,a)].
% 5.89/6.10 Derived: class_HOL_Oplus(tc_nat). [resolve(829,a,741,a)].
% 5.89/6.10 830 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(732,b,682,b)].
% 5.89/6.10 Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A). [resolve(830,a,741,a)].
% 5.89/6.10 831 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 5.89/6.10 832 -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].
% 5.89/6.10 833 -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].
% 5.89/6.10 834 -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].
% 5.89/6.10 835 -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].
% 5.89/6.10 836 -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].
% 5.89/6.10 837 -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].
% 5.89/6.10 838 -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].
% 5.89/6.10 839 -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].
% 5.89/6.10 840 -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].
% 5.89/6.10 841 -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].
% 5.89/6.10 842 -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].
% 5.89/6.10 843 -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].
% 5.89/6.10 844 -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].
% 5.89/6.10 845 -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].
% 5.89/6.10 846 -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].
% 5.89/6.10 847 -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].
% 5.89/6.10 848 -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].
% 5.89/6.10 849 -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].
% 5.89/6.10 850 -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].
% 5.89/6.10 851 -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].
% 5.89/6.10 852 -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].
% 5.89/6.10 853 -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].
% 5.89/6.10 854 -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].
% 5.89/6.10 855 -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].
% 5.89/6.10 856 -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].
% 5.89/6.10 857 -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].
% 5.89/6.10 858 -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].
% 5.89/6.10 859 -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].
% 5.89/6.10 860 -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].
% 5.89/6.10 861 -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].
% 5.89/6.10 862 -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].
% 5.89/6.10 863 -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].
% 5.89/6.10 864 -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].
% 5.89/6.10 865 -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].
% 5.89/6.10 866 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 5.89/6.10 867 -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].
% 5.89/6.10 868 -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].
% 5.89/6.10 869 -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].
% 5.89/6.10 870 -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].
% 5.89/6.10 871 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 5.89/6.10 872 -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].
% 5.89/6.10 873 -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].
% 5.89/6.10 874 -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].
% 5.89/6.10 875 -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].
% 5.89/6.10 876 -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].
% 5.89/6.10 877 -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].
% 5.89/6.10 878 -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].
% 5.89/6.10 879 -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].
% 5.89/6.10 880 -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].
% 5.89/6.10 881 -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].
% 5.89/6.10 882 -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].
% 5.89/6.10 883 -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].
% 5.89/6.10 884 -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].
% 5.89/6.10 885 -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].
% 5.89/6.10 886 -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].
% 5.89/6.10 887 -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].
% 5.89/6.10 888 -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].
% 5.89/6.10 889 -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].
% 5.89/6.10 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(831,a,832,a)].
% 5.89/6.10 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(831,a,833,a)].
% 5.89/6.10 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(831,a,834,a)].
% 5.89/6.10 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(831,a,835,a)].
% 5.89/6.10 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(831,a,836,a)].
% 5.89/6.10 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(831,a,837,a)].
% 5.89/6.10 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(831,a,838,a)].
% 5.89/6.10 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(831,a,839,a)].
% 5.89/6.10 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(831,a,840,a)].
% 5.89/6.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,841,a)].
% 5.89/6.10 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(831,a,842,a)].
% 5.89/6.10 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(831,a,843,a)].
% 5.89/6.11 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(831,a,844,a)].
% 5.89/6.11 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(831,a,845,a)].
% 5.89/6.11 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(831,a,846,a)].
% 5.89/6.11 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(831,a,847,a)].
% 5.89/6.11 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(831,a,848,a)].
% 5.89/6.11 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(831,a,849,a)].
% 5.89/6.11 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(831,a,850,a)].
% 5.89/6.11 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,851,a)].
% 5.89/6.11 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(831,a,852,a)].
% 5.89/6.11 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(831,a,853,a)].
% 5.89/6.11 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(831,a,854,a)].
% 5.89/6.11 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(831,a,855,b)].
% 5.89/6.11 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(831,a,856,b)].
% 5.89/6.11 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(831,a,857,a)].
% 5.89/6.11 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(831,a,858,a)].
% 5.89/6.11 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(831,a,859,a)].
% 5.89/6.11 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(831,a,860,a)].
% 5.89/6.11 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(831,a,861,a)].
% 5.89/6.11 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(831,a,862,a)].
% 5.89/6.11 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(831,a,863,a)].
% 5.89/6.11 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(831,a,864,a)].
% 5.89/6.11 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(831,a,865,a)].
% 5.89/6.12 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(831,a,866,a)].
% 5.89/6.12 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(831,a,867,a)].
% 5.89/6.12 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(831,a,868,a)].
% 5.89/6.12 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(831,a,869,a)].
% 5.89/6.12 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(831,a,870,a)].
% 5.89/6.12 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(831,a,871,a)].
% 5.89/6.12 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(831,a,872,a)].
% 5.89/6.12 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(831,a,873,a)].
% 5.89/6.12 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(831,a,874,a)].
% 5.89/6.12 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(831,a,875,a)].
% 5.89/6.12 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(831,a,876,a)].
% 5.89/6.12 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(831,a,877,a)].
% 5.89/6.12 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(831,a,878,a)].
% 5.89/6.12 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(831,a,879,a)].
% 5.89/6.12 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(831,a,880,a)].
% 5.89/6.12 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(831,a,881,a)].
% 5.89/6.12 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(831,a,882,a)].
% 5.89/6.12 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(831,a,883,a)].
% 5.89/6.12 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(831,a,884,a)].
% 5.89/6.12 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(831,a,885,a)].
% 5.89/6.12 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(831,a,886,a)].
% 5.89/6.12 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(831,a,887,a)].
% 5.89/6.12 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(831,a,888,a)].
% 5.89/6.12 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(831,a,889,a)].
% 5.89/6.12 890 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 5.89/6.12 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(890,a,832,a)].
% 5.89/6.12 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(890,a,833,a)].
% 5.89/6.12 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(890,a,834,a)].
% 5.89/6.12 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(890,a,835,a)].
% 5.89/6.12 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(890,a,836,a)].
% 5.89/6.12 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(890,a,837,a)].
% 5.89/6.12 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(890,a,838,a)].
% 5.89/6.12 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(890,a,839,a)].
% 5.89/6.12 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(890,a,840,a)].
% 5.89/6.12 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(890,a,841,a)].
% 5.89/6.12 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(890,a,842,a)].
% 5.89/6.12 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(890,a,843,a)].
% 5.89/6.12 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(890,a,844,a)].
% 5.89/6.12 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(890,a,845,a)].
% 5.89/6.12 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(890,a,846,a)].
% 5.89/6.12 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(890,a,847,a)].
% 5.89/6.12 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(890,a,848,a)].
% 5.89/6.12 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(890,a,849,a)].
% 5.89/6.12 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(890,a,850,a)].
% 5.89/6.12 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(890,a,851,a)].
% 5.89/6.12 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(890,a,852,a)].
% 5.89/6.12 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(890,a,853,a)].
% 5.89/6.12 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(890,a,854,a)].
% 5.89/6.13 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(890,a,855,b)].
% 5.89/6.13 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(890,a,856,b)].
% 5.89/6.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(890,a,857,a)].
% 5.89/6.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(890,a,858,a)].
% 5.89/6.13 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(890,a,859,a)].
% 5.89/6.13 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(890,a,860,a)].
% 5.89/6.13 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(890,a,861,a)].
% 5.89/6.13 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(890,a,862,a)].
% 5.89/6.13 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(890,a,863,a)].
% 5.89/6.13 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(890,a,864,a)].
% 5.89/6.13 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(890,a,865,a)].
% 5.89/6.13 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(890,a,866,a)].
% 5.89/6.13 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(890,a,867,a)].
% 5.89/6.13 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(890,a,868,a)].
% 5.89/6.13 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(890,a,869,a)].
% 5.89/6.13 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(890,a,870,a)].
% 5.89/6.13 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(890,a,871,a)].
% 5.89/6.13 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(890,a,872,a)].
% 5.89/6.13 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(890,a,873,a)].
% 5.89/6.13 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(890,a,874,a)].
% 5.89/6.13 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(890,a,875,a)].
% 5.89/6.13 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(890,a,876,a)].
% 5.89/6.13 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(890,a,877,a)].
% 5.89/6.13 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(890,a,878,a)].
% 5.89/6.13 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(890,a,879,a)].
% 5.89/6.13 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(890,a,880,a)].
% 5.89/6.13 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(890,a,881,a)].
% 5.89/6.13 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(890,a,882,a)].
% 5.89/6.13 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(890,a,883,a)].
% 5.89/6.13 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(890,a,884,a)].
% 5.89/6.13 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(890,a,885,a)].
% 5.89/6.14 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(890,a,886,a)].
% 5.89/6.14 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(890,a,887,a)].
% 5.89/6.14 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(890,a,888,a)].
% 5.89/6.14 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(890,a,889,a)].
% 5.89/6.14 891 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 5.89/6.14 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(891,b,832,a)].
% 5.89/6.14 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(891,b,833,a)].
% 5.89/6.14 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(891,b,834,a)].
% 5.89/6.14 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(891,b,835,a)].
% 5.89/6.14 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(891,b,836,a)].
% 5.89/6.14 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(891,b,837,a)].
% 5.89/6.14 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(891,b,838,a)].
% 5.89/6.14 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(891,b,839,a)].
% 5.89/6.14 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(891,b,840,a)].
% 5.89/6.14 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 5.89/6.14 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(891,b,842,a)].
% 5.89/6.14 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(891,b,843,a)].
% 5.89/6.14 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(891,b,844,a)].
% 5.89/6.14 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(891,b,845,a)].
% 5.89/6.15 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(891,b,846,a)].
% 5.89/6.15 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(891,b,847,a)].
% 5.89/6.15 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(891,b,848,a)].
% 5.89/6.15 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(891,b,849,a)].
% 5.89/6.15 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(891,b,850,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,851,a)].
% 5.89/6.15 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(891,b,852,a)].
% 5.89/6.15 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(891,b,853,a)].
% 5.89/6.15 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(891,b,854,a)].
% 5.89/6.15 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(891,b,855,b)].
% 5.89/6.15 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(891,b,856,b)].
% 5.89/6.15 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(891,b,857,a)].
% 5.89/6.15 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(891,b,858,a)].
% 5.89/6.15 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(891,b,859,a)].
% 5.89/6.15 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(891,b,860,a)].
% 5.89/6.15 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(891,b,861,a)].
% 5.89/6.15 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(891,b,862,a)].
% 5.89/6.15 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(891,b,863,a)].
% 5.89/6.15 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(891,b,864,a)].
% 5.89/6.15 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(891,b,865,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,866,a)].
% 5.89/6.15 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(891,b,867,a)].
% 5.89/6.15 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(891,b,868,a)].
% 5.89/6.15 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(891,b,869,a)].
% 5.89/6.15 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(891,b,870,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,871,a)].
% 5.89/6.15 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(891,b,872,a)].
% 5.89/6.15 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(891,b,873,a)].
% 5.89/6.15 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(891,b,874,a)].
% 5.89/6.15 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(891,b,875,a)].
% 5.89/6.15 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(891,b,876,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,877,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,878,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,879,a)].
% 5.89/6.15 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(891,b,880,a)].
% 5.89/6.15 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(891,b,881,a)].
% 5.89/6.15 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(891,b,882,a)].
% 5.89/6.15 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(891,b,883,a)].
% 5.89/6.15 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(891,b,884,a)].
% 5.89/6.15 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(891,b,885,a)].
% 5.89/6.15 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(891,b,886,a)].
% 5.89/6.15 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,887,a)].
% 5.89/6.15 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(891,b,888,a)].
% 5.89/6.15 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(891,b,889,a)].
% 5.89/6.16 892 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 5.89/6.16 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(892,a,831,a)].
% 5.89/6.16 Derived: class_LOrder_Olorder(tc_nat). [resolve(892,a,890,a)].
% 5.89/6.16 Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(892,a,891,b)].
% 5.89/6.16 893 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 5.89/6.16 Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(893,a,831,a)].
% 5.89/6.16 Derived: class_LOrder_Ojoin__semilorder(tc_nat). [resolve(893,a,890,a)].
% 5.89/6.16 Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(893,a,891,b)].
% 5.89/6.16 894 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 5.89/6.16 Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(894,a,831,a)].
% 5.89/6.16 Derived: class_LOrder_Omeet__semilorder(tc_nat). [resolve(894,a,890,a)].
% 5.89/6.16 Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(894,a,891,b)].
% 5.89/6.16 895 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 5.89/6.16 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(895,a,831,a)].
% 5.89/6.16 Derived: class_Orderings_Oord(tc_nat). [resolve(895,a,890,a)].
% 5.89/6.16 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(895,a,891,b)].
% 5.89/6.16 896 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 5.89/6.16 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(896,a,831,a)].
% 5.89/6.16 Derived: class_Orderings_Oorder(tc_nat). [resolve(896,a,890,a)].
% 5.89/6.16 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(896,a,891,b)].
% 5.89/6.16 897 -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].
% 5.89/6.16 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(897,b,832,a)].
% 5.89/6.16 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(897,b,833,a)].
% 5.89/6.16 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(897,b,834,a)].
% 5.89/6.16 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(897,b,835,a)].
% 5.89/6.16 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(897,b,836,a)].
% 5.89/6.16 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(897,b,837,a)].
% 5.89/6.16 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(897,b,838,a)].
% 5.89/6.16 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(897,b,839,a)].
% 5.89/6.17 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(897,b,840,a)].
% 5.89/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,841,a)].
% 5.89/6.17 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(897,b,842,a)].
% 5.89/6.17 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(897,b,843,a)].
% 5.89/6.17 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(897,b,844,a)].
% 5.89/6.17 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(897,b,845,a)].
% 5.89/6.17 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(897,b,846,a)].
% 5.89/6.17 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(897,b,847,a)].
% 5.89/6.17 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(897,b,848,a)].
% 5.89/6.17 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(897,b,849,a)].
% 5.89/6.17 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(897,b,850,a)].
% 5.89/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,851,a)].
% 5.89/6.17 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(897,b,852,a)].
% 5.89/6.17 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(897,b,853,a)].
% 5.89/6.17 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(897,b,854,a)].
% 5.89/6.17 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(897,b,855,b)].
% 5.89/6.17 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(897,b,856,b)].
% 5.89/6.17 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(897,b,857,a)].
% 5.89/6.17 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(897,b,858,a)].
% 5.99/6.17 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(897,b,859,a)].
% 5.99/6.17 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(897,b,860,a)].
% 5.99/6.17 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(897,b,861,a)].
% 5.99/6.17 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(897,b,862,a)].
% 5.99/6.17 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(897,b,863,a)].
% 5.99/6.17 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(897,b,864,a)].
% 5.99/6.17 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(897,b,865,a)].
% 5.99/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(897,b,866,a)].
% 5.99/6.17 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(897,b,867,a)].
% 5.99/6.17 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(897,b,868,a)].
% 5.99/6.17 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(897,b,869,a)].
% 5.99/6.17 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(897,b,870,a)].
% 5.99/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(897,b,871,a)].
% 5.99/6.17 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(897,b,872,a)].
% 5.99/6.17 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(897,b,873,a)].
% 5.99/6.17 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(897,b,874,a)].
% 5.99/6.17 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(897,b,875,a)].
% 5.99/6.17 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(897,b,876,a)].
% 5.99/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(897,b,877,a)].
% 5.99/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(897,b,878,a)].
% 5.99/6.17 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(897,b,879,a)].
% 5.99/6.17 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(897,b,880,a)].
% 5.99/6.17 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(897,b,881,a)].
% 5.99/6.17 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(897,b,882,a)].
% 5.99/6.18 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(897,b,883,a)].
% 5.99/6.18 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(897,b,884,a)].
% 5.99/6.18 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(897,b,885,a)].
% 5.99/6.18 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(897,b,886,a)].
% 5.99/6.18 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(897,b,887,a)].
% 5.99/6.18 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(897,b,888,a)].
% 5.99/6.18 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(897,b,889,a)].
% 5.99/6.18 898 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 5.99/6.18 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(898,b,832,a)].
% 5.99/6.18 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(898,b,833,a)].
% 5.99/6.18 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(898,b,834,a)].
% 5.99/6.18 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(898,b,835,a)].
% 5.99/6.18 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(898,b,836,a)].
% 5.99/6.18 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(898,b,837,a)].
% 5.99/6.18 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(898,b,838,a)].
% 5.99/6.18 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(898,b,839,a)].
% 5.99/6.18 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(898,b,840,a)].
% 5.99/6.18 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(898,b,841,a)].
% 5.99/6.18 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(898,b,842,a)].
% 5.99/6.18 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(898,b,843,a)].
% 5.99/6.19 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(898,b,844,a)].
% 5.99/6.19 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(898,b,845,a)].
% 5.99/6.19 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(898,b,846,a)].
% 5.99/6.19 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(898,b,847,a)].
% 5.99/6.19 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(898,b,848,a)].
% 5.99/6.19 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(898,b,849,a)].
% 5.99/6.19 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(898,b,850,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(898,b,851,a)].
% 5.99/6.19 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(898,b,852,a)].
% 5.99/6.19 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(898,b,853,a)].
% 5.99/6.19 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(898,b,854,a)].
% 5.99/6.19 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(898,b,855,b)].
% 5.99/6.19 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(898,b,856,b)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(898,b,857,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(898,b,858,a)].
% 5.99/6.19 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(898,b,859,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(898,b,860,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(898,b,861,a)].
% 5.99/6.19 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(898,b,862,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(898,b,863,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(898,b,864,a)].
% 5.99/6.19 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(898,b,865,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B. [resolve(898,b,866,a)].
% 5.99/6.19 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(898,b,867,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(898,b,868,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(898,b,869,a)].
% 5.99/6.19 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(898,b,870,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B. [resolve(898,b,871,a)].
% 5.99/6.19 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(898,b,872,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(898,b,873,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(898,b,874,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(898,b,875,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(898,b,876,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(898,b,877,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(898,b,878,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(898,b,879,a)].
% 5.99/6.19 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(898,b,880,a)].
% 5.99/6.19 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(898,b,881,a)].
% 5.99/6.19 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(898,b,882,a)].
% 5.99/6.19 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(898,b,883,a)].
% 5.99/6.19 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(898,b,884,a)].
% 5.99/6.19 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(898,b,885,a)].
% 5.99/6.19 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(898,b,886,a)].
% 5.99/6.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(898,b,887,a)].
% 5.99/6.19 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(898,b,888,a)].
% 5.99/6.19 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(898,b,889,a)].
% 5.99/6.19 899 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 5.99/6.20 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(899,b,832,a)].
% 5.99/6.20 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(899,b,833,a)].
% 5.99/6.20 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(899,b,834,a)].
% 5.99/6.20 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(899,b,835,a)].
% 5.99/6.20 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(899,b,836,a)].
% 5.99/6.20 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(899,b,837,a)].
% 5.99/6.20 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(899,b,838,a)].
% 5.99/6.20 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(899,b,839,a)].
% 5.99/6.20 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(899,b,840,a)].
% 5.99/6.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(899,b,841,a)].
% 5.99/6.20 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(899,b,842,a)].
% 5.99/6.20 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(899,b,843,a)].
% 5.99/6.20 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(899,b,844,a)].
% 5.99/6.20 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(899,b,845,a)].
% 5.99/6.20 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(899,b,846,a)].
% 5.99/6.20 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(899,b,847,a)].
% 5.99/6.20 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(899,b,848,a)].
% 5.99/6.20 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(899,b,849,a)].
% 5.99/6.20 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(899,b,850,a)].
% 5.99/6.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(899,b,851,a)].
% 5.99/6.20 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(899,b,852,a)].
% 5.99/6.20 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(899,b,853,a)].
% 5.99/6.20 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(899,b,854,a)].
% 5.99/6.20 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(899,b,855,b)].
% 5.99/6.20 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(899,b,856,b)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(899,b,857,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(899,b,858,a)].
% 5.99/6.21 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(899,b,859,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(899,b,860,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(899,b,861,a)].
% 5.99/6.21 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(899,b,862,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(899,b,863,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(899,b,864,a)].
% 5.99/6.21 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(899,b,865,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(899,b,866,a)].
% 5.99/6.21 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(899,b,867,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(899,b,868,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(899,b,869,a)].
% 5.99/6.21 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(899,b,870,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(899,b,871,a)].
% 5.99/6.21 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(899,b,872,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(899,b,873,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(899,b,874,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(899,b,875,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(899,b,876,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(899,b,877,a)].
% 5.99/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(899,b,878,a)].
% 6.03/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(899,b,879,a)].
% 6.03/6.21 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(899,b,880,a)].
% 6.03/6.21 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(899,b,881,a)].
% 6.03/6.21 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(899,b,882,a)].
% 6.03/6.21 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(899,b,883,a)].
% 6.03/6.21 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(899,b,884,a)].
% 6.03/6.21 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(899,b,885,a)].
% 6.03/6.21 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(899,b,886,a)].
% 6.03/6.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(899,b,887,a)].
% 6.03/6.21 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(899,b,888,a)].
% 6.03/6.21 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(899,b,889,a)].
% 6.03/6.21 900 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 6.03/6.21 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(900,b,832,a)].
% 6.03/6.21 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(900,b,833,a)].
% 6.03/6.21 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(900,b,834,a)].
% 6.03/6.21 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(900,b,835,a)].
% 6.03/6.21 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(900,b,836,a)].
% 6.03/6.21 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(900,b,837,a)].
% 6.03/6.21 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(900,b,838,a)].
% 6.03/6.21 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(900,b,839,a)].
% 6.03/6.22 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(900,b,840,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,841,a)].
% 6.03/6.22 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(900,b,842,a)].
% 6.03/6.22 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(900,b,843,a)].
% 6.03/6.22 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(900,b,844,a)].
% 6.03/6.22 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(900,b,845,a)].
% 6.03/6.22 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(900,b,846,a)].
% 6.03/6.22 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(900,b,847,a)].
% 6.03/6.22 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(900,b,848,a)].
% 6.03/6.22 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(900,b,849,a)].
% 6.03/6.22 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(900,b,850,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,851,a)].
% 6.03/6.22 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(900,b,852,a)].
% 6.03/6.22 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(900,b,853,a)].
% 6.03/6.22 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(900,b,854,a)].
% 6.03/6.22 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(900,b,855,b)].
% 6.03/6.22 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(900,b,856,b)].
% 6.03/6.22 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(900,b,857,a)].
% 6.03/6.22 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(900,b,858,a)].
% 6.03/6.22 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(900,b,859,a)].
% 6.03/6.22 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(900,b,860,a)].
% 6.03/6.22 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(900,b,861,a)].
% 6.03/6.22 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(900,b,862,a)].
% 6.03/6.22 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(900,b,863,a)].
% 6.03/6.22 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(900,b,864,a)].
% 6.03/6.22 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(900,b,865,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(900,b,866,a)].
% 6.03/6.22 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(900,b,867,a)].
% 6.03/6.22 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(900,b,868,a)].
% 6.03/6.22 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(900,b,869,a)].
% 6.03/6.22 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(900,b,870,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(900,b,871,a)].
% 6.03/6.22 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(900,b,872,a)].
% 6.03/6.22 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(900,b,873,a)].
% 6.03/6.22 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(900,b,874,a)].
% 6.03/6.22 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(900,b,875,a)].
% 6.03/6.22 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(900,b,876,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(900,b,877,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(900,b,878,a)].
% 6.03/6.22 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(900,b,879,a)].
% 6.03/6.22 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(900,b,880,a)].
% 6.03/6.22 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(900,b,881,a)].
% 6.03/6.22 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(900,b,882,a)].
% 6.03/6.22 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(900,b,883,a)].
% 6.03/6.22 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(900,b,884,a)].
% 6.03/6.23 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(900,b,885,a)].
% 6.03/6.23 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(900,b,886,a)].
% 6.03/6.23 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(900,b,887,a)].
% 6.03/6.23 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(900,b,888,a)].
% 6.03/6.23 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(900,b,889,a)].
% 6.03/6.23 901 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 6.03/6.23 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(901,b,832,a)].
% 6.03/6.23 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(901,b,833,a)].
% 6.03/6.23 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(901,b,834,a)].
% 6.03/6.23 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(901,b,835,a)].
% 6.03/6.23 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(901,b,836,a)].
% 6.03/6.23 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(901,b,837,a)].
% 6.03/6.23 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(901,b,838,a)].
% 6.03/6.23 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(901,b,839,a)].
% 6.03/6.23 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(901,b,840,a)].
% 6.03/6.23 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,841,a)].
% 6.03/6.23 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(901,b,842,a)].
% 6.03/6.23 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(901,b,843,a)].
% 6.03/6.23 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(901,b,844,a)].
% 6.03/6.23 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(901,b,845,a)].
% 6.05/6.24 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(901,b,846,a)].
% 6.05/6.24 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(901,b,847,a)].
% 6.05/6.24 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(901,b,848,a)].
% 6.05/6.24 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(901,b,849,a)].
% 6.05/6.24 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(901,b,850,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,851,a)].
% 6.05/6.24 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(901,b,852,a)].
% 6.05/6.24 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(901,b,853,a)].
% 6.05/6.24 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(901,b,854,a)].
% 6.05/6.24 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(901,b,855,b)].
% 6.05/6.24 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(901,b,856,b)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(901,b,857,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(901,b,858,a)].
% 6.05/6.24 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(901,b,859,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(901,b,860,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(901,b,861,a)].
% 6.05/6.24 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(901,b,862,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(901,b,863,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(901,b,864,a)].
% 6.05/6.24 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(901,b,865,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(901,b,866,a)].
% 6.05/6.24 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(901,b,867,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(901,b,868,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(901,b,869,a)].
% 6.05/6.24 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(901,b,870,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(901,b,871,a)].
% 6.05/6.24 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(901,b,872,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(901,b,873,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(901,b,874,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(901,b,875,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(901,b,876,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(901,b,877,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(901,b,878,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(901,b,879,a)].
% 6.05/6.24 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(901,b,880,a)].
% 6.05/6.24 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(901,b,881,a)].
% 6.05/6.24 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(901,b,882,a)].
% 6.05/6.24 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(901,b,883,a)].
% 6.05/6.24 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(901,b,884,a)].
% 6.05/6.24 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(901,b,885,a)].
% 6.05/6.24 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(901,b,886,a)].
% 6.05/6.24 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(901,b,887,a)].
% 6.05/6.24 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(901,b,888,a)].
% 6.05/6.24 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(901,b,889,a)].
% 6.05/6.24 902 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 6.05/6.24 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(902,b,832,a)].
% 6.05/6.24 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(902,b,833,a)].
% 6.05/6.25 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(902,b,834,a)].
% 6.05/6.25 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(902,b,835,a)].
% 6.05/6.25 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(902,b,836,a)].
% 6.05/6.25 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(902,b,837,a)].
% 6.05/6.25 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(902,b,838,a)].
% 6.05/6.25 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(902,b,839,a)].
% 6.05/6.25 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(902,b,840,a)].
% 6.05/6.25 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,841,a)].
% 6.05/6.25 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(902,b,842,a)].
% 6.05/6.25 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(902,b,843,a)].
% 6.05/6.25 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(902,b,844,a)].
% 6.05/6.25 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(902,b,845,a)].
% 6.05/6.25 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(902,b,846,a)].
% 6.05/6.25 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(902,b,847,a)].
% 6.05/6.25 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(902,b,848,a)].
% 6.05/6.25 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(902,b,849,a)].
% 6.05/6.25 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(902,b,850,a)].
% 6.05/6.25 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,851,a)].
% 6.05/6.25 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(902,b,852,a)].
% 6.05/6.25 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(902,b,853,a)].
% 6.05/6.25 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(902,b,854,a)].
% 6.05/6.25 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(902,b,855,b)].
% 6.05/6.25 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(902,b,856,b)].
% 6.05/6.25 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(902,b,857,a)].
% 6.05/6.25 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(902,b,858,a)].
% 6.05/6.25 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(902,b,859,a)].
% 6.05/6.25 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(902,b,860,a)].
% 6.05/6.25 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(902,b,861,a)].
% 6.05/6.25 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(902,b,862,a)].
% 6.05/6.25 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(902,b,863,a)].
% 6.05/6.25 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(902,b,864,a)].
% 6.05/6.25 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(902,b,865,a)].
% 6.05/6.25 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(902,b,866,a)].
% 6.05/6.25 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(902,b,867,a)].
% 6.05/6.25 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(902,b,868,a)].
% 6.05/6.25 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(902,b,869,a)].
% 6.05/6.25 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(902,b,870,a)].
% 6.05/6.25 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(902,b,871,a)].
% 6.05/6.25 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(902,b,872,a)].
% 6.05/6.25 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(902,b,873,a)].
% 6.05/6.25 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(902,b,874,a)].
% 6.05/6.25 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(902,b,875,a)].
% 6.05/6.25 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(902,b,876,a)].
% 6.05/6.26 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(902,b,877,a)].
% 6.05/6.26 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(902,b,878,a)].
% 6.05/6.26 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(902,b,879,a)].
% 6.05/6.26 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(902,b,880,a)].
% 6.05/6.26 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(902,b,881,a)].
% 6.05/6.26 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(902,b,882,a)].
% 6.05/6.26 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(902,b,883,a)].
% 6.05/6.26 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(902,b,884,a)].
% 6.05/6.26 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(902,b,885,a)].
% 6.05/6.26 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(902,b,886,a)].
% 6.05/6.26 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(902,b,887,a)].
% 6.05/6.26 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(902,b,888,a)].
% 6.05/6.26 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(902,b,889,a)].
% 6.05/6.26 903 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 6.05/6.26 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(903,b,832,a)].
% 6.05/6.26 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(903,b,833,a)].
% 6.05/6.26 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(903,b,834,a)].
% 6.05/6.26 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(903,b,835,a)].
% 6.05/6.26 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(903,b,836,a)].
% 6.05/6.26 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(903,b,837,a)].
% 6.05/6.27 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(903,b,838,a)].
% 6.05/6.27 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(903,b,839,a)].
% 6.05/6.27 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(903,b,840,a)].
% 6.05/6.27 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,841,a)].
% 6.05/6.27 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(903,b,842,a)].
% 6.05/6.27 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(903,b,843,a)].
% 6.05/6.27 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(903,b,844,a)].
% 6.05/6.27 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(903,b,845,a)].
% 6.05/6.27 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(903,b,846,a)].
% 6.05/6.27 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(903,b,847,a)].
% 6.05/6.27 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(903,b,848,a)].
% 6.05/6.27 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(903,b,849,a)].
% 6.05/6.27 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(903,b,850,a)].
% 6.05/6.27 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,851,a)].
% 6.05/6.27 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(903,b,852,a)].
% 6.05/6.27 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(903,b,853,a)].
% 6.05/6.27 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(903,b,854,a)].
% 6.05/6.27 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(903,b,855,b)].
% 6.05/6.27 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(903,b,856,b)].
% 6.05/6.27 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(903,b,857,a)].
% 6.05/6.27 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(903,b,858,a)].
% 6.05/6.28 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(903,b,859,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(903,b,860,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(903,b,861,a)].
% 6.05/6.28 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(903,b,862,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(903,b,863,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(903,b,864,a)].
% 6.05/6.28 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(903,b,865,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(903,b,866,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(903,b,867,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(903,b,868,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(903,b,869,a)].
% 6.05/6.28 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(903,b,870,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(903,b,871,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(903,b,872,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(903,b,873,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(903,b,874,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(903,b,875,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(903,b,876,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(903,b,877,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(903,b,878,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(903,b,879,a)].
% 6.05/6.28 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(903,b,880,a)].
% 6.05/6.28 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(903,b,881,a)].
% 6.05/6.28 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(903,b,882,a)].
% 6.05/6.28 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(903,b,883,a)].
% 6.05/6.28 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(903,b,884,a)].
% 6.05/6.28 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(903,b,885,a)].
% 6.05/6.28 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(903,b,886,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(903,b,887,a)].
% 6.05/6.28 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(903,b,888,a)].
% 6.05/6.28 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(903,b,889,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(903,b,892,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(903,b,893,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(903,b,894,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(903,b,895,a)].
% 6.05/6.28 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(903,b,896,a)].
% 6.05/6.28 904 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Omax(B,C,A),A) # label(cls_Orderings_Ole__maxI1_0) # label(axiom). [assumption].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(904,a,831,a)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(904,a,890,a)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(904,a,891,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(904,a,897,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(904,a,898,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(904,a,899,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(904,a,900,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(904,a,901,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(904,a,902,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(904,a,903,b)].
% 6.05/6.28 905 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Omax(C,B,A),A) # label(cls_Orderings_Ole__maxI2_0) # label(axiom). [assumption].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(905,a,831,a)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(905,a,890,a)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(905,a,891,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(905,a,897,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(905,a,898,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(905,a,899,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(905,a,900,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(905,a,901,b)].
% 6.05/6.28 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(905,a,902,b)].
% 6.38/6.56 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(905,a,903,b)].
% 6.38/6.56 906 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 6.38/6.56 907 -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].
% 6.38/6.56 908 -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].
% 6.38/6.56 909 -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].
% 6.38/6.56 910 -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].
% 6.38/6.56 911 -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].
% 6.38/6.56 912 -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].
% 6.38/6.56 913 -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].
% 6.38/6.56 914 -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].
% 6.38/6.56 915 -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].
% 6.38/6.56 916 -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].
% 6.38/6.56 917 -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].
% 6.38/6.56 918 -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].
% 6.38/6.56 919 -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].
% 6.38/6.56 920 -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].
% 6.38/6.56 921 -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].
% 6.38/6.56 922 -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].
% 6.38/6.56 923 -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].
% 6.38/6.56 924 -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].
% 6.38/6.56 925 -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].
% 6.38/6.56 926 -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].
% 6.38/6.56 927 -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].
% 6.38/6.56 928 -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].
% 6.38/6.56 929 -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].
% 6.38/6.56 930 -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].
% 6.38/6.56 931 -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].
% 6.38/6.56 932 -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].
% 6.38/6.56 933 -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].
% 6.38/6.56 934 -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].
% 6.38/6.56 935 -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].
% 6.38/6.56 936 -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].
% 6.38/6.56 937 -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].
% 6.38/6.56 938 -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].
% 6.38/6.56 939 -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].
% 6.38/6.56 940 -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].
% 6.38/6.56 941 -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].
% 6.38/6.56 942 -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].
% 6.38/6.56 943 -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].
% 6.38/6.56 944 -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].
% 6.38/6.56 945 -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].
% 6.38/6.56 946 -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].
% 6.38/6.56 947 -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].
% 6.38/6.56 948 -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].
% 6.38/6.56 949 -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].
% 6.38/6.56 950 -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].
% 6.38/6.56 951 -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].
% 6.38/6.56 952 -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].
% 6.38/6.56 953 -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].
% 6.38/6.56 954 -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].
% 6.38/6.56 955 -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].
% 6.38/6.56 956 -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].
% 6.38/6.56 957 -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].
% 6.38/6.56 958 -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].
% 6.38/6.56 959 -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].
% 6.38/6.56 960 -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].
% 6.38/6.56 961 -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].
% 6.38/6.56 962 -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].
% 6.38/6.56 963 -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].
% 6.38/6.56 964 -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].
% 6.38/6.56 965 -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].
% 6.38/6.56 966 -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].
% 6.38/6.56 967 -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].
% 6.38/6.56 968 -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].
% 6.38/6.56 969 -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].
% 6.38/6.56 970 -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].
% 6.38/6.56 971 -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].
% 6.38/6.56 972 -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].
% 6.38/6.56 973 -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].
% 6.38/6.56 974 -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].
% 6.38/6.56 975 -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].
% 6.38/6.56 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(906,a,907,a)].
% 6.38/6.56 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(906,a,908,a)].
% 6.38/6.56 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(906,a,909,a)].
% 6.38/6.56 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(906,a,910,a)].
% 6.38/6.56 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(906,a,911,a)].
% 6.38/6.56 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(906,a,912,a)].
% 6.38/6.56 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(906,a,913,a)].
% 6.38/6.56 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(906,a,914,a)].
% 6.38/6.56 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(906,a,915,a)].
% 6.38/6.56 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(906,a,916,a)].
% 6.38/6.56 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(906,a,917,a)].
% 6.38/6.56 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(906,a,918,a)].
% 6.38/6.56 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(906,a,919,a)].
% 6.38/6.56 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(906,a,920,a)].
% 6.38/6.56 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(906,a,921,a)].
% 6.38/6.56 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(906,a,922,a)].
% 6.38/6.56 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(906,a,923,a)].
% 6.38/6.56 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(906,a,924,a)].
% 6.38/6.56 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(906,a,925,a)].
% 6.38/6.57 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(906,a,926,a)].
% 6.38/6.57 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(906,a,927,a)].
% 6.38/6.57 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(906,a,928,a)].
% 6.38/6.57 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(906,a,929,a)].
% 6.38/6.57 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(906,a,930,a)].
% 6.38/6.57 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(906,a,931,a)].
% 6.38/6.57 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(906,a,932,a)].
% 6.38/6.57 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(906,a,933,a)].
% 6.38/6.57 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(906,a,934,a)].
% 6.38/6.57 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(906,a,935,a)].
% 6.38/6.57 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(906,a,936,a)].
% 6.38/6.57 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(906,a,937,a)].
% 6.38/6.57 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(906,a,938,a)].
% 6.38/6.57 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(906,a,939,a)].
% 6.38/6.57 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(906,a,940,a)].
% 6.38/6.57 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(906,a,941,a)].
% 6.38/6.57 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(906,a,942,a)].
% 6.38/6.57 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(906,a,943,a)].
% 6.38/6.58 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(906,a,944,a)].
% 6.38/6.58 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(906,a,945,a)].
% 6.38/6.58 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(906,a,946,a)].
% 6.38/6.58 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(906,a,947,a)].
% 6.38/6.58 Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(906,a,948,a)].
% 6.38/6.58 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(906,a,949,a)].
% 6.38/6.58 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(906,a,950,a)].
% 6.38/6.58 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(906,a,951,a)].
% 6.38/6.58 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(906,a,952,a)].
% 6.38/6.58 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(906,a,953,a)].
% 6.38/6.58 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(906,a,954,a)].
% 6.38/6.58 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(906,a,955,a)].
% 6.38/6.58 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(906,a,956,a)].
% 6.38/6.58 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(906,a,957,a)].
% 6.38/6.58 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(906,a,958,a)].
% 6.38/6.58 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(906,a,959,a)].
% 6.38/6.58 Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,960,a)].
% 6.38/6.58 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,961,a)].
% 6.38/6.58 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(906,a,962,a)].
% 6.38/6.58 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(906,a,963,a)].
% 6.38/6.58 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(906,a,964,a)].
% 6.38/6.58 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(906,a,965,a)].
% 6.38/6.58 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(906,a,966,a)].
% 6.38/6.58 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(906,a,967,a)].
% 6.38/6.58 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(906,a,968,a)].
% 6.38/6.58 Derived: c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(906,a,969,a)].
% 6.38/6.58 Derived: c_times(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(906,a,970,a)].
% 6.38/6.58 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(906,a,971,a)].
% 6.38/6.58 Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0. [resolve(906,a,972,a)].
% 6.38/6.58 Derived: c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_IntDef_Oint) = c_1. [resolve(906,a,973,a)].
% 6.38/6.58 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(906,a,974,a)].
% 6.38/6.58 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(906,a,975,a)].
% 6.38/6.58 976 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom). [assumption].
% 6.38/6.58 977 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom). [assumption].
% 6.38/6.58 978 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom). [assumption].
% 6.38/6.58 979 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 6.38/6.58 980 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 6.38/6.58 981 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 6.38/6.58 982 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 6.47/6.64 Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(982,a,906,a)].
% 6.47/6.64 983 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom). [assumption].
% 6.47/6.64 984 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom). [assumption].
% 6.47/6.64 Derived: class_Numeral_Onumber(tc_IntDef_Oint). [resolve(984,a,906,a)].
% 6.47/6.64 985 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 6.47/6.64 986 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom). [assumption].
% 6.47/6.64 987 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 6.47/6.64 988 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 6.47/6.64 989 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 6.47/6.64 990 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 6.47/6.64 991 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 6.47/6.64 992 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 6.47/6.64 993 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 6.47/6.64 994 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 6.47/6.64 995 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 6.47/6.64 996 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 6.47/6.64 997 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 6.47/6.64 998 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(114,b,108,a)].
% 6.47/6.64 999 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(114,b,111,a)].
% 6.47/6.64 1000 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(116,a,114,b)].
% 6.47/6.64 1001 -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)].
% 6.47/6.64 1002 -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)].
% 6.47/6.64 1003 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(171,a,136,b)].
% 6.47/6.64 1004 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(172,a,136,b)].
% 6.47/6.64 1005 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(201,b,177,b)].
% 6.47/6.64 1006 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 6.47/6.64 1007 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 6.47/6.64 1008 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 6.47/6.64 1009 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(205,b,177,b)].
% 6.47/6.64 1010 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(206,b,177,b)].
% 6.47/6.64 1011 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 6.47/6.64 1012 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 6.47/6.64 1013 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(284,b,253,b)].
% 6.47/6.64 1014 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(285,b,253,b)].
% 6.47/6.64 1015 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(286,b,253,b)].
% 6.47/6.64 1016 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(287,b,253,b)].
% 6.47/6.67 1017 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,288,a)].
% 6.47/6.67 1018 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,290,a)].
% 6.47/6.67 1019 -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(338,b,331,b)].
% 6.47/6.67 1020 -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(338,b,333,b)].
% 6.47/6.67 1021 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,334,a)].
% 6.47/6.67 1022 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,335,a)].
% 6.47/6.67 1023 -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,336,a)].
% 6.47/6.67 1024 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(354,a,338,b)].
% 6.47/6.67 1025 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(355,a,338,b)].
% 6.47/6.67 1026 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(374,a,338,b)].
% 6.47/6.67 1027 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(375,a,338,b)].
% 6.47/6.67 1028 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(376,c,338,b)].
% 6.47/6.67 1029 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(377,c,338,b)].
% 6.47/6.67 1030 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(411,b,383,b)].
% 6.47/6.67 1031 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(412,b,383,b)].
% 6.47/6.67 1032 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 6.47/6.67 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1032,b,906,a)].
% 6.47/6.67 1033 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(454,b,424,b)].
% 6.47/6.67 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1033,b,906,a)].
% 6.47/6.67 1034 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(459,b,424,b)].
% 6.47/6.67 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1034,b,906,a)].
% 6.47/6.67 1035 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(460,b,424,b)].
% 6.47/6.67 1036 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(461,b,424,b)].
% 6.47/6.67 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1036,b,906,a)].
% 6.47/6.67 1037 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(462,b,424,b)].
% 6.47/6.67 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1037,b,906,a)].
% 6.47/6.67 1038 -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(467,a,424,b)].
% 6.47/6.67 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(1038,c,906,a)].
% 6.47/6.67 1039 -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(468,a,424,b)].
% 6.47/6.67 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(1039,c,906,a)].
% 6.47/6.69 1040 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(469,a,424,b)].
% 6.47/6.69 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(1040,b,906,a)].
% 6.47/6.69 1041 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(470,a,424,b)].
% 6.47/6.69 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(1041,b,906,a)].
% 6.47/6.69 1042 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(471,a,424,b)].
% 6.47/6.69 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(1042,b,906,a)].
% 6.47/6.69 1043 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(472,b,424,b)].
% 6.47/6.69 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1043,b,906,a)].
% 6.47/6.69 1044 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(473,b,424,b)].
% 6.47/6.69 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1044,b,906,a)].
% 6.47/6.69 1045 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(474,b,424,b)].
% 6.47/6.69 1046 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(475,b,424,b)].
% 6.47/6.69 1047 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(476,c,424,b)].
% 6.47/6.69 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1047,c,906,a)].
% 6.47/6.69 1048 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(477,c,424,b)].
% 6.47/6.69 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1048,c,906,a)].
% 6.47/6.69 1049 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(479,b,424,b)].
% 6.47/6.69 1050 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,424,b)].
% 6.47/6.69 1051 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(524,a,505,b)].
% 6.47/6.69 1052 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(525,a,505,b)].
% 6.47/6.69 1053 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(543,a,536,b)].
% 6.47/6.69 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(1053,b,906,a)].
% 6.47/6.69 1054 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(568,b,536,b)].
% 6.47/6.69 1055 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(569,b,536,b)].
% 6.47/6.69 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1055,b,906,a)].
% 6.47/6.69 1056 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(570,b,536,b)].
% 6.47/6.69 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1056,b,906,a)].
% 6.47/6.69 1057 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(571,b,536,b)].
% 6.47/6.69 1058 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(572,b,536,b)].
% 6.47/6.69 1059 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(663,b,615,b)].
% 6.47/6.69 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1059,b,906,a)].
% 6.47/6.69 1060 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(664,b,615,b)].
% 6.47/6.69 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1060,b,906,a)].
% 6.47/6.69 1061 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(666,b,615,b)].
% 6.47/6.69 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1061,b,906,a)].
% 6.47/6.69 1062 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(667,b,615,b)].
% 6.47/6.69 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1062,b,906,a)].
% 6.47/6.69 1063 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(681,b,668,a)].
% 6.47/6.69 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1063,a,906,a)].
% 6.47/6.69 1064 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(681,b,670,a)].
% 6.47/6.69 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1064,a,906,a)].
% 6.47/6.69 1065 -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(681,b,671,a)].
% 6.47/6.69 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(1065,a,906,a)].
% 6.71/6.90 1066 -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(681,b,672,a)].
% 6.71/6.90 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(1066,a,906,a)].
% 6.71/6.90 1067 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(681,b,673,a)].
% 6.71/6.90 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1067,a,906,a)].
% 6.71/6.90 1068 -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(681,b,674,a)].
% 6.71/6.90 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(1068,a,906,a)].
% 6.71/6.90 1069 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(681,b,675,a)].
% 6.71/6.90 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1069,a,906,a)].
% 6.71/6.90 1070 -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(681,b,676,a)].
% 6.71/6.90 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(1070,a,906,a)].
% 6.71/6.90 1071 -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(681,b,677,a)].
% 6.71/6.90 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(1071,a,906,a)].
% 6.71/6.90 1072 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(681,b,678,a)].
% 6.71/6.90 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1072,a,906,a)].
% 6.71/6.90 1073 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,681,b)].
% 6.71/6.90 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(1073,b,906,a)].
% 6.71/6.90 1074 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(823,a,734,a)].
% 6.71/6.90 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1074,a,906,a)].
% 6.71/6.90 1075 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 6.71/6.90 1076 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 6.71/6.90 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1075,a,1076,a)].
% 6.71/6.90 1077 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 6.71/6.90 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1077,a,1076,a)].
% 6.71/6.90 1078 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 6.71/6.90 1079 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 6.71/6.90 1080 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 6.71/6.90 Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1076,a)].
% 6.71/6.90 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1080,b,1078,a)].
% 6.71/6.90 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1080,b,1079,a)].
% 6.71/6.90 1081 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 6.71/6.90 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1076,a)].
% 6.71/6.90 1082 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 6.71/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1076,a)].
% 6.99/7.18 1083 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1076,a)].
% 6.99/7.18 1084 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1076,a)].
% 6.99/7.18 1085 -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].
% 6.99/7.18 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1076,a)].
% 6.99/7.18 1086 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1086,b,1076,a)].
% 6.99/7.18 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1086,b,1078,a)].
% 6.99/7.18 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1086,b,1079,a)].
% 6.99/7.18 1087 -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].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1087,b,1076,a)].
% 6.99/7.18 1088 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1088,b,1076,a)].
% 6.99/7.18 1089 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1089,b,1076,a)].
% 6.99/7.18 1090 -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].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1090,b,1076,a)].
% 6.99/7.18 1091 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1091,b,1076,a)].
% 6.99/7.18 1092 -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].
% 6.99/7.18 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1092,b,1076,a)].
% 6.99/7.18 1093 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 6.99/7.18 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1093,b,1076,a)].
% 6.99/7.18 1094 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(893,a,831,a)].
% 6.99/7.18 1095 class_LOrder_Ojoin__semilorder(tc_nat). [resolve(893,a,890,a)].
% 6.99/7.18 1096 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(893,a,891,b)].
% 6.99/7.18 1097 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(903,b,893,a)].
% 6.99/7.18 1098 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 6.99/7.18 1099 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 6.99/7.18 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1098,a,1099,a)].
% 6.99/7.20 1100 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 6.99/7.20 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1100,a,1099,a)].
% 6.99/7.20 1101 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 6.99/7.20 Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1099,a)].
% 6.99/7.20 1102 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 6.99/7.20 1103 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 6.99/7.20 1104 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 6.99/7.20 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1099,a)].
% 6.99/7.20 1105 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 6.99/7.20 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1099,a)].
% 6.99/7.20 1106 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 6.99/7.20 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1099,a)].
% 6.99/7.20 1107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 6.99/7.20 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1099,a)].
% 6.99/7.20 1108 -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].
% 6.99/7.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1099,a)].
% 6.99/7.21 1109 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 6.99/7.21 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1109,b,1099,a)].
% 6.99/7.21 1110 -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].
% 6.99/7.21 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1110,b,1099,a)].
% 6.99/7.21 1111 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 6.99/7.21 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1111,b,1099,a)].
% 6.99/7.21 1112 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 6.99/7.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1112,b,1099,a)].
% 6.99/7.21 1113 -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].
% 6.99/7.21 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1113,b,1099,a)].
% 6.99/7.21 1114 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 6.99/7.21 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1114,b,1099,a)].
% 6.99/7.21 1115 -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].
% 7.31/7.47 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1115,b,1099,a)].
% 7.31/7.47 1116 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 7.31/7.47 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1116,b,1099,a)].
% 7.31/7.47 1117 class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(894,a,831,a)].
% 7.31/7.47 1118 class_LOrder_Omeet__semilorder(tc_nat). [resolve(894,a,890,a)].
% 7.31/7.47 1119 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(894,a,891,b)].
% 7.31/7.47 1120 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(903,b,894,a)].
% 7.31/7.47 1121 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 7.31/7.47 1122 -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].
% 7.31/7.47 1123 -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].
% 7.31/7.47 1124 -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].
% 7.31/7.47 1125 -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].
% 7.31/7.47 1126 -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].
% 7.31/7.47 1127 -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].
% 7.31/7.47 1128 -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].
% 7.31/7.47 1129 -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].
% 7.31/7.47 1130 -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].
% 7.31/7.47 1131 -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].
% 7.31/7.47 1132 -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].
% 7.31/7.47 1133 -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].
% 7.31/7.47 1134 -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].
% 7.31/7.47 1135 -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].
% 7.31/7.47 1136 -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].
% 7.31/7.47 1137 -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].
% 7.31/7.47 1138 -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].
% 7.31/7.48 1139 -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].
% 7.31/7.48 1140 -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].
% 7.31/7.48 1141 -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].
% 7.31/7.48 1142 -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].
% 7.31/7.48 1143 -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].
% 7.31/7.48 1144 -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].
% 7.31/7.48 1145 -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].
% 7.31/7.48 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(1121,a,1122,a)].
% 7.31/7.48 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(1121,a,1123,a)].
% 7.31/7.48 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1124,a)].
% 7.31/7.48 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(1121,a,1125,a)].
% 7.31/7.48 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1126,a)].
% 7.31/7.48 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1121,a,1127,a)].
% 7.31/7.48 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(1121,a,1128,a)].
% 7.31/7.48 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(1121,a,1129,a)].
% 7.31/7.48 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1121,a,1130,a)].
% 7.31/7.48 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1121,a,1131,a)].
% 7.31/7.48 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(1121,a,1132,a)].
% 7.31/7.48 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(1121,a,1133,a)].
% 7.31/7.48 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1121,a,1134,a)].
% 7.31/7.48 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(1121,a,1135,a)].
% 7.31/7.48 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(1121,a,1136,a)].
% 7.31/7.48 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(1121,a,1137,b)].
% 7.31/7.48 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(1121,a,1138,b)].
% 7.31/7.48 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(1121,a,1139,b)].
% 7.31/7.48 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(1121,a,1140,b)].
% 7.31/7.50 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(1121,a,1141,b)].
% 7.31/7.50 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(1121,a,1142,a)].
% 7.31/7.50 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(1121,a,1143,a)].
% 7.31/7.50 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(1121,a,1144,a)].
% 7.31/7.50 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(1121,a,1145,a)].
% 7.31/7.50 1146 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 7.31/7.50 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(1146,a,1122,a)].
% 7.31/7.50 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(1146,a,1123,a)].
% 7.31/7.50 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1146,a,1124,a)].
% 7.31/7.50 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat). [resolve(1146,a,1125,a)].
% 7.31/7.50 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1146,a,1126,a)].
% 7.31/7.50 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(1146,a,1127,a)].
% 7.31/7.50 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(1146,a,1128,a)].
% 7.31/7.50 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(1146,a,1129,a)].
% 7.31/7.50 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(1146,a,1130,a)].
% 7.31/7.50 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(1146,a,1131,a)].
% 7.31/7.50 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(1146,a,1132,a)].
% 7.31/7.50 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(1146,a,1133,a)].
% 7.31/7.50 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat). [resolve(1146,a,1134,a)].
% 7.31/7.50 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(1146,a,1135,a)].
% 7.31/7.50 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(1146,a,1136,a)].
% 7.31/7.50 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(1146,a,1137,b)].
% 7.31/7.50 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(1146,a,1138,b)].
% 7.31/7.50 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(1146,a,1139,b)].
% 7.31/7.50 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(1146,a,1140,b)].
% 7.31/7.50 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(1146,a,1141,b)].
% 7.31/7.50 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(1146,a,1142,a)].
% 7.31/7.50 Derived: -c_less(c_1,c_0,tc_nat). [resolve(1146,a,1143,a)].
% 7.31/7.50 Derived: c_less(c_0,c_1,tc_nat). [resolve(1146,a,1144,a)].
% 7.31/7.50 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(1146,a,1145,a)].
% 7.31/7.50 1147 -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].
% 7.31/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1147,b,1122,a)].
% 7.31/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1147,b,1123,a)].
% 7.31/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1147,b,1124,a)].
% 7.31/7.50 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(1147,b,1125,a)].
% 7.31/7.51 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(1147,b,1126,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1147,b,1127,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1147,b,1128,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1147,b,1129,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1147,b,1130,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1147,b,1131,a)].
% 7.31/7.51 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(1147,b,1132,a)].
% 7.31/7.51 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(1147,b,1133,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1147,b,1134,a)].
% 7.31/7.51 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(1147,b,1135,a)].
% 7.31/7.51 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(1147,b,1136,a)].
% 7.31/7.51 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(1147,b,1137,b)].
% 7.31/7.51 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(1147,b,1138,b)].
% 7.31/7.51 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(1147,b,1139,b)].
% 7.31/7.51 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(1147,b,1140,b)].
% 7.31/7.51 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(1147,b,1141,b)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A). [resolve(1147,b,1142,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A). [resolve(1147,b,1143,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A). [resolve(1147,b,1144,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A). [resolve(1147,b,1145,a)].
% 7.31/7.51 1148 -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].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1148,b,1122,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1148,b,1123,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1148,b,1124,a)].
% 7.31/7.51 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(1148,b,1125,a)].
% 7.31/7.51 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(1148,b,1126,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1148,b,1127,a)].
% 7.31/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1148,b,1128,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1148,b,1129,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1148,b,1130,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1148,b,1131,a)].
% 7.31/7.52 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(1148,b,1132,a)].
% 7.31/7.52 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(1148,b,1133,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1148,b,1134,a)].
% 7.31/7.52 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(1148,b,1135,a)].
% 7.31/7.52 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(1148,b,1136,a)].
% 7.31/7.52 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(1148,b,1137,b)].
% 7.31/7.52 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(1148,b,1138,b)].
% 7.31/7.52 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(1148,b,1139,b)].
% 7.31/7.52 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(1148,b,1140,b)].
% 7.31/7.52 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(1148,b,1141,b)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A). [resolve(1148,b,1142,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A). [resolve(1148,b,1143,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A). [resolve(1148,b,1144,a)].
% 7.31/7.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A). [resolve(1148,b,1145,a)].
% 7.31/7.52 1149 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 7.31/7.52 1150 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom). [assumption].
% 7.31/7.52 1151 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 7.31/7.52 1152 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom). [assumption].
% 7.31/7.52 1153 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 7.31/7.52 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1148,b)].
% 7.31/7.52 1154 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 7.31/7.52 1155 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom). [assumption].
% 7.31/7.52 1156 -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].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1156,a,1121,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1156,a,1146,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1147,b)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1148,b)].
% 7.36/7.53 1157 -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].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1157,a,1121,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1157,a,1146,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1147,b)].
% 7.36/7.53 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1148,b)].
% 7.36/7.53 1158 -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].
% 7.36/7.53 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1121,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1158,a,1146,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1147,b)].
% 7.36/7.53 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1148,b)].
% 7.36/7.53 1159 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 7.36/7.53 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1147,b)].
% 7.36/7.53 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1148,b)].
% 7.36/7.53 1160 -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].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1160,a,1121,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1160,a,1146,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1147,b)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1148,b)].
% 7.36/7.53 1161 -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].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1161,a,1121,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1161,a,1146,a)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1161,a,1147,b)].
% 7.36/7.53 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1161,a,1148,b)].
% 7.36/7.53 1162 -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].
% 7.36/7.53 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1162,a,1121,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1162,a,1146,a)].
% 7.36/7.53 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1162,a,1147,b)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1162,a,1148,b)].
% 7.36/7.55 1163 -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].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1163,a,1121,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1163,a,1146,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1163,a,1147,b)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1163,a,1148,b)].
% 7.36/7.55 1164 -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].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1164,a,1121,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1164,a,1146,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1164,a,1147,b)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1164,a,1148,b)].
% 7.36/7.55 1165 -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].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1165,a,1121,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1165,a,1146,a)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1165,a,1147,b)].
% 7.36/7.55 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1165,a,1148,b)].
% 7.36/7.55 1166 -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].
% 7.36/7.55 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1166,a,1121,a)].
% 7.36/7.55 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1166,a,1146,a)].
% 7.36/7.55 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1166,a,1147,b)].
% 7.36/7.55 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1166,a,1148,b)].
% 7.36/7.55 1167 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 7.36/7.55 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1167,a,1147,b)].
% 7.36/7.55 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1167,a,1148,b)].
% 7.36/7.55 1168 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 7.36/7.55 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1168,a,1147,b)].
% 7.36/7.55 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1168,a,1148,b)].
% 7.36/7.55 1169 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 7.36/7.55 1170 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(31,b,1,a)].
% 7.36/7.55 1171 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(31,b,3,a)].
% 7.36/7.55 1172 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 7.39/7.62 1173 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 7.39/7.62 1174 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(127,b,108,a)].
% 7.39/7.62 1175 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(127,b,111,a)].
% 7.39/7.62 1176 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(127,b,117,a)].
% 7.39/7.62 1177 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(127,b,118,a)].
% 7.39/7.62 1178 -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)].
% 7.39/7.62 1179 -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)].
% 7.39/7.62 1180 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(171,a,152,b)].
% 7.39/7.62 1181 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(172,a,152,b)].
% 7.39/7.62 1182 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(201,b,194,b)].
% 7.39/7.62 1183 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(202,b,194,b)].
% 7.39/7.62 1184 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 7.39/7.62 1185 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 7.39/7.62 1186 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 7.39/7.62 1187 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 7.39/7.62 1188 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(247,b,226,b)].
% 7.39/7.62 1189 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(248,b,226,b)].
% 7.39/7.62 1190 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,288,a)].
% 7.39/7.62 1191 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,290,a)].
% 7.39/7.62 1192 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(322,a,306,b)].
% 7.39/7.62 1193 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(323,a,306,b)].
% 7.39/7.62 1194 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(517,a,514,b)].
% 7.39/7.62 1195 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(524,a,514,b)].
% 7.39/7.62 1196 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(525,a,514,b)].
% 7.39/7.62 1197 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(531,a,514,b)].
% 7.39/7.62 1198 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(571,b,552,b)].
% 7.39/7.62 1199 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(607,a,585,b)].
% 7.39/7.62 1200 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(608,a,585,b)].
% 7.39/7.62 1201 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(611,b,585,b)].
% 7.39/7.62 1202 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(697,b,668,a)].
% 7.39/7.62 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(1202,a,1146,a)].
% 7.39/7.62 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1202,a,1147,b)].
% 7.39/7.62 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1202,a,1148,b)].
% 7.39/7.62 1203 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(697,b,670,a)].
% 7.39/7.62 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(1203,a,1146,a)].
% 7.39/7.62 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1203,a,1147,b)].
% 7.39/7.62 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1203,a,1148,b)].
% 7.39/7.62 1204 -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(697,b,671,a)].
% 7.39/7.62 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(1204,a,1146,a)].
% 7.39/7.62 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(1204,a,1147,b)].
% 7.39/7.62 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(1204,a,1148,b)].
% 7.39/7.62 1205 -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(697,b,672,a)].
% 7.39/7.62 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(1205,a,1146,a)].
% 7.39/7.62 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(1205,a,1147,b)].
% 7.39/7.62 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(1205,a,1148,b)].
% 7.39/7.62 1206 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(697,b,673,a)].
% 7.39/7.62 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1206,a,1146,a)].
% 7.39/7.62 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1206,a,1147,b)].
% 7.39/7.62 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1206,a,1148,b)].
% 7.39/7.62 1207 -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(697,b,674,a)].
% 7.39/7.62 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(1207,a,1146,a)].
% 7.39/7.62 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(1207,a,1147,b)].
% 7.39/7.62 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(1207,a,1148,b)].
% 7.39/7.62 1208 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(697,b,675,a)].
% 7.39/7.62 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(1208,a,1146,a)].
% 7.39/7.62 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1208,a,1147,b)].
% 7.39/7.62 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1208,a,1148,b)].
% 7.39/7.62 1209 -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(697,b,676,a)].
% 7.39/7.62 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(1209,a,1146,a)].
% 7.39/7.62 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(1209,a,1147,b)].
% 7.39/7.62 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(1209,a,1148,b)].
% 7.39/7.62 1210 -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(697,b,677,a)].
% 7.39/7.62 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(1210,a,1146,a)].
% 7.39/7.62 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(1210,a,1147,b)].
% 7.50/7.68 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(1210,a,1148,b)].
% 7.50/7.68 1211 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(697,b,678,a)].
% 7.50/7.68 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(1211,a,1146,a)].
% 7.50/7.68 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1211,a,1147,b)].
% 7.50/7.68 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1211,a,1148,b)].
% 7.50/7.68 1212 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(728,b,697,b)].
% 7.50/7.68 Derived: class_HOL_Oone(tc_nat). [resolve(1212,b,1146,a)].
% 7.50/7.68 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1212,b,1147,b)].
% 7.50/7.68 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1212,b,1148,b)].
% 7.50/7.68 1213 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(820,a,734,a)].
% 7.50/7.68 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1213,a,1146,a)].
% 7.50/7.68 1214 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(820,a,741,a)].
% 7.50/7.68 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1214,a,1147,b)].
% 7.50/7.68 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1214,a,1148,b)].
% 7.50/7.68 1215 -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(901,b,832,a)].
% 7.50/7.68 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(1215,a,1121,a)].
% 7.50/7.68 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(1215,a,1146,a)].
% 7.50/7.68 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(1215,a,1147,b)].
% 7.50/7.68 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(1215,a,1148,b)].
% 7.50/7.68 1216 -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(901,b,833,a)].
% 7.50/7.68 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(1216,a,1121,a)].
% 7.50/7.68 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(1216,a,1146,a)].
% 7.50/7.68 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(1216,a,1147,b)].
% 7.50/7.68 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(1216,a,1148,b)].
% 7.50/7.68 1217 -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(901,b,834,a)].
% 7.50/7.68 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(1217,a,1121,a)].
% 7.50/7.68 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(1217,a,1146,a)].
% 7.50/7.68 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(1217,a,1147,b)].
% 7.50/7.68 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(1217,a,1148,b)].
% 7.50/7.68 1218 -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(901,b,835,a)].
% 7.50/7.68 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(1218,a,1121,a)].
% 7.50/7.68 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(1218,a,1146,a)].
% 7.50/7.68 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(1218,a,1147,b)].
% 7.50/7.68 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(1218,a,1148,b)].
% 7.50/7.68 1219 -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(901,b,836,a)].
% 7.50/7.68 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(1219,a,1121,a)].
% 7.50/7.68 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(1219,a,1146,a)].
% 7.50/7.68 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(1219,a,1147,b)].
% 7.50/7.68 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(1219,a,1148,b)].
% 7.50/7.68 1220 -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(901,b,837,a)].
% 7.50/7.68 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(1220,a,1121,a)].
% 7.50/7.68 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(1220,a,1146,a)].
% 7.50/7.68 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(1220,a,1147,b)].
% 7.50/7.68 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(1220,a,1148,b)].
% 7.50/7.68 1221 -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(901,b,838,a)].
% 7.50/7.68 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(1221,a,1121,a)].
% 7.50/7.68 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(1221,a,1146,a)].
% 7.50/7.68 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(1221,a,1147,b)].
% 7.50/7.68 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(1221,a,1148,b)].
% 7.50/7.68 1222 -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(901,b,839,a)].
% 7.50/7.68 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(1222,a,1121,a)].
% 7.50/7.68 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(1222,a,1146,a)].
% 7.50/7.68 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(1222,a,1147,b)].
% 7.50/7.68 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(1222,a,1148,b)].
% 7.50/7.68 1223 -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(901,b,840,a)].
% 7.50/7.68 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(1223,a,1121,a)].
% 7.50/7.68 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(1223,a,1146,a)].
% 7.50/7.68 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(1223,a,1147,b)].
% 7.50/7.68 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(1223,a,1148,b)].
% 7.50/7.68 1224 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,841,a)].
% 7.50/7.68 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1224,a,1121,a)].
% 7.50/7.68 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1224,a,1146,a)].
% 7.50/7.68 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1224,a,1147,b)].
% 7.50/7.68 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1148,b)].
% 7.50/7.68 1225 -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(901,b,842,a)].
% 7.50/7.68 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(1225,a,1121,a)].
% 7.50/7.68 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(1225,a,1146,a)].
% 7.50/7.68 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(1225,a,1147,b)].
% 7.50/7.68 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(1225,a,1148,b)].
% 7.50/7.68 1226 -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(901,b,843,a)].
% 7.50/7.68 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(1226,a,1121,a)].
% 7.50/7.68 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(1226,a,1146,a)].
% 7.50/7.68 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(1226,a,1147,b)].
% 7.50/7.68 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(1226,a,1148,b)].
% 7.50/7.68 1227 -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(901,b,844,a)].
% 7.50/7.68 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(1227,a,1121,a)].
% 7.50/7.68 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(1227,a,1146,a)].
% 7.50/7.68 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(1227,a,1147,b)].
% 7.50/7.68 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(1227,a,1148,b)].
% 7.50/7.68 1228 -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(901,b,845,a)].
% 7.50/7.68 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(1228,a,1121,a)].
% 7.50/7.68 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(1228,a,1146,a)].
% 7.50/7.68 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(1228,a,1147,b)].
% 7.50/7.68 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(1228,a,1148,b)].
% 7.50/7.68 1229 -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(901,b,846,a)].
% 7.50/7.69 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(1229,a,1121,a)].
% 7.50/7.69 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(1229,a,1146,a)].
% 7.50/7.69 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(1229,a,1147,b)].
% 7.50/7.69 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(1229,a,1148,b)].
% 7.50/7.69 1230 -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(901,b,847,a)].
% 7.50/7.69 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(1230,a,1121,a)].
% 7.50/7.69 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(1230,a,1146,a)].
% 7.50/7.69 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(1230,a,1147,b)].
% 7.50/7.69 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(1230,a,1148,b)].
% 7.50/7.69 1231 -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(901,b,848,a)].
% 7.50/7.69 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(1231,a,1121,a)].
% 7.50/7.69 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(1231,a,1146,a)].
% 7.50/7.69 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(1231,a,1147,b)].
% 7.50/7.69 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(1231,a,1148,b)].
% 7.50/7.69 1232 -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(901,b,849,a)].
% 7.50/7.69 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(1232,a,1121,a)].
% 7.50/7.69 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(1232,a,1146,a)].
% 7.50/7.69 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(1232,a,1147,b)].
% 7.50/7.69 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(1232,a,1148,b)].
% 7.50/7.69 1233 -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(901,b,850,a)].
% 7.50/7.69 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(1233,a,1121,a)].
% 7.50/7.69 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(1233,a,1146,a)].
% 7.50/7.69 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(1233,a,1147,b)].
% 7.50/7.69 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(1233,a,1148,b)].
% 7.50/7.69 1234 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,851,a)].
% 7.50/7.69 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1234,a,1121,a)].
% 7.50/7.69 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1234,a,1146,a)].
% 7.50/7.69 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1234,a,1147,b)].
% 7.50/7.69 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1234,a,1148,b)].
% 7.50/7.69 1235 -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(901,b,852,a)].
% 7.50/7.69 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(1235,a,1121,a)].
% 7.50/7.69 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(1235,a,1146,a)].
% 7.50/7.69 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(1235,a,1147,b)].
% 7.50/7.69 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(1235,a,1148,b)].
% 7.50/7.69 1236 -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(901,b,853,a)].
% 7.50/7.69 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(1236,a,1121,a)].
% 7.50/7.69 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(1236,a,1146,a)].
% 7.50/7.69 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(1236,a,1147,b)].
% 7.50/7.69 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(1236,a,1148,b)].
% 7.50/7.69 1237 -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(901,b,854,a)].
% 7.50/7.69 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(1237,a,1121,a)].
% 7.50/7.69 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(1237,a,1146,a)].
% 7.50/7.69 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(1237,a,1147,b)].
% 7.50/7.69 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(1237,a,1148,b)].
% 7.50/7.69 1238 -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(901,b,855,b)].
% 7.50/7.69 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(1238,a,1121,a)].
% 7.50/7.69 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(1238,a,1146,a)].
% 7.50/7.69 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(1238,a,1147,b)].
% 7.50/7.69 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(1238,a,1148,b)].
% 7.50/7.69 1239 -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(901,b,856,b)].
% 7.50/7.69 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(1239,a,1121,a)].
% 7.50/7.69 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(1239,a,1146,a)].
% 7.50/7.69 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(1239,a,1147,b)].
% 7.50/7.69 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(1239,a,1148,b)].
% 7.50/7.69 1240 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(901,b,857,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1240,a,1121,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1240,a,1146,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1240,a,1147,b)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1240,a,1148,b)].
% 7.50/7.69 1241 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(901,b,858,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1241,a,1121,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1241,a,1146,a)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1241,a,1147,b)].
% 7.50/7.69 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1241,a,1148,b)].
% 7.50/7.69 1242 -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(901,b,859,a)].
% 7.50/7.69 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(1242,a,1121,a)].
% 7.50/7.69 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(1242,a,1146,a)].
% 7.50/7.69 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(1242,a,1147,b)].
% 7.50/7.69 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(1242,a,1148,b)].
% 7.50/7.69 1243 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(901,b,860,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1243,a,1121,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1243,a,1146,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1243,a,1147,b)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1243,a,1148,b)].
% 7.50/7.69 1244 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(901,b,861,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1244,a,1121,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1244,a,1146,a)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1244,a,1147,b)].
% 7.50/7.69 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1244,a,1148,b)].
% 7.50/7.69 1245 -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(901,b,862,a)].
% 7.50/7.69 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(1245,a,1121,a)].
% 7.50/7.69 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(1245,a,1146,a)].
% 7.50/7.69 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(1245,a,1147,b)].
% 7.50/7.69 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(1245,a,1148,b)].
% 7.50/7.69 1246 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(901,b,863,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1246,a,1121,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1246,a,1146,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1246,a,1147,b)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1246,a,1148,b)].
% 7.50/7.69 1247 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(901,b,864,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1247,a,1121,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1247,a,1146,a)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1247,a,1147,b)].
% 7.50/7.69 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1247,a,1148,b)].
% 7.50/7.69 1248 -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(901,b,865,a)].
% 7.50/7.69 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(1248,a,1121,a)].
% 7.50/7.69 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(1248,a,1146,a)].
% 7.50/7.70 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(1248,a,1147,b)].
% 7.50/7.70 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(1248,a,1148,b)].
% 7.50/7.70 1249 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(901,b,866,a)].
% 7.50/7.70 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1249,a,1121,a)].
% 7.50/7.70 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1249,a,1146,a)].
% 7.50/7.70 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1249,a,1147,b)].
% 7.50/7.70 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1249,a,1148,b)].
% 7.50/7.70 1250 -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(901,b,867,a)].
% 7.50/7.70 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(1250,a,1121,a)].
% 7.50/7.70 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(1250,a,1146,a)].
% 7.50/7.70 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(1250,a,1147,b)].
% 7.50/7.70 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(1250,a,1148,b)].
% 7.50/7.70 1251 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(901,b,868,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1251,a,1121,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1251,a,1146,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1251,a,1147,b)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1251,a,1148,b)].
% 7.50/7.70 1252 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(901,b,869,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1252,a,1121,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1252,a,1146,a)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1252,a,1147,b)].
% 7.50/7.70 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1252,a,1148,b)].
% 7.50/7.70 1253 -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(901,b,870,a)].
% 7.50/7.70 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(1253,a,1121,a)].
% 7.50/7.70 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(1253,a,1146,a)].
% 7.50/7.70 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(1253,a,1147,b)].
% 7.50/7.70 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(1253,a,1148,b)].
% 7.50/7.70 1254 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(901,b,871,a)].
% 7.50/7.70 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1254,a,1121,a)].
% 7.50/7.70 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1254,a,1146,a)].
% 7.50/7.70 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1254,a,1147,b)].
% 7.50/7.70 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1254,a,1148,b)].
% 7.50/7.70 1255 -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(901,b,872,a)].
% 7.50/7.70 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(1255,a,1121,a)].
% 7.50/7.70 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(1255,a,1146,a)].
% 7.50/7.70 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(1255,a,1147,b)].
% 7.50/7.70 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(1255,a,1148,b)].
% 7.50/7.70 1256 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(901,b,873,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1256,a,1121,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1256,a,1146,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1256,a,1147,b)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1256,a,1148,b)].
% 7.50/7.70 1257 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(901,b,874,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1257,a,1121,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1257,a,1146,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1257,a,1147,b)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1257,a,1148,b)].
% 7.50/7.70 1258 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(901,b,875,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1258,a,1121,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1258,a,1146,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1258,a,1147,b)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1258,a,1148,b)].
% 7.50/7.70 1259 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(901,b,876,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1259,a,1121,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1259,a,1146,a)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1259,a,1147,b)].
% 7.50/7.70 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1259,a,1148,b)].
% 7.50/7.70 1260 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(901,b,877,a)].
% 7.50/7.70 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1260,a,1121,a)].
% 7.50/7.70 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1260,a,1146,a)].
% 7.50/7.70 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1260,a,1147,b)].
% 7.50/7.70 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1260,a,1148,b)].
% 7.50/7.70 1261 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(901,b,878,a)].
% 7.50/7.70 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1261,a,1121,a)].
% 7.50/7.70 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1261,a,1146,a)].
% 7.50/7.70 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1261,a,1147,b)].
% 7.50/7.70 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1261,a,1148,b)].
% 7.50/7.70 1262 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(901,b,879,a)].
% 7.50/7.70 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1262,a,1121,a)].
% 7.50/7.70 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1262,a,1146,a)].
% 7.50/7.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1262,a,1147,b)].
% 7.50/7.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1262,a,1148,b)].
% 7.50/7.70 1263 -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(901,b,880,a)].
% 7.50/7.70 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(1263,a,1121,a)].
% 7.50/7.70 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(1263,a,1146,a)].
% 7.50/7.70 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(1263,a,1147,b)].
% 7.50/7.70 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(1263,a,1148,b)].
% 7.50/7.70 1264 -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(901,b,881,a)].
% 7.50/7.70 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(1264,a,1121,a)].
% 7.50/7.70 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(1264,a,1146,a)].
% 7.50/7.70 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(1264,a,1147,b)].
% 7.50/7.70 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(1264,a,1148,b)].
% 7.50/7.70 1265 -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(901,b,882,a)].
% 7.50/7.70 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(1265,a,1121,a)].
% 7.50/7.70 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(1265,a,1146,a)].
% 7.50/7.70 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(1265,a,1147,b)].
% 7.50/7.70 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(1265,a,1148,b)].
% 7.50/7.70 1266 -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(901,b,883,a)].
% 7.50/7.70 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(1266,a,1121,a)].
% 7.50/7.70 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(1266,a,1146,a)].
% 7.50/7.70 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(1266,a,1147,b)].
% 7.50/7.70 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(1266,a,1148,b)].
% 7.50/7.70 1267 -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(901,b,884,a)].
% 7.50/7.70 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(1267,a,1121,a)].
% 7.50/7.70 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(1267,a,1146,a)].
% 7.50/7.70 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(1267,a,1147,b)].
% 7.50/7.70 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(1267,a,1148,b)].
% 7.50/7.70 1268 -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(901,b,885,a)].
% 7.50/7.70 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(1268,a,1121,a)].
% 7.50/7.70 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(1268,a,1146,a)].
% 7.50/7.70 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(1268,a,1147,b)].
% 7.50/7.70 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(1268,a,1148,b)].
% 7.50/7.72 1269 -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(901,b,886,a)].
% 7.50/7.72 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(1269,a,1121,a)].
% 7.50/7.72 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(1269,a,1146,a)].
% 7.50/7.72 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(1269,a,1147,b)].
% 7.50/7.72 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(1269,a,1148,b)].
% 7.50/7.72 1270 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(901,b,887,a)].
% 7.50/7.72 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1270,a,1121,a)].
% 7.50/7.72 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1270,a,1146,a)].
% 7.50/7.72 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1270,a,1147,b)].
% 7.50/7.72 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1270,a,1148,b)].
% 7.50/7.72 1271 -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(901,b,888,a)].
% 7.50/7.72 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(1271,a,1121,a)].
% 7.50/7.72 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(1271,a,1146,a)].
% 7.50/7.72 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(1271,a,1147,b)].
% 7.50/7.72 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(1271,a,1148,b)].
% 7.50/7.72 1272 -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(901,b,889,a)].
% 7.50/7.72 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(1272,a,1121,a)].
% 7.50/7.72 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(1272,a,1146,a)].
% 7.50/7.72 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(1272,a,1147,b)].
% 7.50/7.72 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(1272,a,1148,b)].
% 7.50/7.72 1273 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(904,a,901,b)].
% 7.50/7.72 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1273,b,1121,a)].
% 7.50/7.72 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(1273,b,1146,a)].
% 7.50/7.72 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1273,b,1147,b)].
% 7.70/7.90 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1273,b,1148,b)].
% 7.70/7.90 1274 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(905,a,901,b)].
% 7.70/7.90 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1274,b,1121,a)].
% 7.70/7.90 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(1274,b,1146,a)].
% 7.70/7.90 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1274,b,1147,b)].
% 7.70/7.90 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1274,b,1148,b)].
% 7.70/7.90 1275 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1091,b,1076,a)].
% 7.70/7.90 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1275,a,1121,a)].
% 7.70/7.90 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1275,a,1146,a)].
% 7.70/7.90 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1275,a,1147,b)].
% 7.70/7.90 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1275,a,1148,b)].
% 7.70/7.90 1276 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1114,b,1099,a)].
% 7.70/7.90 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1276,a,1121,a)].
% 7.70/7.90 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1276,a,1146,a)].
% 7.70/7.90 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1276,a,1147,b)].
% 7.70/7.90 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1276,a,1148,b)].
% 7.70/7.90 1277 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 7.70/7.90 1278 -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].
% 7.70/7.90 1279 -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].
% 7.70/7.90 1280 -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].
% 7.70/7.90 1281 -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].
% 7.70/7.90 1282 -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].
% 7.70/7.90 1283 -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].
% 7.70/7.90 1284 -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].
% 7.70/7.90 1285 -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].
% 7.70/7.90 1286 -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].
% 7.70/7.90 1287 -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].
% 7.70/7.90 1288 -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].
% 7.70/7.90 1289 -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].
% 7.70/7.90 1290 -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].
% 7.70/7.90 1291 -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].
% 7.70/7.90 1292 -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].
% 7.70/7.90 1293 -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].
% 7.70/7.90 1294 -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].
% 7.70/7.90 1295 -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].
% 7.70/7.90 1296 -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].
% 7.70/7.90 1297 -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].
% 7.70/7.90 1298 -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].
% 7.70/7.90 1299 -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].
% 7.70/7.90 1300 -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].
% 7.70/7.90 1301 -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].
% 7.70/7.90 1302 -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].
% 7.70/7.90 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(1277,a,1278,b)].
% 7.70/7.90 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(1277,a,1279,b)].
% 7.70/7.90 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(1277,a,1280,b)].
% 7.70/7.90 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(1277,a,1281,b)].
% 7.70/7.90 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(1277,a,1282,b)].
% 7.70/7.90 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(1277,a,1283,b)].
% 7.70/7.90 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(1277,a,1284,b)].
% 7.70/7.91 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(1277,a,1285,b)].
% 7.70/7.91 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(1277,a,1286,b)].
% 7.70/7.91 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(1277,a,1287,b)].
% 7.70/7.91 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(1277,a,1288,b)].
% 7.70/7.91 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(1277,a,1289,b)].
% 7.70/7.91 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(1277,a,1290,b)].
% 7.70/7.91 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(1277,a,1291,b)].
% 7.70/7.91 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(1277,a,1292,b)].
% 7.70/7.91 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(1277,a,1293,b)].
% 7.70/7.91 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(1277,a,1294,b)].
% 7.70/7.91 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(1277,a,1295,b)].
% 7.70/7.91 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(1277,a,1296,b)].
% 7.77/7.92 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(1277,a,1297,b)].
% 7.77/7.92 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(1277,a,1298,b)].
% 7.77/7.92 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(1277,a,1299,b)].
% 7.77/7.92 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(1277,a,1300,b)].
% 7.77/7.92 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(1277,a,1301,b)].
% 7.77/7.92 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(1277,a,1302,a)].
% 7.77/7.92 1303 -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].
% 7.77/7.92 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(1303,b,1278,b)].
% 7.77/7.92 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(1303,b,1279,b)].
% 7.77/7.92 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(1303,b,1280,b)].
% 7.77/7.92 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(1303,b,1281,b)].
% 7.77/7.92 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(1303,b,1282,b)].
% 7.77/7.92 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(1303,b,1283,b)].
% 7.77/7.92 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(1303,b,1284,b)].
% 7.77/7.93 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(1303,b,1285,b)].
% 7.77/7.93 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(1303,b,1286,b)].
% 7.77/7.93 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(1303,b,1287,b)].
% 7.77/7.93 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(1303,b,1288,b)].
% 7.77/7.93 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(1303,b,1289,b)].
% 7.77/7.93 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(1303,b,1290,b)].
% 7.77/7.93 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(1303,b,1291,b)].
% 7.77/7.93 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(1303,b,1292,b)].
% 7.77/7.93 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(1303,b,1293,b)].
% 7.77/7.93 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(1303,b,1294,b)].
% 7.77/7.93 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(1303,b,1295,b)].
% 7.77/7.93 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(1303,b,1296,b)].
% 7.77/7.93 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(1303,b,1297,b)].
% 7.77/7.93 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(1303,b,1298,b)].
% 7.77/7.93 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(1303,b,1299,b)].
% 7.77/7.94 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(1303,b,1300,b)].
% 7.77/7.94 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(1303,b,1301,b)].
% 7.77/7.94 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1303,b,1302,a)].
% 7.77/7.94 1304 -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].
% 7.77/7.94 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(1304,b,1278,b)].
% 7.77/7.94 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(1304,b,1279,b)].
% 7.77/7.94 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(1304,b,1280,b)].
% 7.77/7.94 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(1304,b,1281,b)].
% 7.77/7.94 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(1304,b,1282,b)].
% 7.77/7.94 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(1304,b,1283,b)].
% 7.77/7.94 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(1304,b,1284,b)].
% 7.77/7.94 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(1304,b,1285,b)].
% 7.77/7.94 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(1304,b,1286,b)].
% 7.77/7.94 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(1304,b,1287,b)].
% 7.77/7.94 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(1304,b,1288,b)].
% 7.77/7.94 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(1304,b,1289,b)].
% 7.77/7.95 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(1304,b,1290,b)].
% 7.77/7.95 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(1304,b,1291,b)].
% 7.77/7.95 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(1304,b,1292,b)].
% 7.77/7.95 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(1304,b,1293,b)].
% 7.77/7.95 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(1304,b,1294,b)].
% 7.77/7.95 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(1304,b,1295,b)].
% 7.77/7.95 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(1304,b,1296,b)].
% 7.77/7.95 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(1304,b,1297,b)].
% 7.77/7.95 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(1304,b,1298,b)].
% 7.77/7.95 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(1304,b,1299,b)].
% 7.77/7.95 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(1304,b,1300,b)].
% 7.77/7.95 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(1304,b,1301,b)].
% 7.77/7.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1304,b,1302,a)].
% 7.77/7.95 1305 -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].
% 7.77/7.95 1306 -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].
% 7.77/7.95 1307 -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].
% 7.77/7.95 1308 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_13) # label(axiom). [assumption].
% 7.77/7.95 1309 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_14) # label(axiom). [assumption].
% 7.77/7.96 1310 -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].
% 7.77/7.96 1311 -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].
% 7.77/7.96 1312 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 7.77/7.96 1313 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_2) # label(axiom). [assumption].
% 7.77/7.96 1314 -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].
% 7.77/7.96 1315 -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].
% 7.77/7.96 1316 -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].
% 7.77/7.96 1317 -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].
% 7.77/7.96 1318 -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].
% 7.77/7.96 1319 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom). [assumption].
% 7.77/7.96 1320 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 7.77/7.96 1321 -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].
% 7.77/7.96 Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1321,a,1277,a)].
% 7.77/7.96 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1321,a,1303,b)].
% 7.77/7.96 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1321,a,1304,b)].
% 7.77/7.96 1322 -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].
% 7.77/7.96 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1322,a,1277,a)].
% 7.77/7.96 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1322,a,1303,b)].
% 7.77/7.96 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1322,a,1304,b)].
% 7.77/7.96 1323 -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].
% 7.77/7.96 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1323,a,1277,a)].
% 7.77/7.96 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1323,a,1303,b)].
% 7.77/7.96 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1323,a,1304,b)].
% 7.77/7.96 1324 -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].
% 7.77/7.96 Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1324,a,1277,a)].
% 7.83/7.98 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1324,a,1303,b)].
% 7.83/7.98 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1324,a,1304,b)].
% 7.83/7.98 1325 -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].
% 7.83/7.98 Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1325,a,1277,a)].
% 7.83/7.98 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1325,a,1303,b)].
% 7.83/7.98 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1325,a,1304,b)].
% 7.83/7.98 1326 -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].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1326,a,1277,a)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1326,a,1303,b)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1326,a,1304,b)].
% 7.83/7.98 1327 -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].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1327,a,1277,a)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1327,a,1303,b)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1327,a,1304,b)].
% 7.83/7.98 1328 -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].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1328,a,1277,a)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1328,a,1303,b)].
% 7.83/7.98 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1328,a,1304,b)].
% 7.83/7.98 1329 -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].
% 7.83/7.98 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1329,a,1277,a)].
% 7.83/7.98 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1329,a,1303,b)].
% 7.83/7.98 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1329,a,1304,b)].
% 7.83/7.98 1330 -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].
% 7.83/7.98 1331 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_9) # label(axiom). [assumption].
% 7.83/7.98 1332 -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)].
% 7.83/7.98 1333 -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)].
% 7.83/7.98 1334 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 7.83/7.98 1335 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 7.83/7.98 1336 -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)].
% 7.83/7.98 1337 -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)].
% 7.83/8.01 1338 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(165,a,151,b)].
% 7.83/8.01 1339 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(166,a,151,b)].
% 7.83/8.01 1340 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(171,a,151,b)].
% 7.83/8.01 1341 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(172,a,151,b)].
% 7.83/8.01 1342 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 7.83/8.01 1343 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 7.83/8.01 1344 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(247,b,225,b)].
% 7.83/8.01 1345 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(248,b,225,b)].
% 7.83/8.01 1346 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,288,a)].
% 7.83/8.01 1347 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,290,a)].
% 7.83/8.01 1348 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(322,a,305,b)].
% 7.83/8.01 1349 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(323,a,305,b)].
% 7.83/8.01 1350 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(325,a,305,b)].
% 7.83/8.01 1351 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(326,a,305,b)].
% 7.83/8.01 1352 -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(346,b,331,b)].
% 7.83/8.01 1353 -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(346,b,333,b)].
% 7.83/8.01 1354 -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(346,b,334,a)].
% 7.83/8.01 1355 -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(346,b,335,a)].
% 7.83/8.01 1356 -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(346,b,336,a)].
% 7.83/8.01 1357 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,a,346,b)].
% 7.83/8.01 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1357,b,1303,b)].
% 7.83/8.01 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1357,b,1304,b)].
% 7.83/8.01 1358 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(355,a,346,b)].
% 7.83/8.01 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1358,b,1303,b)].
% 7.83/8.01 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1358,b,1304,b)].
% 7.83/8.01 1359 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,b,346,b)].
% 7.83/8.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1359,b,1303,b)].
% 7.83/8.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1359,b,1304,b)].
% 7.83/8.01 1360 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,b,346,b)].
% 7.83/8.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1360,b,1303,b)].
% 7.93/8.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1360,b,1304,b)].
% 7.93/8.09 1361 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(370,b,346,b)].
% 7.93/8.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1361,b,1303,b)].
% 7.93/8.09 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1361,b,1304,b)].
% 7.93/8.09 1362 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(371,b,346,b)].
% 7.93/8.09 1363 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(372,b,346,b)].
% 7.93/8.09 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1363,b,1303,b)].
% 7.93/8.09 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1363,b,1304,b)].
% 7.93/8.09 1364 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(373,b,346,b)].
% 7.93/8.09 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1364,b,1303,b)].
% 7.93/8.09 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1364,b,1304,b)].
% 7.93/8.09 1365 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(374,a,346,b)].
% 7.93/8.09 1366 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(375,a,346,b)].
% 7.93/8.09 1367 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(376,c,346,b)].
% 7.93/8.09 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1367,c,1303,b)].
% 7.93/8.09 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1367,c,1304,b)].
% 7.93/8.09 1368 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(377,c,346,b)].
% 7.93/8.09 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1368,c,1303,b)].
% 7.93/8.09 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1368,c,1304,b)].
% 7.93/8.09 1369 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(812,a,734,a)].
% 7.93/8.09 1370 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(812,a,741,a)].
% 7.93/8.09 1371 -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(900,b,832,a)].
% 7.93/8.09 1372 -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(900,b,833,a)].
% 7.93/8.09 1373 -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(900,b,834,a)].
% 7.93/8.09 1374 -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(900,b,835,a)].
% 7.93/8.09 1375 -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(900,b,836,a)].
% 7.93/8.09 1376 -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(900,b,837,a)].
% 7.93/8.09 1377 -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(900,b,838,a)].
% 7.93/8.10 1378 -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(900,b,839,a)].
% 7.93/8.10 1379 -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(900,b,840,a)].
% 7.93/8.10 1380 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,841,a)].
% 7.93/8.10 1381 -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(900,b,842,a)].
% 7.93/8.10 1382 -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(900,b,843,a)].
% 7.93/8.10 1383 -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(900,b,844,a)].
% 7.93/8.10 1384 -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(900,b,845,a)].
% 7.93/8.10 1385 -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(900,b,846,a)].
% 7.93/8.10 1386 -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(900,b,847,a)].
% 7.93/8.10 1387 -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(900,b,848,a)].
% 7.93/8.10 1388 -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(900,b,849,a)].
% 7.93/8.10 1389 -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(900,b,850,a)].
% 7.93/8.10 1390 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,851,a)].
% 7.93/8.10 1391 -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(900,b,852,a)].
% 7.93/8.10 1392 -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(900,b,853,a)].
% 7.93/8.10 1393 -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(900,b,854,a)].
% 7.93/8.10 1394 -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(900,b,855,b)].
% 7.93/8.10 1395 -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(900,b,856,b)].
% 7.93/8.10 1396 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(900,b,857,a)].
% 7.93/8.10 1397 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(900,b,858,a)].
% 7.93/8.10 1398 -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(900,b,859,a)].
% 7.93/8.11 1399 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(900,b,860,a)].
% 7.93/8.11 1400 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(900,b,861,a)].
% 7.93/8.11 1401 -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(900,b,862,a)].
% 7.93/8.11 1402 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(900,b,863,a)].
% 7.93/8.11 1403 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(900,b,864,a)].
% 7.93/8.11 1404 -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(900,b,865,a)].
% 7.93/8.11 1405 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(900,b,866,a)].
% 7.93/8.11 1406 -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(900,b,867,a)].
% 7.93/8.11 1407 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(900,b,868,a)].
% 7.93/8.11 1408 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(900,b,869,a)].
% 7.93/8.11 1409 -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(900,b,870,a)].
% 7.93/8.11 1410 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(900,b,871,a)].
% 7.93/8.11 1411 -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(900,b,872,a)].
% 7.93/8.11 1412 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(900,b,873,a)].
% 7.93/8.11 1413 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(900,b,874,a)].
% 7.93/8.11 1414 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(900,b,875,a)].
% 7.93/8.11 1415 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(900,b,876,a)].
% 7.93/8.11 1416 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(900,b,877,a)].
% 7.93/8.11 1417 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(900,b,878,a)].
% 7.93/8.11 1418 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(900,b,879,a)].
% 7.93/8.11 1419 -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(900,b,880,a)].
% 7.93/8.11 1420 -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(900,b,881,a)].
% 7.93/8.11 1421 -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(900,b,882,a)].
% 7.93/8.11 1422 -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(900,b,883,a)].
% 7.93/8.11 1423 -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(900,b,884,a)].
% 8.12/8.32 1424 -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(900,b,885,a)].
% 8.12/8.32 1425 -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(900,b,886,a)].
% 8.12/8.32 1426 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(900,b,887,a)].
% 8.12/8.32 1427 -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(900,b,888,a)].
% 8.12/8.32 1428 -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(900,b,889,a)].
% 8.12/8.32 1429 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(904,a,900,b)].
% 8.12/8.32 1430 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(905,a,900,b)].
% 8.12/8.32 1431 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1090,b,1076,a)].
% 8.12/8.32 1432 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1113,b,1099,a)].
% 8.12/8.32 1433 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 8.12/8.32 1434 -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].
% 8.12/8.32 1435 -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].
% 8.12/8.32 1436 -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].
% 8.12/8.32 1437 -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].
% 8.12/8.32 1438 -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].
% 8.12/8.32 1439 -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].
% 8.12/8.32 1440 -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].
% 8.12/8.32 1441 -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].
% 8.12/8.32 1442 -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].
% 8.12/8.32 1443 -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].
% 8.12/8.32 1444 -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].
% 8.12/8.32 1445 -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].
% 8.12/8.32 1446 -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].
% 8.12/8.32 1447 -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].
% 8.12/8.33 1448 -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].
% 8.12/8.33 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1434,a)].
% 8.12/8.33 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(1433,a,1435,a)].
% 8.12/8.33 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(1433,a,1436,a)].
% 8.12/8.33 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1433,a,1437,a)].
% 8.12/8.33 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(1433,a,1438,a)].
% 8.12/8.33 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1433,a,1439,a)].
% 8.12/8.33 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1433,a,1440,a)].
% 8.12/8.33 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1441,a)].
% 8.12/8.33 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1433,a,1442,a)].
% 8.12/8.33 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1433,a,1443,a)].
% 8.12/8.33 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1433,a,1444,a)].
% 8.12/8.33 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(1433,a,1445,a)].
% 8.12/8.33 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(1433,a,1446,a)].
% 8.12/8.33 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1433,a,1447,a)].
% 8.12/8.33 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1448,a)].
% 8.12/8.33 1449 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 8.12/8.33 1450 -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].
% 8.12/8.33 1451 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 8.12/8.33 1452 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom). [assumption].
% 8.12/8.33 1453 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 8.12/8.33 1454 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 8.12/8.33 1455 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 8.12/8.33 1456 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 8.12/8.33 1457 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom). [assumption].
% 8.12/8.33 1458 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 8.12/8.33 1459 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom). [assumption].
% 8.12/8.33 1460 -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].
% 8.12/8.33 1461 -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].
% 8.12/8.35 1462 -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].
% 8.12/8.35 1463 -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].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1463,b,1434,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1463,b,1435,a)].
% 8.12/8.35 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(1463,b,1436,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1463,b,1437,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1463,b,1438,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1463,b,1439,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1440,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1463,b,1441,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1463,b,1442,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1443,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1463,b,1444,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1463,b,1445,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1463,b,1446,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1463,b,1447,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1463,b,1448,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1463,b,1450,a)].
% 8.12/8.35 1464 -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].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1464,b,1434,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1464,b,1435,a)].
% 8.12/8.35 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(1464,b,1436,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1464,b,1437,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1464,b,1438,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1464,b,1439,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1464,b,1440,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1464,b,1441,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1464,b,1442,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1464,b,1443,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1464,b,1444,a)].
% 8.12/8.35 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1464,b,1445,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1464,b,1446,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1464,b,1447,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1464,b,1448,a)].
% 8.38/8.57 1465 -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].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1465,b,1434,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1465,b,1435,a)].
% 8.38/8.57 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(1465,b,1436,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1465,b,1437,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1465,b,1438,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1465,b,1439,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1465,b,1440,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1465,b,1441,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1465,b,1442,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1465,b,1443,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1465,b,1444,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1465,b,1445,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1465,b,1446,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1465,b,1447,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1465,b,1448,a)].
% 8.38/8.57 1466 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_HOL_Oabs(c_plus(B,C,A),A),c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) # label(cls_OrderedGroup_Oabs__triangle__ineq_0) # label(axiom). [assumption].
% 8.38/8.57 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,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),tc_IntDef_Oint). [resolve(1466,a,1433,a)].
% 8.38/8.57 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1466,a,1463,b)].
% 8.38/8.57 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1466,a,1464,b)].
% 8.38/8.57 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1466,a,1465,b)].
% 8.38/8.57 1467 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(12,b,1,a)].
% 8.38/8.57 1468 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(12,b,3,a)].
% 8.38/8.57 1469 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 8.38/8.57 1470 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 8.38/8.57 1471 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1076,a)].
% 8.38/8.57 1472 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1099,a)].
% 8.38/8.57 1473 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1326,a,1277,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1473,a,1449,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1473,a,1450,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1473,a,1451,a)].
% 8.38/8.57 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1473,a,1452,a)].
% 8.38/8.57 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1473,a,1453,a)].
% 8.38/8.57 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1473,a,1454,a)].
% 8.38/8.57 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1473,a,1455,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1473,a,1456,a)].
% 8.38/8.57 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1473,a,1457,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1473,a,1458,a)].
% 8.38/8.57 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1473,a,1459,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1473,a,1460,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1461,a)].
% 8.38/8.57 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1462,a)].
% 8.38/8.57 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1473,a,1467,a)].
% 8.38/8.57 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1473,a,1468,a)].
% 8.38/8.57 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1473,a,1471,a)].
% 8.38/8.57 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1473,a,1472,a)].
% 8.38/8.57 1474 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1326,a,1303,b)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1474,a,1449,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1474,a,1450,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1474,a,1451,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1474,a,1452,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1474,a,1453,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1474,a,1454,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1474,a,1455,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A). [resolve(1474,a,1459,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1474,a,1460,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1474,a,1461,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1474,a,1462,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1474,a,1471,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1474,a,1472,a)].
% 8.38/8.57 1475 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1326,a,1304,b)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1475,a,1449,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1475,a,1450,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1475,a,1451,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1475,a,1452,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1475,a,1453,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1475,a,1454,a)].
% 8.38/8.57 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1475,a,1455,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(1475,a,1459,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1475,a,1460,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1475,a,1461,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1475,a,1462,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1475,a,1471,a)].
% 8.54/8.69 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1475,a,1472,a)].
% 8.54/8.69 1476 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 8.54/8.69 1477 -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].
% 8.54/8.69 1478 -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].
% 8.54/8.69 1479 -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].
% 8.54/8.69 1480 -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].
% 8.54/8.69 1481 -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].
% 8.54/8.69 1482 -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].
% 8.54/8.69 1483 -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].
% 8.54/8.69 1484 -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].
% 8.54/8.69 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(1476,a,1477,a)].
% 8.54/8.69 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(1476,a,1478,a)].
% 8.54/8.69 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(1476,a,1479,a)].
% 8.54/8.69 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(1476,a,1480,a)].
% 8.54/8.69 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(1476,a,1481,a)].
% 8.54/8.69 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(1476,a,1482,a)].
% 8.54/8.69 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(1476,a,1483,a)].
% 8.54/8.69 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(1476,a,1484,a)].
% 8.54/8.69 1485 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 8.54/8.69 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1485,a,1477,a)].
% 8.54/8.69 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1485,a,1478,a)].
% 8.54/8.70 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1485,a,1479,a)].
% 8.54/8.70 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1485,a,1480,a)].
% 8.54/8.70 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1485,a,1481,a)].
% 8.54/8.70 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1485,a,1482,a)].
% 8.54/8.70 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1485,a,1483,a)].
% 8.54/8.70 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1485,a,1484,a)].
% 8.54/8.70 1486 -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].
% 8.54/8.70 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(1486,b,1477,a)].
% 8.54/8.70 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(1486,b,1478,a)].
% 8.54/8.70 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(1486,b,1479,a)].
% 8.54/8.70 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(1486,b,1480,a)].
% 8.54/8.70 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(1486,b,1481,a)].
% 8.54/8.70 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(1486,b,1482,a)].
% 8.54/8.70 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(1486,b,1483,a)].
% 8.54/8.70 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(1486,b,1484,a)].
% 8.54/8.70 1487 -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].
% 8.54/8.70 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(1487,b,1477,a)].
% 8.54/8.70 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(1487,b,1478,a)].
% 8.54/8.70 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(1487,b,1479,a)].
% 8.54/8.70 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(1487,b,1480,a)].
% 8.54/8.70 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(1487,b,1481,a)].
% 8.54/8.70 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(1487,b,1482,a)].
% 8.54/8.70 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(1487,b,1483,a)].
% 8.54/8.70 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(1487,b,1484,a)].
% 8.54/8.70 1488 -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].
% 8.54/8.70 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(1488,b,1477,a)].
% 8.54/8.70 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(1488,b,1478,a)].
% 8.54/8.70 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(1488,b,1479,a)].
% 8.57/8.71 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(1488,b,1480,a)].
% 8.57/8.71 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(1488,b,1481,a)].
% 8.57/8.71 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(1488,b,1482,a)].
% 8.57/8.71 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(1488,b,1483,a)].
% 8.57/8.71 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(1488,b,1484,a)].
% 8.57/8.71 1489 -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].
% 8.57/8.71 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(1489,b,1477,a)].
% 8.57/8.71 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(1489,b,1478,a)].
% 8.57/8.71 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(1489,b,1479,a)].
% 8.57/8.71 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(1489,b,1480,a)].
% 8.57/8.71 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(1489,b,1481,a)].
% 8.57/8.71 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(1489,b,1482,a)].
% 8.57/8.71 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(1489,b,1483,a)].
% 8.57/8.71 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(1489,b,1484,a)].
% 8.57/8.71 1490 -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].
% 8.57/8.71 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(1490,b,1477,a)].
% 8.57/8.71 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(1490,b,1478,a)].
% 8.57/8.71 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(1490,b,1479,a)].
% 8.57/8.71 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(1490,b,1480,a)].
% 8.57/8.71 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(1490,b,1481,a)].
% 8.57/8.71 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(1490,b,1482,a)].
% 8.57/8.71 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(1490,b,1483,a)].
% 8.57/8.71 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(1490,b,1484,a)].
% 8.57/8.71 1491 -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].
% 8.57/8.71 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,a,1486,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,a,1487,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,a,1488,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,a,1489,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,a,1490,b)].
% 8.58/8.73 1492 -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].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1492,a,1486,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1492,a,1487,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1492,a,1488,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1492,a,1489,b)].
% 8.58/8.73 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1492,a,1490,b)].
% 8.58/8.73 1493 -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].
% 8.58/8.73 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1493,a,1486,b)].
% 8.58/8.73 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1493,a,1487,b)].
% 8.58/8.73 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1493,a,1488,b)].
% 8.58/8.73 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1493,a,1490,b)].
% 8.58/8.73 1494 -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].
% 8.58/8.73 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1494,a,1486,b)].
% 8.58/8.73 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1494,a,1487,b)].
% 8.58/8.73 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1494,a,1488,b)].
% 8.58/8.73 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1494,a,1490,b)].
% 8.58/8.73 1495 -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].
% 8.58/8.73 1496 -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].
% 8.58/8.73 1497 -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].
% 8.58/8.73 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(1497,b,1477,a)].
% 8.58/8.73 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(1497,b,1478,a)].
% 8.58/8.73 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(1497,b,1479,a)].
% 8.58/8.73 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(1497,b,1480,a)].
% 8.58/8.73 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(1497,b,1481,a)].
% 8.58/8.74 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(1497,b,1482,a)].
% 8.58/8.74 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(1497,b,1483,a)].
% 8.58/8.74 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(1497,b,1484,a)].
% 8.58/8.74 1498 -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].
% 8.58/8.74 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(1498,b,1477,a)].
% 8.58/8.74 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(1498,b,1478,a)].
% 8.58/8.74 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(1498,b,1479,a)].
% 8.58/8.74 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(1498,b,1480,a)].
% 8.58/8.74 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(1498,b,1481,a)].
% 8.58/8.74 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(1498,b,1482,a)].
% 8.58/8.74 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(1498,b,1483,a)].
% 8.58/8.74 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(1498,b,1484,a)].
% 8.58/8.74 1499 -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].
% 8.58/8.74 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(1499,b,1477,a)].
% 8.58/8.74 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(1499,b,1478,a)].
% 8.58/8.74 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(1499,b,1479,a)].
% 8.58/8.74 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(1499,b,1480,a)].
% 8.58/8.74 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(1499,b,1481,a)].
% 8.58/8.74 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(1499,b,1482,a)].
% 8.58/8.74 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(1499,b,1483,a)].
% 8.58/8.74 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(1499,b,1484,a)].
% 8.58/8.74 1500 -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].
% 8.58/8.74 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(1500,b,1477,a)].
% 8.58/8.74 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(1500,b,1478,a)].
% 8.58/8.74 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(1500,b,1479,a)].
% 8.58/8.74 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(1500,b,1480,a)].
% 8.58/8.76 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(1500,b,1481,a)].
% 8.58/8.76 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(1500,b,1482,a)].
% 8.58/8.76 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(1500,b,1483,a)].
% 8.58/8.76 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(1500,b,1484,a)].
% 8.58/8.76 1501 -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].
% 8.58/8.76 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(1501,b,1477,a)].
% 8.58/8.76 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(1501,b,1478,a)].
% 8.58/8.76 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(1501,b,1479,a)].
% 8.58/8.76 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(1501,b,1480,a)].
% 8.58/8.76 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(1501,b,1481,a)].
% 8.58/8.76 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(1501,b,1482,a)].
% 8.58/8.76 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(1501,b,1483,a)].
% 8.58/8.76 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(1501,b,1484,a)].
% 8.58/8.76 1502 -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].
% 8.58/8.76 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(1502,b,1477,a)].
% 8.58/8.76 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(1502,b,1478,a)].
% 8.58/8.76 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(1502,b,1479,a)].
% 8.58/8.76 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(1502,b,1480,a)].
% 8.58/8.76 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(1502,b,1481,a)].
% 8.58/8.76 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(1502,b,1482,a)].
% 8.58/8.76 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(1502,b,1483,a)].
% 8.58/8.76 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(1502,b,1484,a)].
% 8.58/8.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1502,b,1492,a)].
% 8.58/8.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1502,b,1493,a)].
% 8.58/8.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1502,b,1494,a)].
% 8.58/8.76 1503 -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)].
% 8.58/8.76 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1503,a,1486,b)].
% 8.58/8.76 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1503,a,1487,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1503,a,1488,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1503,a,1489,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1503,a,1490,b)].
% 8.83/8.97 1504 -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)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1504,a,1486,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1504,a,1487,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1504,a,1488,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1504,a,1489,b)].
% 8.83/8.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1504,a,1490,b)].
% 8.83/8.97 1505 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1505,b,1486,b)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1505,b,1487,b)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1505,b,1488,b)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1505,b,1489,b)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1505,b,1490,b)].
% 8.83/8.97 1506 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 8.83/8.97 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1506,b,1486,b)].
% 8.83/8.97 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1506,b,1487,b)].
% 8.83/8.97 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1506,b,1488,b)].
% 8.83/8.97 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1506,b,1489,b)].
% 8.83/8.97 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1506,b,1490,b)].
% 8.83/8.97 1507 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1160,a,1121,a)].
% 8.83/8.97 1508 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1160,a,1146,a)].
% 8.83/8.97 Derived: class_Orderings_Oorder(tc_nat). [resolve(1508,a,1493,a)].
% 8.83/8.97 Derived: class_Orderings_Oord(tc_nat). [resolve(1508,a,1494,a)].
% 8.83/8.97 Derived: class_HOL_Oplus(tc_nat). [resolve(1508,a,1496,a)].
% 8.83/8.97 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1508,a,1503,a)].
% 8.83/8.97 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1508,a,1504,a)].
% 8.83/8.97 1509 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1147,b)].
% 8.83/8.97 1510 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1148,b)].
% 8.83/8.97 1511 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1473,a,1460,a)].
% 8.83/8.97 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1511,a,1493,a)].
% 8.83/8.97 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1511,a,1494,a)].
% 8.83/8.97 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1511,a,1495,a)].
% 8.83/8.97 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1511,a,1496,a)].
% 8.83/8.97 1512 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1474,a,1460,a)].
% 8.83/8.97 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1512,b,1493,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1512,b,1494,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1512,b,1495,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1512,b,1496,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1512,b,1503,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1512,b,1504,a)].
% 8.89/9.10 1513 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1475,a,1460,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1513,b,1493,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1513,b,1494,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1513,b,1495,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1513,b,1496,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1513,b,1503,a)].
% 8.89/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1513,b,1504,a)].
% 8.89/9.10 1514 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 8.89/9.10 1515 -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].
% 8.89/9.10 1516 -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].
% 8.89/9.10 1517 -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].
% 8.89/9.10 1518 -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].
% 8.89/9.10 1519 -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].
% 8.89/9.10 1520 -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].
% 8.89/9.10 1521 -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].
% 8.89/9.10 1522 -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].
% 8.89/9.10 1523 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 8.89/9.10 1524 -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].
% 8.89/9.10 1525 -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].
% 8.89/9.10 1526 -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].
% 8.89/9.10 1527 -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].
% 8.89/9.10 1528 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 8.89/9.11 1529 -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].
% 8.89/9.11 1530 -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].
% 8.89/9.11 1531 -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].
% 8.89/9.11 1532 -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].
% 8.89/9.11 1533 -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].
% 8.89/9.11 1534 -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].
% 8.89/9.11 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(1514,a,1515,a)].
% 8.89/9.11 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1514,a,1516,a)].
% 8.89/9.11 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1514,a,1517,a)].
% 8.89/9.11 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1514,a,1518,a)].
% 8.89/9.11 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1514,a,1519,a)].
% 8.89/9.11 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1514,a,1520,a)].
% 8.89/9.11 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(1514,a,1521,a)].
% 8.89/9.11 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(1514,a,1522,a)].
% 8.89/9.11 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1514,a,1523,a)].
% 8.89/9.11 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(1514,a,1524,a)].
% 8.89/9.11 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(1514,a,1525,a)].
% 8.89/9.11 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1514,a,1526,a)].
% 8.89/9.11 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(1514,a,1527,a)].
% 8.89/9.11 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1514,a,1528,a)].
% 8.89/9.11 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(1514,a,1529,a)].
% 8.89/9.11 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(1514,a,1530,a)].
% 8.89/9.11 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(1514,a,1531,a)].
% 8.89/9.11 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(1514,a,1532,a)].
% 8.89/9.11 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1533,a)].
% 8.89/9.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1534,a)].
% 8.89/9.11 1535 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 8.89/9.11 1536 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 8.98/9.12 1537 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 8.98/9.12 1538 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom). [assumption].
% 8.98/9.12 1539 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 8.98/9.12 1540 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom). [assumption].
% 8.98/9.12 1541 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 8.98/9.12 1542 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom). [assumption].
% 8.98/9.12 1543 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 8.98/9.12 1544 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 8.98/9.12 1545 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 8.98/9.12 1546 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 8.98/9.12 1547 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 8.98/9.12 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(1547,b,1515,a)].
% 8.98/9.12 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(1547,b,1516,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1517,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1518,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1519,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1520,a)].
% 8.98/9.12 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(1547,b,1521,a)].
% 8.98/9.12 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(1547,b,1522,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1547,b,1523,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1547,b,1524,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1547,b,1525,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1547,b,1526,a)].
% 8.98/9.12 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(1547,b,1527,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1547,b,1528,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1547,b,1529,a)].
% 8.98/9.12 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1547,b,1530,a)].
% 8.98/9.13 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(1547,b,1531,a)].
% 8.98/9.13 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(1547,b,1532,a)].
% 8.98/9.13 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(1547,b,1533,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1547,b,1534,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1547,b,1535,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1536,a)].
% 8.98/9.13 1548 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 8.98/9.13 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(1548,b,1515,a)].
% 8.98/9.13 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(1548,b,1516,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1517,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1518,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1519,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1520,a)].
% 8.98/9.13 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(1548,b,1521,a)].
% 8.98/9.13 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(1548,b,1522,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1548,b,1523,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1548,b,1524,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1548,b,1525,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1548,b,1526,a)].
% 8.98/9.13 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(1548,b,1527,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1548,b,1528,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1548,b,1529,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1548,b,1530,a)].
% 8.98/9.13 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(1548,b,1531,a)].
% 8.98/9.13 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(1548,b,1532,a)].
% 8.98/9.13 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(1548,b,1533,a)].
% 8.98/9.13 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1548,b,1534,a)].
% 8.98/9.15 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1548,b,1535,a)].
% 8.98/9.15 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1536,a)].
% 8.98/9.15 1549 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 8.98/9.15 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(1549,b,1515,a)].
% 8.98/9.15 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(1549,b,1516,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1517,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1518,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1519,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1520,a)].
% 8.98/9.15 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(1549,b,1521,a)].
% 8.98/9.15 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(1549,b,1522,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1549,b,1523,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1549,b,1524,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1549,b,1525,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1549,b,1526,a)].
% 8.98/9.15 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(1549,b,1527,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1549,b,1528,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1549,b,1529,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1549,b,1530,a)].
% 8.98/9.15 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(1549,b,1531,a)].
% 8.98/9.15 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(1549,b,1532,a)].
% 8.98/9.15 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(1549,b,1533,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1549,b,1534,a)].
% 8.98/9.15 1550 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 8.98/9.15 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(1550,b,1515,a)].
% 8.98/9.15 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(1550,b,1516,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1550,b,1517,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1550,b,1518,a)].
% 8.98/9.15 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1550,b,1519,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1550,b,1520,a)].
% 8.98/9.16 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(1550,b,1521,a)].
% 8.98/9.16 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(1550,b,1522,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1550,b,1523,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1550,b,1524,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1550,b,1525,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1550,b,1526,a)].
% 8.98/9.16 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(1550,b,1527,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1550,b,1528,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1550,b,1529,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1550,b,1530,a)].
% 8.98/9.16 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(1550,b,1531,a)].
% 8.98/9.16 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(1550,b,1532,a)].
% 8.98/9.16 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(1550,b,1533,a)].
% 8.98/9.16 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1550,b,1534,a)].
% 8.98/9.17 1551 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 8.98/9.17 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(1551,b,1515,a)].
% 8.98/9.17 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(1551,b,1516,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1551,b,1517,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1551,b,1518,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1551,b,1519,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1551,b,1520,a)].
% 8.98/9.17 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(1551,b,1521,a)].
% 8.98/9.17 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(1551,b,1522,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1551,b,1523,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1551,b,1524,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1551,b,1525,a)].
% 8.98/9.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1551,b,1526,a)].
% 8.98/9.17 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(1551,b,1527,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1551,b,1528,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1551,b,1529,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1551,b,1530,a)].
% 9.26/9.40 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(1551,b,1531,a)].
% 9.26/9.40 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(1551,b,1532,a)].
% 9.26/9.40 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(1551,b,1533,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1551,b,1534,a)].
% 9.26/9.40 1552 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 9.26/9.40 1553 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 9.26/9.40 1554 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 9.26/9.40 1555 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 9.26/9.40 1556 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1076,a)].
% 9.26/9.40 1557 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1099,a)].
% 9.26/9.40 1558 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1322,a,1277,a)].
% 9.26/9.40 1559 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1322,a,1303,b)].
% 9.26/9.40 1560 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1322,a,1304,b)].
% 9.26/9.40 1561 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1473,a,1449,a)].
% 9.26/9.40 1562 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1474,a,1449,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1562,b,1536,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A). [resolve(1562,b,1540,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1562,b,1541,a)].
% 9.26/9.40 1563 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1475,a,1449,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1563,b,1536,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A). [resolve(1563,b,1540,a)].
% 9.26/9.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1563,b,1541,a)].
% 9.26/9.40 1564 -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(1486,b,1477,a)].
% 9.26/9.40 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(1564,a,1514,a)].
% 9.26/9.40 1565 -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(1486,b,1478,a)].
% 9.26/9.40 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(1565,a,1514,a)].
% 9.26/9.40 1566 -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(1486,b,1479,a)].
% 9.26/9.40 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(1566,a,1514,a)].
% 9.26/9.40 1567 -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(1486,b,1480,a)].
% 9.26/9.40 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(1567,a,1514,a)].
% 9.36/9.54 1568 -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(1486,b,1481,a)].
% 9.36/9.54 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(1568,a,1514,a)].
% 9.36/9.54 1569 -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(1486,b,1482,a)].
% 9.36/9.54 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(1569,a,1514,a)].
% 9.36/9.54 1570 -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(1486,b,1483,a)].
% 9.36/9.54 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(1570,a,1514,a)].
% 9.36/9.54 1571 -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(1486,b,1484,a)].
% 9.36/9.54 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(1571,a,1514,a)].
% 9.36/9.54 1572 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,a,1486,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1572,b,1514,a)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1572,b,1549,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1572,b,1550,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1572,b,1551,b)].
% 9.36/9.54 1573 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1492,a,1486,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1573,b,1514,a)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1573,b,1549,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1573,b,1550,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1573,b,1551,b)].
% 9.36/9.54 1574 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1493,a,1486,b)].
% 9.36/9.54 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1574,b,1549,b)].
% 9.36/9.54 1575 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1494,a,1486,b)].
% 9.36/9.54 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1575,b,1549,b)].
% 9.36/9.54 1576 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1503,a,1486,b)].
% 9.36/9.54 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1576,c,1514,a)].
% 9.36/9.54 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1576,c,1549,b)].
% 9.36/9.54 1577 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1504,a,1486,b)].
% 9.36/9.54 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1577,c,1514,a)].
% 9.36/9.54 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1577,c,1549,b)].
% 9.36/9.54 1578 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1505,b,1486,b)].
% 9.36/9.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1578,b,1549,b)].
% 9.36/9.54 1579 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1506,b,1486,b)].
% 9.36/9.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1579,b,1549,b)].
% 9.36/9.54 1580 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 9.36/9.55 1581 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 9.36/9.55 1582 -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].
% 9.36/9.55 1583 -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].
% 9.36/9.55 1584 -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].
% 9.36/9.55 1585 -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].
% 9.36/9.55 1586 -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].
% 9.36/9.55 1587 -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].
% 9.36/9.55 1588 -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].
% 9.36/9.55 1589 -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].
% 9.36/9.55 1590 -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].
% 9.36/9.55 1591 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 9.36/9.55 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1580,a,1581,a)].
% 9.36/9.55 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1582,a)].
% 9.36/9.55 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1580,a,1583,a)].
% 9.36/9.55 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1584,a)].
% 9.36/9.55 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(1580,a,1585,a)].
% 9.36/9.55 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(1580,a,1586,a)].
% 9.36/9.55 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(1580,a,1587,a)].
% 9.36/9.55 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(1580,a,1588,a)].
% 9.36/9.55 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1589,a)].
% 9.36/9.55 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(1580,a,1590,a)].
% 9.36/9.55 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1580,a,1591,a)].
% 9.36/9.55 1592 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 9.36/9.55 Derived: -c_less(A,A,tc_nat). [resolve(1592,a,1581,a)].
% 9.36/9.55 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1582,a)].
% 9.36/9.55 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1592,a,1583,a)].
% 9.36/9.56 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1584,a)].
% 9.36/9.56 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(1592,a,1585,a)].
% 9.36/9.56 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(1592,a,1586,a)].
% 9.36/9.56 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(1592,a,1587,a)].
% 9.36/9.56 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(1592,a,1588,a)].
% 9.36/9.56 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1589,a)].
% 9.36/9.56 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(1592,a,1590,a)].
% 9.36/9.56 Derived: c_lessequals(A,A,tc_nat). [resolve(1592,a,1591,a)].
% 9.36/9.56 1593 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 9.36/9.56 Derived: -c_less(A,A,tc_set(B)). [resolve(1593,a,1581,a)].
% 9.36/9.56 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1582,a)].
% 9.36/9.56 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(1593,a,1583,a)].
% 9.36/9.56 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1584,a)].
% 9.36/9.56 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(1593,a,1585,a)].
% 9.36/9.56 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(1593,a,1586,a)].
% 9.36/9.56 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(1593,a,1587,a)].
% 9.36/9.56 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(1593,a,1588,a)].
% 9.36/9.56 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1589,a)].
% 9.36/9.56 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(1593,a,1590,a)].
% 9.36/9.56 Derived: c_lessequals(A,A,tc_set(B)). [resolve(1593,a,1591,a)].
% 9.36/9.56 1594 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 9.36/9.56 Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1594,b,1581,a)].
% 9.36/9.56 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1582,a)].
% 9.36/9.56 Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1594,b,1583,a)].
% 9.36/9.56 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1594,b,1584,a)].
% 9.36/9.56 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(1594,b,1585,a)].
% 9.36/9.56 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(1594,b,1586,a)].
% 9.36/9.56 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(1594,b,1587,a)].
% 9.36/9.56 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(1594,b,1588,a)].
% 9.36/9.56 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1589,a)].
% 9.44/9.57 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(1594,b,1590,a)].
% 9.44/9.57 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1594,b,1591,a)].
% 9.44/9.57 1595 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1595,b,1581,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1582,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1583,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1584,a)].
% 9.44/9.57 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(1595,b,1585,a)].
% 9.44/9.57 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(1595,b,1586,a)].
% 9.44/9.57 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(1595,b,1587,a)].
% 9.44/9.57 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(1595,b,1588,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1589,a)].
% 9.44/9.57 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(1595,b,1590,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1595,b,1591,a)].
% 9.44/9.57 1596 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1596,b,1581,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1582,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1583,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1584,a)].
% 9.44/9.57 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(1596,b,1585,a)].
% 9.44/9.57 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(1596,b,1586,a)].
% 9.44/9.57 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(1596,b,1587,a)].
% 9.44/9.57 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(1596,b,1588,a)].
% 9.44/9.57 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1589,a)].
% 9.44/9.57 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(1596,b,1590,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1596,b,1591,a)].
% 9.44/9.58 1597 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1597,b,1581,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1582,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1583,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1584,a)].
% 9.44/9.58 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(1597,b,1585,a)].
% 9.44/9.58 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(1597,b,1586,a)].
% 9.44/9.58 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(1597,b,1587,a)].
% 9.44/9.58 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(1597,b,1588,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1589,a)].
% 9.44/9.58 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(1597,b,1590,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1597,b,1591,a)].
% 9.44/9.58 1598 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A). [resolve(1598,b,1581,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1582,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1583,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1584,a)].
% 9.44/9.58 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(1598,b,1585,a)].
% 9.44/9.58 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(1598,b,1586,a)].
% 9.44/9.58 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(1598,b,1587,a)].
% 9.44/9.58 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(1598,b,1588,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1589,a)].
% 9.44/9.58 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(1598,b,1590,a)].
% 9.44/9.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(1598,b,1591,a)].
% 9.44/9.59 1599 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1599,b,1581,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1582,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1599,b,1583,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1599,b,1584,a)].
% 9.44/9.59 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(1599,b,1585,a)].
% 9.44/9.59 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(1599,b,1586,a)].
% 9.44/9.59 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(1599,b,1587,a)].
% 9.44/9.59 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(1599,b,1588,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1589,a)].
% 9.44/9.59 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(1599,b,1590,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1599,b,1591,a)].
% 9.44/9.59 1600 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1600,b,1581,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1582,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1600,b,1583,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1600,b,1584,a)].
% 9.44/9.59 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(1600,b,1585,a)].
% 9.44/9.59 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(1600,b,1586,a)].
% 9.44/9.59 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(1600,b,1587,a)].
% 9.44/9.59 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(1600,b,1588,a)].
% 9.44/9.59 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1589,a)].
% 9.44/9.59 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(1600,b,1590,a)].
% 9.44/9.61 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1600,b,1591,a)].
% 9.44/9.61 1601 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 9.44/9.61 Derived: class_Orderings_Oord(tc_set(A)). [resolve(1601,a,1593,a)].
% 9.44/9.61 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1601,a,1599,b)].
% 9.44/9.61 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1601,a,1600,b)].
% 9.44/9.61 1602 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1602,b,1581,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1582,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1602,b,1583,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1602,b,1584,a)].
% 9.44/9.61 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(1602,b,1585,a)].
% 9.44/9.61 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(1602,b,1586,a)].
% 9.44/9.61 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(1602,b,1587,a)].
% 9.44/9.61 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(1602,b,1588,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1589,a)].
% 9.44/9.61 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(1602,b,1590,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1602,b,1591,a)].
% 9.44/9.61 1603 -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].
% 9.44/9.61 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1603,b,1581,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1582,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1603,b,1583,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1603,b,1584,a)].
% 9.44/9.61 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(1603,b,1585,a)].
% 9.44/9.61 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(1603,b,1586,a)].
% 9.44/9.61 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(1603,b,1587,a)].
% 9.44/9.61 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(1603,b,1588,a)].
% 9.44/9.61 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1589,a)].
% 9.44/9.62 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(1603,b,1590,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1603,b,1591,a)].
% 9.44/9.62 1604 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A). [resolve(1604,b,1581,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1604,b,1582,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1604,b,1583,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1604,b,1584,a)].
% 9.44/9.62 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(1604,b,1585,a)].
% 9.44/9.62 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(1604,b,1586,a)].
% 9.44/9.62 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(1604,b,1587,a)].
% 9.44/9.62 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(1604,b,1588,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1604,b,1589,a)].
% 9.44/9.62 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(1604,b,1590,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(1604,b,1591,a)].
% 9.44/9.62 1605 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A). [resolve(1605,b,1581,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1605,b,1582,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1605,b,1583,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1605,b,1584,a)].
% 9.44/9.62 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(1605,b,1585,a)].
% 9.44/9.62 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(1605,b,1586,a)].
% 9.44/9.62 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(1605,b,1587,a)].
% 9.44/9.62 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(1605,b,1588,a)].
% 9.44/9.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1605,b,1589,a)].
% 9.44/9.62 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(1605,b,1590,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(1605,b,1591,a)].
% 9.44/9.63 1606 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom). [assumption].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1606,b,1581,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1582,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1606,b,1583,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1606,b,1584,a)].
% 9.44/9.63 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(1606,b,1585,a)].
% 9.44/9.63 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(1606,b,1586,a)].
% 9.44/9.63 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(1606,b,1587,a)].
% 9.44/9.63 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(1606,b,1588,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1589,a)].
% 9.44/9.63 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(1606,b,1590,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1606,b,1591,a)].
% 9.44/9.63 1607 -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].
% 9.44/9.63 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1607,b,1581,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1582,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1607,b,1583,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1607,b,1584,a)].
% 9.44/9.63 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(1607,b,1585,a)].
% 9.44/9.63 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(1607,b,1586,a)].
% 9.44/9.63 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(1607,b,1587,a)].
% 9.44/9.63 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(1607,b,1588,a)].
% 9.44/9.63 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1589,a)].
% 9.44/9.63 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(1607,b,1590,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1607,b,1591,a)].
% 9.44/9.64 1608 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom). [assumption].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1608,b,1581,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1582,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1608,b,1583,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1608,b,1584,a)].
% 9.44/9.64 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(1608,b,1585,a)].
% 9.44/9.64 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(1608,b,1586,a)].
% 9.44/9.64 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(1608,b,1587,a)].
% 9.44/9.64 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(1608,b,1588,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1589,a)].
% 9.44/9.64 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(1608,b,1590,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1608,b,1591,a)].
% 9.44/9.64 1609 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom). [assumption].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A). [resolve(1609,b,1581,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1609,b,1582,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1609,b,1583,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1609,b,1584,a)].
% 9.44/9.64 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(1609,b,1585,a)].
% 9.44/9.64 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(1609,b,1586,a)].
% 9.44/9.64 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(1609,b,1587,a)].
% 9.44/9.64 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(1609,b,1588,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1609,b,1589,a)].
% 9.44/9.64 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(1609,b,1590,a)].
% 9.44/9.64 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(1609,b,1591,a)].
% 9.44/9.65 1610 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom). [assumption].
% 9.44/9.65 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1610,b,1581,a)].
% 9.44/9.65 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1582,a)].
% 9.44/9.65 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1610,b,1583,a)].
% 9.44/9.65 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1610,b,1584,a)].
% 9.44/9.65 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(1610,b,1585,a)].
% 9.44/9.65 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(1610,b,1586,a)].
% 9.44/9.66 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(1610,b,1587,a)].
% 9.44/9.66 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(1610,b,1588,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1589,a)].
% 9.44/9.66 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(1610,b,1590,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1610,b,1591,a)].
% 9.44/9.66 1611 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1611,b,1581,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1582,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1611,b,1583,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1611,b,1584,a)].
% 9.44/9.66 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(1611,b,1585,a)].
% 9.44/9.66 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(1611,b,1586,a)].
% 9.44/9.66 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(1611,b,1587,a)].
% 9.44/9.66 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(1611,b,1588,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1589,a)].
% 9.44/9.66 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(1611,b,1590,a)].
% 9.44/9.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1611,b,1591,a)].
% 9.44/9.66 1612 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1612,b,1581,a)].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1582,a)].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1612,b,1583,a)].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1612,b,1584,a)].
% 9.44/9.67 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(1612,b,1585,a)].
% 9.44/9.67 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(1612,b,1586,a)].
% 9.44/9.67 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(1612,b,1587,a)].
% 9.44/9.67 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(1612,b,1588,a)].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1589,a)].
% 9.44/9.67 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(1612,b,1590,a)].
% 9.44/9.67 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1612,b,1591,a)].
% 9.44/9.67 1613 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1613,b,1581,a)].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1582,a)].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1613,b,1583,a)].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1613,b,1584,a)].
% 9.44/9.67 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(1613,b,1585,a)].
% 9.44/9.67 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(1613,b,1586,a)].
% 9.44/9.67 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(1613,b,1587,a)].
% 9.44/9.67 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(1613,b,1588,a)].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1589,a)].
% 9.44/9.67 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(1613,b,1590,a)].
% 9.44/9.67 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1613,b,1591,a)].
% 9.44/9.67 1614 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_lessequals(D,C,A) # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 9.44/9.67 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1614,a,1580,a)].
% 9.44/9.67 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1614,a,1592,a)].
% 9.55/9.68 Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_lessequals(D,B,tc_set(C)). [resolve(1614,a,1593,a)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1614,a,1594,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1614,a,1595,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1614,a,1596,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1597,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1614,a,1598,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1614,a,1599,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1600,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1614,a,1602,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1614,a,1603,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1614,a,1604,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1614,a,1605,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1614,a,1606,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1614,a,1607,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1614,a,1608,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1614,a,1609,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1614,a,1610,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1614,a,1611,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1614,a,1612,b)].
% 9.55/9.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1614,a,1613,b)].
% 9.55/9.68 1615 -class_Orderings_Oorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_less(B,D,A) # label(cls_Orderings_Oorder__less__le__trans_0) # label(axiom). [assumption].
% 9.55/9.68 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1615,a,1580,a)].
% 9.55/9.68 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(1615,a,1592,a)].
% 9.55/9.68 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(B,D,tc_set(C)) | c_less(A,D,tc_set(C)). [resolve(1615,a,1593,a)].
% 9.55/9.68 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_LOrder_Olorder(C). [resolve(1615,a,1594,b)].
% 9.55/9.68 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1615,a,1595,b)].
% 9.55/9.68 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1615,a,1596,b)].
% 9.55/9.68 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1597,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1615,a,1598,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1615,a,1599,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1600,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1615,a,1602,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1615,a,1603,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1615,a,1604,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1615,a,1605,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1615,a,1606,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1615,a,1607,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1615,a,1608,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1615,a,1609,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1615,a,1610,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1615,a,1611,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1615,a,1612,b)].
% 9.74/9.94 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1615,a,1613,b)].
% 9.74/9.94 1616 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(896,a,831,a)].
% 9.74/9.94 1617 class_Orderings_Oorder(tc_nat). [resolve(896,a,890,a)].
% 9.74/9.94 1618 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(896,a,891,b)].
% 9.74/9.94 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1618,a,1601,a)].
% 9.74/9.94 1619 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(903,b,896,a)].
% 9.74/9.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1619,b,1601,a)].
% 9.74/9.94 1620 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1080,b,1079,a)].
% 9.74/9.94 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1620,b,1601,a)].
% 9.74/9.94 1621 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1086,b,1079,a)].
% 9.74/9.94 1622 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1167,a,1147,b)].
% 9.74/9.94 1623 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1167,a,1148,b)].
% 9.74/9.94 1624 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1473,a,1454,a)].
% 9.74/9.94 1625 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1474,a,1454,a)].
% 9.74/9.94 1626 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1475,a,1454,a)].
% 9.74/9.94 1627 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1493,a,1487,b)].
% 9.74/9.94 1628 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1493,a,1488,b)].
% 9.74/9.94 1629 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1493,a,1490,b)].
% 9.74/9.94 1630 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1502,b,1493,a)].
% 9.74/9.94 1631 class_Orderings_Oorder(tc_nat). [resolve(1508,a,1493,a)].
% 9.74/9.94 1632 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1511,a,1493,a)].
% 9.98/10.11 1633 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1512,b,1493,a)].
% 9.98/10.11 1634 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1513,b,1493,a)].
% 9.98/10.11 1635 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1574,b,1549,b)].
% 9.98/10.11 1636 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 9.98/10.11 1637 -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].
% 9.98/10.11 1638 -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].
% 9.98/10.11 1639 -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].
% 9.98/10.11 1640 -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].
% 9.98/10.11 1641 -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].
% 9.98/10.11 1642 -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].
% 9.98/10.11 1643 -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].
% 9.98/10.11 1644 -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].
% 9.98/10.11 1645 -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].
% 9.98/10.11 1646 -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].
% 9.98/10.11 1647 -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].
% 9.98/10.11 1648 -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].
% 9.98/10.11 1649 -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].
% 9.98/10.11 1650 -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].
% 9.98/10.11 1651 -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].
% 9.98/10.11 1652 -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].
% 9.98/10.11 1653 -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].
% 9.98/10.11 1654 -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].
% 9.98/10.11 1655 -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].
% 9.98/10.11 1656 -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].
% 9.98/10.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1637,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1636,a,1638,a)].
% 9.98/10.13 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(1636,a,1639,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1640,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1636,a,1641,a)].
% 9.98/10.13 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(1636,a,1642,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1643,a)].
% 9.98/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1644,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1636,a,1645,a)].
% 9.98/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1646,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1647,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1636,a,1648,a)].
% 9.98/10.13 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(1636,a,1649,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1650,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1636,a,1651,a)].
% 9.98/10.13 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(1636,a,1652,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1653,a)].
% 9.98/10.13 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1654,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1636,a,1655,a)].
% 9.98/10.13 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1656,a)].
% 9.98/10.13 1657 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1637,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1657,a,1638,a)].
% 9.98/10.13 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(1657,a,1639,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1640,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1657,a,1641,a)].
% 9.98/10.13 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(1657,a,1642,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1643,a)].
% 9.98/10.13 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1657,a,1644,a)].
% 9.98/10.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1657,a,1645,a)].
% 9.98/10.14 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1657,a,1646,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1647,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1657,a,1648,a)].
% 9.98/10.14 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(1657,a,1649,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1650,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1657,a,1651,a)].
% 9.98/10.14 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(1657,a,1652,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1653,a)].
% 9.98/10.14 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1657,a,1654,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1657,a,1655,a)].
% 9.98/10.14 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1657,a,1656,a)].
% 9.98/10.14 1658 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1658,a,1637,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1658,a,1638,a)].
% 9.98/10.14 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(1658,a,1639,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1658,a,1640,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1658,a,1641,a)].
% 9.98/10.14 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(1658,a,1642,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1658,a,1643,a)].
% 9.98/10.14 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1658,a,1644,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1658,a,1645,a)].
% 9.98/10.14 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1658,a,1646,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1658,a,1647,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1658,a,1648,a)].
% 9.98/10.14 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(1658,a,1649,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1658,a,1650,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1658,a,1651,a)].
% 9.98/10.14 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(1658,a,1652,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1658,a,1653,a)].
% 9.98/10.14 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1658,a,1654,a)].
% 9.98/10.14 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1658,a,1655,a)].
% 9.98/10.14 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1658,a,1656,a)].
% 9.98/10.14 1659 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1637,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1638,a)].
% 9.98/10.16 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(1659,b,1639,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1640,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1641,a)].
% 9.98/10.16 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(1659,b,1642,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1643,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1644,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1645,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1646,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1647,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1648,a)].
% 9.98/10.16 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(1659,b,1649,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1650,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1651,a)].
% 9.98/10.16 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(1659,b,1652,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1653,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1654,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1655,a)].
% 9.98/10.16 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1656,a)].
% 9.98/10.16 1660 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1637,a)].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1638,a)].
% 9.98/10.16 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(1660,b,1639,a)].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1640,a)].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1641,a)].
% 9.98/10.16 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(1660,b,1642,a)].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1643,a)].
% 9.98/10.16 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1644,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1645,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1646,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1647,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1648,a)].
% 10.04/10.17 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(1660,b,1649,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1650,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1651,a)].
% 10.04/10.17 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(1660,b,1652,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1653,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1654,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1655,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1656,a)].
% 10.04/10.17 1661 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1637,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1638,a)].
% 10.04/10.17 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(1661,b,1639,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1640,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1641,a)].
% 10.04/10.17 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(1661,b,1642,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1643,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1644,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1645,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1646,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1647,a)].
% 10.04/10.17 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1648,a)].
% 10.04/10.17 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(1661,b,1649,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1650,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1651,a)].
% 10.04/10.18 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(1661,b,1652,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1653,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1654,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1655,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1656,a)].
% 10.04/10.18 1662 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 10.04/10.18 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(1662,b,1637,a)].
% 10.04/10.18 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(1662,b,1638,a)].
% 10.04/10.18 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(1662,b,1639,a)].
% 10.04/10.18 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(1662,b,1640,a)].
% 10.04/10.18 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(1662,b,1641,a)].
% 10.04/10.18 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(1662,b,1642,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1643,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1644,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1645,a)].
% 10.04/10.18 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1646,a)].
% 10.04/10.18 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(1662,b,1647,a)].
% 10.04/10.18 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(1662,b,1648,a)].
% 10.04/10.18 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(1662,b,1649,a)].
% 10.04/10.18 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(1662,b,1650,a)].
% 10.04/10.18 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(1662,b,1651,a)].
% 10.04/10.18 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(1662,b,1652,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1653,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1654,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1655,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1656,a)].
% 10.04/10.19 1663 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1637,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1638,a)].
% 10.04/10.19 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(1663,b,1639,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1640,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1641,a)].
% 10.04/10.19 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(1663,b,1642,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1643,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1663,b,1644,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1663,b,1645,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1663,b,1646,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1647,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1648,a)].
% 10.04/10.19 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(1663,b,1649,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1650,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1651,a)].
% 10.04/10.19 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(1663,b,1652,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1663,b,1653,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1663,b,1654,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1663,b,1655,a)].
% 10.04/10.19 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1663,b,1656,a)].
% 10.04/10.19 1664 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1637,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1638,a)].
% 10.04/10.20 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(1664,b,1639,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1640,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1641,a)].
% 10.04/10.20 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(1664,b,1642,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1643,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1664,b,1644,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1664,b,1645,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1664,b,1646,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1647,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1648,a)].
% 10.04/10.20 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(1664,b,1649,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1650,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1651,a)].
% 10.04/10.20 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(1664,b,1652,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1664,b,1653,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1664,b,1654,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1664,b,1655,a)].
% 10.04/10.20 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1664,b,1656,a)].
% 10.04/10.20 1665 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 10.04/10.20 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(1665,b,1637,a)].
% 10.04/10.20 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(1665,b,1638,a)].
% 10.04/10.20 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(1665,b,1639,a)].
% 10.04/10.20 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(1665,b,1640,a)].
% 10.04/10.22 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(1665,b,1641,a)].
% 10.04/10.22 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(1665,b,1642,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1643,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1665,b,1644,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1665,b,1645,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1665,b,1646,a)].
% 10.04/10.22 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(1665,b,1647,a)].
% 10.04/10.22 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(1665,b,1648,a)].
% 10.04/10.22 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(1665,b,1649,a)].
% 10.04/10.22 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(1665,b,1650,a)].
% 10.04/10.22 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(1665,b,1651,a)].
% 10.04/10.22 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(1665,b,1652,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1665,b,1653,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1665,b,1654,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1665,b,1655,a)].
% 10.04/10.22 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1665,b,1656,a)].
% 10.04/10.22 1666 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 10.04/10.22 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(1666,b,1637,a)].
% 10.04/10.22 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(1666,b,1638,a)].
% 10.04/10.22 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(1666,b,1639,a)].
% 10.04/10.22 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(1666,b,1640,a)].
% 10.04/10.22 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(1666,b,1641,a)].
% 10.04/10.22 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(1666,b,1642,a)].
% 10.04/10.22 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1643,a)].
% 10.04/10.22 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1666,b,1644,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1666,b,1645,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1666,b,1646,a)].
% 10.04/10.23 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(1666,b,1647,a)].
% 10.04/10.23 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(1666,b,1648,a)].
% 10.04/10.23 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(1666,b,1649,a)].
% 10.04/10.23 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(1666,b,1650,a)].
% 10.04/10.23 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(1666,b,1651,a)].
% 10.04/10.23 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(1666,b,1652,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1666,b,1653,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1666,b,1654,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1666,b,1655,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1666,b,1656,a)].
% 10.04/10.23 1667 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1637,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1638,a)].
% 10.04/10.23 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(1667,b,1639,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1640,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1641,a)].
% 10.04/10.23 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(1667,b,1642,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1643,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1667,b,1644,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1667,b,1645,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1667,b,1646,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1647,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1648,a)].
% 10.04/10.23 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(1667,b,1649,a)].
% 10.04/10.23 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1650,a)].
% 10.04/10.24 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1651,a)].
% 10.04/10.24 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(1667,b,1652,a)].
% 10.04/10.24 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1667,b,1653,a)].
% 10.04/10.24 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1667,b,1654,a)].
% 10.04/10.24 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1667,b,1655,a)].
% 10.04/10.24 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1667,b,1656,a)].
% 10.04/10.24 1668 -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].
% 10.04/10.24 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(1668,b,1637,a)].
% 10.04/10.24 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(1668,b,1638,a)].
% 10.04/10.24 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(1668,b,1639,a)].
% 10.04/10.24 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(1668,b,1640,a)].
% 10.04/10.24 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(1668,b,1641,a)].
% 10.04/10.24 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(1668,b,1642,a)].
% 10.04/10.24 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(1668,b,1643,a)].
% 10.04/10.24 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(1668,b,1644,a)].
% 10.04/10.24 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(1668,b,1645,a)].
% 10.04/10.24 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(1668,b,1646,a)].
% 10.04/10.24 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(1668,b,1647,a)].
% 10.04/10.24 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(1668,b,1648,a)].
% 10.04/10.24 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(1668,b,1649,a)].
% 10.04/10.24 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(1668,b,1650,a)].
% 10.04/10.24 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(1668,b,1651,a)].
% 10.04/10.24 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(1668,b,1652,a)].
% 10.04/10.24 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(1668,b,1653,a)].
% 10.04/10.24 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(1668,b,1654,a)].
% 10.04/10.26 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(1668,b,1655,a)].
% 10.04/10.26 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(1668,b,1656,a)].
% 10.04/10.26 1669 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1637,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1669,b,1638,a)].
% 10.04/10.26 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(1669,b,1639,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1640,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1669,b,1641,a)].
% 10.04/10.26 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(1669,b,1642,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1643,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1669,b,1644,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1669,b,1645,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1669,b,1646,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1669,b,1647,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1669,b,1648,a)].
% 10.04/10.26 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(1669,b,1649,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1669,b,1650,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1669,b,1651,a)].
% 10.04/10.26 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(1669,b,1652,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1669,b,1653,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1669,b,1654,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1669,b,1655,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1669,b,1656,a)].
% 10.04/10.26 1670 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1637,a)].
% 10.04/10.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1670,b,1638,a)].
% 10.04/10.26 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(1670,b,1639,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1640,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1670,b,1641,a)].
% 10.16/10.27 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(1670,b,1642,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1643,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1670,b,1644,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1670,b,1645,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1670,b,1646,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1670,b,1647,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1670,b,1648,a)].
% 10.16/10.27 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(1670,b,1649,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1670,b,1650,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1670,b,1651,a)].
% 10.16/10.27 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(1670,b,1652,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1670,b,1653,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1670,b,1654,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1670,b,1655,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1670,b,1656,a)].
% 10.16/10.27 1671 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 10.16/10.27 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(1671,b,1637,a)].
% 10.16/10.27 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(1671,b,1638,a)].
% 10.16/10.27 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(1671,b,1639,a)].
% 10.16/10.27 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(1671,b,1640,a)].
% 10.16/10.27 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(1671,b,1641,a)].
% 10.16/10.27 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(1671,b,1642,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1643,a)].
% 10.16/10.27 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1671,b,1644,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1671,b,1645,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1671,b,1646,a)].
% 10.16/10.28 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(1671,b,1647,a)].
% 10.16/10.28 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(1671,b,1648,a)].
% 10.16/10.28 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(1671,b,1649,a)].
% 10.16/10.28 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(1671,b,1650,a)].
% 10.16/10.28 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(1671,b,1651,a)].
% 10.16/10.28 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(1671,b,1652,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1671,b,1653,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1671,b,1654,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1671,b,1655,a)].
% 10.16/10.28 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1671,b,1656,a)].
% 10.16/10.28 1672 -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].
% 10.16/10.28 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(1672,b,1637,a)].
% 10.16/10.28 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(1672,b,1638,a)].
% 10.16/10.28 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(1672,b,1639,a)].
% 10.16/10.28 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(1672,b,1640,a)].
% 10.16/10.28 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(1672,b,1641,a)].
% 10.16/10.28 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(1672,b,1642,a)].
% 10.16/10.28 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(1672,b,1643,a)].
% 10.16/10.28 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(1672,b,1644,a)].
% 10.16/10.28 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(1672,b,1645,a)].
% 10.16/10.28 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(1672,b,1646,a)].
% 10.16/10.28 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(1672,b,1647,a)].
% 10.16/10.28 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(1672,b,1648,a)].
% 10.16/10.30 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(1672,b,1649,a)].
% 10.16/10.30 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(1672,b,1650,a)].
% 10.16/10.30 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(1672,b,1651,a)].
% 10.16/10.30 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(1672,b,1652,a)].
% 10.16/10.30 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(1672,b,1653,a)].
% 10.16/10.30 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(1672,b,1654,a)].
% 10.16/10.30 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(1672,b,1655,a)].
% 10.16/10.30 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(1672,b,1656,a)].
% 10.16/10.30 1673 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 10.16/10.30 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(1673,b,1637,a)].
% 10.16/10.30 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(1673,b,1638,a)].
% 10.16/10.30 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(1673,b,1639,a)].
% 10.16/10.30 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(1673,b,1640,a)].
% 10.16/10.30 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(1673,b,1641,a)].
% 10.16/10.30 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(1673,b,1642,a)].
% 10.16/10.30 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1643,a)].
% 10.16/10.30 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1673,b,1644,a)].
% 10.16/10.30 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1673,b,1645,a)].
% 10.16/10.30 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1673,b,1646,a)].
% 10.16/10.30 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(1673,b,1647,a)].
% 10.16/10.30 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(1673,b,1648,a)].
% 10.16/10.30 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(1673,b,1649,a)].
% 10.16/10.30 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(1673,b,1650,a)].
% 10.16/10.30 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(1673,b,1651,a)].
% 10.16/10.31 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(1673,b,1652,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1673,b,1653,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1673,b,1654,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1673,b,1655,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1673,b,1656,a)].
% 10.16/10.31 1674 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 10.16/10.31 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(1674,b,1637,a)].
% 10.16/10.31 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(1674,b,1638,a)].
% 10.16/10.31 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(1674,b,1639,a)].
% 10.16/10.31 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(1674,b,1640,a)].
% 10.16/10.31 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(1674,b,1641,a)].
% 10.16/10.31 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(1674,b,1642,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1674,b,1643,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1674,b,1644,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1674,b,1645,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1674,b,1646,a)].
% 10.16/10.31 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(1674,b,1647,a)].
% 10.16/10.31 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(1674,b,1648,a)].
% 10.16/10.31 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(1674,b,1649,a)].
% 10.16/10.31 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(1674,b,1650,a)].
% 10.16/10.31 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(1674,b,1651,a)].
% 10.16/10.31 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(1674,b,1652,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1674,b,1653,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1674,b,1654,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1674,b,1655,a)].
% 10.16/10.31 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1674,b,1656,a)].
% 10.21/10.32 1675 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 10.21/10.32 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(1675,b,1637,a)].
% 10.21/10.32 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(1675,b,1638,a)].
% 10.21/10.32 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(1675,b,1639,a)].
% 10.21/10.32 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(1675,b,1640,a)].
% 10.21/10.32 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(1675,b,1641,a)].
% 10.21/10.32 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(1675,b,1642,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1643,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1675,b,1644,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1675,b,1645,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1675,b,1646,a)].
% 10.21/10.32 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(1675,b,1647,a)].
% 10.21/10.32 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(1675,b,1648,a)].
% 10.21/10.32 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(1675,b,1649,a)].
% 10.21/10.32 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(1675,b,1650,a)].
% 10.21/10.32 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(1675,b,1651,a)].
% 10.21/10.32 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(1675,b,1652,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1675,b,1653,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1675,b,1654,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1675,b,1655,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1675,b,1656,a)].
% 10.21/10.32 1676 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1637,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1638,a)].
% 10.21/10.32 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(1676,b,1639,a)].
% 10.21/10.32 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1640,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1641,a)].
% 10.21/10.33 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(1676,b,1642,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1643,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1676,b,1644,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1676,b,1645,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1676,b,1646,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1647,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1648,a)].
% 10.21/10.33 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(1676,b,1649,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1650,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1651,a)].
% 10.21/10.33 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(1676,b,1652,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1676,b,1653,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1676,b,1654,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1676,b,1655,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1676,b,1656,a)].
% 10.21/10.33 1677 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1637,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1638,a)].
% 10.21/10.33 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(1677,b,1639,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1640,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1641,a)].
% 10.21/10.33 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(1677,b,1642,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1643,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1677,b,1644,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1677,b,1645,a)].
% 10.21/10.33 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1677,b,1646,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1647,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1648,a)].
% 10.21/10.35 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(1677,b,1649,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1650,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1651,a)].
% 10.21/10.35 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(1677,b,1652,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1677,b,1653,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1677,b,1654,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1677,b,1655,a)].
% 10.21/10.35 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1677,b,1656,a)].
% 10.21/10.35 1678 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1637,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1638,a)].
% 10.21/10.35 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(1678,b,1639,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1640,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1641,a)].
% 10.21/10.35 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(1678,b,1642,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1643,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1678,b,1644,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1678,b,1645,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1678,b,1646,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1647,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1648,a)].
% 10.21/10.35 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(1678,b,1649,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1650,a)].
% 10.21/10.35 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1651,a)].
% 11.39/11.51 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(1678,b,1652,a)].
% 11.39/11.51 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1678,b,1653,a)].
% 11.39/11.51 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1678,b,1654,a)].
% 11.39/11.51 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1678,b,1655,a)].
% 11.39/11.51 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1678,b,1656,a)].
% 11.39/11.51 1679 class_Orderings_Oord(tc_IntDef_Oint). [resolve(895,a,831,a)].
% 11.39/11.51 1680 class_Orderings_Oord(tc_nat). [resolve(895,a,890,a)].
% 11.39/11.51 1681 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(895,a,891,b)].
% 11.39/11.51 1682 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(903,b,895,a)].
% 11.39/11.51 1683 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1080,b,1078,a)].
% 11.39/11.51 1684 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1086,b,1078,a)].
% 11.39/11.51 1685 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1168,a,1147,b)].
% 11.39/11.51 1686 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1168,a,1148,b)].
% 11.39/11.51 1687 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1473,a,1455,a)].
% 11.39/11.51 1688 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1474,a,1455,a)].
% 11.39/11.51 1689 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1475,a,1455,a)].
% 11.39/11.51 1690 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1494,a,1487,b)].
% 11.39/11.51 1691 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1494,a,1488,b)].
% 11.39/11.51 1692 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1494,a,1490,b)].
% 11.39/11.51 1693 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1502,b,1494,a)].
% 11.39/11.51 1694 class_Orderings_Oord(tc_nat). [resolve(1508,a,1494,a)].
% 11.39/11.51 1695 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1511,a,1494,a)].
% 11.39/11.51 1696 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1512,b,1494,a)].
% 11.39/11.51 1697 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1513,b,1494,a)].
% 11.39/11.51 1698 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1575,b,1549,b)].
% 11.39/11.51 1699 class_Orderings_Oord(tc_set(A)). [resolve(1601,a,1593,a)].
% 11.39/11.51 1700 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1601,a,1599,b)].
% 11.39/11.51 1701 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1601,a,1600,b)].
% 11.39/11.51 1702 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1618,a,1601,a)].
% 11.39/11.51 1703 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1619,b,1601,a)].
% 11.39/11.51 1704 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1620,b,1601,a)].
% 11.39/11.51 1705 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1076,a)].
% 11.39/11.51 1706 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 11.39/11.51 1707 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 11.39/11.51 1708 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 11.39/11.51 1709 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 11.39/11.51 1710 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 11.39/11.51 1711 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 11.51/11.64 1712 -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].
% 11.51/11.64 1713 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 11.51/11.64 1714 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 11.51/11.64 1715 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 11.51/11.64 1716 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 11.51/11.64 1717 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(892,a,831,a)].
% 11.51/11.64 1718 class_LOrder_Olorder(tc_nat). [resolve(892,a,890,a)].
% 11.51/11.64 1719 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(892,a,891,b)].
% 11.51/11.64 1720 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(903,b,892,a)].
% 11.51/11.64 1721 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1099,a)].
% 11.51/11.64 1722 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1147,b)].
% 11.51/11.64 1723 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1148,b)].
% 11.51/11.64 1724 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1473,a,1453,a)].
% 11.51/11.64 1725 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1474,a,1453,a)].
% 11.51/11.64 1726 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1475,a,1453,a)].
% 11.51/11.64 1727 -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1594,b,1581,a)].
% 11.51/11.64 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1727,a,1706,a)].
% 11.51/11.64 Derived: -c_less(A,A,tc_nat). [resolve(1727,a,1707,a)].
% 11.51/11.64 1728 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1582,a)].
% 11.51/11.64 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1728,a,1706,a)].
% 11.51/11.64 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1728,a,1707,a)].
% 11.51/11.64 1729 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1594,b,1583,a)].
% 11.51/11.64 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1729,a,1706,a)].
% 11.51/11.64 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1729,a,1707,a)].
% 11.51/11.64 1730 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1594,b,1584,a)].
% 11.51/11.64 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1730,a,1706,a)].
% 11.51/11.64 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1730,a,1707,a)].
% 11.51/11.64 1731 -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(1594,b,1585,a)].
% 11.51/11.64 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(1731,a,1706,a)].
% 11.51/11.64 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(1731,a,1707,a)].
% 11.51/11.64 1732 -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(1594,b,1586,a)].
% 11.51/11.64 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(1732,a,1706,a)].
% 11.51/11.64 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(1732,a,1707,a)].
% 11.57/11.69 1733 -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(1594,b,1587,a)].
% 11.57/11.69 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(1733,a,1706,a)].
% 11.57/11.69 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(1733,a,1707,a)].
% 11.57/11.69 1734 -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(1594,b,1588,a)].
% 11.57/11.69 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(1734,a,1706,a)].
% 11.57/11.69 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(1734,a,1707,a)].
% 11.57/11.69 1735 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1589,a)].
% 11.57/11.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1735,a,1706,a)].
% 11.57/11.69 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1735,a,1707,a)].
% 11.57/11.69 1736 -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(1594,b,1590,a)].
% 11.57/11.69 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(1736,a,1706,a)].
% 11.57/11.69 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(1736,a,1707,a)].
% 11.57/11.69 1737 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1594,b,1591,a)].
% 11.57/11.69 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1737,a,1706,a)].
% 11.57/11.69 Derived: c_lessequals(A,A,tc_nat). [resolve(1737,a,1707,a)].
% 11.57/11.69 1738 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1614,a,1594,b)].
% 11.57/11.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1738,d,1706,a)].
% 11.57/11.69 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1738,d,1707,a)].
% 11.57/11.69 1739 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_LOrder_Olorder(C). [resolve(1615,a,1594,b)].
% 11.57/11.69 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1739,d,1706,a)].
% 11.57/11.69 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(1739,d,1707,a)].
% 11.57/11.69 1740 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1637,a)].
% 11.57/11.69 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1740,a,1706,a)].
% 11.57/11.69 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1740,a,1707,a)].
% 11.57/11.69 1741 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1638,a)].
% 11.57/11.69 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1741,a,1706,a)].
% 11.57/11.69 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1741,a,1707,a)].
% 11.57/11.69 1742 -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(1659,b,1639,a)].
% 11.57/11.69 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(1742,a,1706,a)].
% 11.57/11.70 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(1742,a,1707,a)].
% 11.57/11.70 1743 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1640,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1743,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1743,a,1707,a)].
% 11.57/11.70 1744 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1641,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1744,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1744,a,1707,a)].
% 11.57/11.70 1745 -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(1659,b,1642,a)].
% 11.57/11.70 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(1745,a,1706,a)].
% 11.57/11.70 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(1745,a,1707,a)].
% 11.57/11.70 1746 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1643,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1746,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1746,a,1707,a)].
% 11.57/11.70 1747 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1644,a)].
% 11.57/11.70 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1747,a,1706,a)].
% 11.57/11.70 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1747,a,1707,a)].
% 11.57/11.70 1748 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1645,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1748,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1748,a,1707,a)].
% 11.57/11.70 1749 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1646,a)].
% 11.57/11.70 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1749,a,1706,a)].
% 11.57/11.70 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1749,a,1707,a)].
% 11.57/11.70 1750 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1647,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1750,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1750,a,1707,a)].
% 11.57/11.70 1751 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1648,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1751,a,1706,a)].
% 11.57/11.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1751,a,1707,a)].
% 11.57/11.70 1752 -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(1659,b,1649,a)].
% 11.57/11.70 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(1752,a,1706,a)].
% 11.57/11.70 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(1752,a,1707,a)].
% 11.74/11.90 1753 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1650,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1753,a,1706,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1753,a,1707,a)].
% 11.74/11.90 1754 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1651,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1754,a,1706,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1754,a,1707,a)].
% 11.74/11.90 1755 -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(1659,b,1652,a)].
% 11.74/11.90 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(1755,a,1706,a)].
% 11.74/11.90 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(1755,a,1707,a)].
% 11.74/11.90 1756 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1653,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1756,a,1706,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1756,a,1707,a)].
% 11.74/11.90 1757 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1654,a)].
% 11.74/11.90 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1757,a,1706,a)].
% 11.74/11.90 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1757,a,1707,a)].
% 11.74/11.90 1758 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1655,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1758,a,1706,a)].
% 11.74/11.90 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1758,a,1707,a)].
% 11.74/11.90 1759 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1656,a)].
% 11.74/11.90 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1759,a,1706,a)].
% 11.74/11.90 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1759,a,1707,a)].
% 11.74/11.90 1760 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 11.74/11.90 1761 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 11.74/11.90 1762 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 11.74/11.90 1763 -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].
% 11.74/11.90 1764 -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].
% 11.74/11.90 1765 -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].
% 11.74/11.90 1766 -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].
% 11.74/11.90 1767 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom). [assumption].
% 11.74/11.91 1768 -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].
% 11.74/11.91 1769 -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].
% 11.74/11.91 1770 -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].
% 11.74/11.91 1771 -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].
% 11.74/11.91 1772 -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].
% 11.74/11.91 1773 -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].
% 11.74/11.91 1774 -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].
% 11.74/11.91 1775 -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].
% 11.74/11.91 1776 -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].
% 11.74/11.91 1777 -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].
% 11.74/11.91 1778 -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].
% 11.74/11.91 1779 -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].
% 11.74/11.91 1780 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_plus(D,B,A),c_plus(E,C,A),A) # label(cls_OrderedGroup_Oadd__mono_0) # label(axiom). [assumption].
% 11.74/11.91 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1780,a,1761,a)].
% 11.74/11.91 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(1780,a,1762,a)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1763,b)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1764,b)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1765,b)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1780,a,1766,b)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1768,b)].
% 11.74/11.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1780,a,1769,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1780,a,1770,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1780,a,1771,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1780,a,1772,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1780,a,1773,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1780,a,1774,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1780,a,1775,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1780,a,1776,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1780,a,1777,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1780,a,1778,b)].
% 12.03/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1780,a,1779,b)].
% 12.03/12.16 1781 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1166,a,1121,a)].
% 12.03/12.16 1782 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1166,a,1146,a)].
% 12.03/12.16 1783 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1166,a,1147,b)].
% 12.03/12.16 1784 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1166,a,1148,b)].
% 12.03/12.16 1785 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1462,a)].
% 12.03/12.16 1786 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1474,a,1462,a)].
% 12.03/12.16 1787 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1475,a,1462,a)].
% 12.03/12.16 1788 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1492,a,1487,b)].
% 12.03/12.16 1789 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1492,a,1488,b)].
% 12.03/12.16 1790 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1492,a,1489,b)].
% 12.03/12.16 1791 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1492,a,1490,b)].
% 12.03/12.16 1792 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1502,b,1492,a)].
% 12.03/12.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1792,b,1760,a)].
% 12.03/12.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1792,b,1767,a)].
% 12.03/12.16 1793 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1573,b,1514,a)].
% 12.03/12.16 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1793,a,1760,a)].
% 12.03/12.16 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1793,a,1767,a)].
% 12.03/12.16 1794 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1573,b,1549,b)].
% 12.03/12.16 1795 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1573,b,1550,b)].
% 12.03/12.16 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1795,a,1760,a)].
% 12.03/12.18 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1795,a,1767,a)].
% 12.03/12.18 1796 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1573,b,1551,b)].
% 12.03/12.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1796,a,1760,a)].
% 12.03/12.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1796,a,1767,a)].
% 12.03/12.18 1797 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1599,b,1581,a)].
% 12.03/12.18 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1797,a,1763,b)].
% 12.03/12.18 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1797,a,1764,b)].
% 12.03/12.18 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1797,a,1765,b)].
% 12.03/12.18 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1797,a,1766,b)].
% 12.03/12.18 1798 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1582,a)].
% 12.03/12.18 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1798,a,1763,b)].
% 12.03/12.18 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1798,a,1764,b)].
% 12.03/12.18 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1798,a,1765,b)].
% 12.03/12.18 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1798,a,1766,b)].
% 12.03/12.18 1799 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1599,b,1583,a)].
% 12.03/12.18 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1799,a,1763,b)].
% 12.03/12.18 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1799,a,1764,b)].
% 12.03/12.18 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1799,a,1765,b)].
% 12.03/12.18 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1799,a,1766,b)].
% 12.03/12.18 1800 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1599,b,1584,a)].
% 12.03/12.18 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1763,b)].
% 12.03/12.18 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1764,b)].
% 12.03/12.18 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1765,b)].
% 12.03/12.18 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1800,a,1766,b)].
% 12.03/12.18 1801 -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(1599,b,1585,a)].
% 12.03/12.18 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(1801,a,1763,b)].
% 12.03/12.18 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(1801,a,1764,b)].
% 12.03/12.18 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(1801,a,1765,b)].
% 12.03/12.19 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(1801,a,1766,b)].
% 12.03/12.19 1802 -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(1599,b,1586,a)].
% 12.03/12.19 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(1802,a,1763,b)].
% 12.03/12.19 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(1802,a,1764,b)].
% 12.03/12.19 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(1802,a,1765,b)].
% 12.03/12.19 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(1802,a,1766,b)].
% 12.03/12.19 1803 -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(1599,b,1587,a)].
% 12.03/12.19 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(1803,a,1763,b)].
% 12.03/12.19 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(1803,a,1764,b)].
% 12.03/12.19 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(1803,a,1765,b)].
% 12.03/12.19 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(1803,a,1766,b)].
% 12.03/12.19 1804 -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(1599,b,1588,a)].
% 12.03/12.19 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(1804,a,1763,b)].
% 12.03/12.19 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(1804,a,1764,b)].
% 12.03/12.19 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(1804,a,1765,b)].
% 12.03/12.19 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(1804,a,1766,b)].
% 12.03/12.19 1805 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1589,a)].
% 12.03/12.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1763,b)].
% 12.03/12.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1764,b)].
% 12.03/12.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1765,b)].
% 12.03/12.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1805,a,1766,b)].
% 12.03/12.19 1806 -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(1599,b,1590,a)].
% 12.11/12.24 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(1806,a,1763,b)].
% 12.11/12.24 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(1806,a,1764,b)].
% 12.11/12.24 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(1806,a,1765,b)].
% 12.11/12.24 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(1806,a,1766,b)].
% 12.11/12.24 1807 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1599,b,1591,a)].
% 12.11/12.24 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1807,a,1763,b)].
% 12.11/12.24 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1807,a,1764,b)].
% 12.11/12.24 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1807,a,1765,b)].
% 12.11/12.24 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1807,a,1766,b)].
% 12.11/12.24 1808 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1614,a,1599,b)].
% 12.11/12.24 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1808,d,1763,b)].
% 12.11/12.24 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1808,d,1764,b)].
% 12.11/12.24 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1808,d,1765,b)].
% 12.11/12.24 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1808,d,1766,b)].
% 12.11/12.24 1809 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1615,a,1599,b)].
% 12.11/12.24 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1809,d,1763,b)].
% 12.11/12.24 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1809,d,1764,b)].
% 12.11/12.24 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1809,d,1765,b)].
% 12.11/12.24 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1809,d,1766,b)].
% 12.11/12.24 1810 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1637,a)].
% 12.11/12.24 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1810,a,1763,b)].
% 12.11/12.24 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1810,a,1764,b)].
% 12.11/12.24 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(1810,a,1765,b)].
% 12.11/12.24 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1810,a,1766,b)].
% 12.11/12.24 1811 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1638,a)].
% 12.11/12.24 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1811,a,1763,b)].
% 12.11/12.24 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1811,a,1764,b)].
% 12.11/12.25 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(1811,a,1765,b)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1811,a,1766,b)].
% 12.11/12.25 1812 -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(1664,b,1639,a)].
% 12.11/12.25 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(1812,a,1763,b)].
% 12.11/12.25 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(1812,a,1764,b)].
% 12.11/12.25 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(1812,a,1765,b)].
% 12.11/12.25 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(1812,a,1766,b)].
% 12.11/12.25 1813 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1640,a)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1813,a,1763,b)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1813,a,1764,b)].
% 12.11/12.25 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(1813,a,1765,b)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1813,a,1766,b)].
% 12.11/12.25 1814 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1641,a)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1814,a,1763,b)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1814,a,1764,b)].
% 12.11/12.25 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(1814,a,1765,b)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1814,a,1766,b)].
% 12.11/12.25 1815 -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(1664,b,1642,a)].
% 12.11/12.25 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(1815,a,1763,b)].
% 12.11/12.25 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(1815,a,1764,b)].
% 12.11/12.25 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(1815,a,1765,b)].
% 12.11/12.25 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(1815,a,1766,b)].
% 12.11/12.25 1816 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1643,a)].
% 12.11/12.25 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1816,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1816,a,1764,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1816,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1816,a,1766,b)].
% 12.11/12.26 1817 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1664,b,1644,a)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1817,a,1763,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1817,a,1764,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1817,a,1765,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1817,a,1766,b)].
% 12.11/12.26 1818 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1664,b,1645,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1818,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1818,a,1764,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1818,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1818,a,1766,b)].
% 12.11/12.26 1819 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1664,b,1646,a)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1819,a,1763,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1819,a,1764,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1819,a,1765,b)].
% 12.11/12.26 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1819,a,1766,b)].
% 12.11/12.26 1820 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1647,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1820,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1820,a,1764,b)].
% 12.11/12.26 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(1820,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1820,a,1766,b)].
% 12.11/12.26 1821 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1648,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1821,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1821,a,1764,b)].
% 12.11/12.26 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(1821,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1821,a,1766,b)].
% 12.11/12.26 1822 -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(1664,b,1649,a)].
% 12.11/12.26 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(1822,a,1763,b)].
% 12.11/12.26 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(1822,a,1764,b)].
% 12.11/12.26 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(1822,a,1765,b)].
% 12.11/12.26 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(1822,a,1766,b)].
% 12.11/12.26 1823 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1650,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1823,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1823,a,1764,b)].
% 12.11/12.26 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(1823,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1823,a,1766,b)].
% 12.11/12.26 1824 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1651,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1824,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1824,a,1764,b)].
% 12.11/12.26 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(1824,a,1765,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1824,a,1766,b)].
% 12.11/12.26 1825 -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(1664,b,1652,a)].
% 12.11/12.26 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(1825,a,1763,b)].
% 12.11/12.26 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(1825,a,1764,b)].
% 12.11/12.26 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(1825,a,1765,b)].
% 12.11/12.26 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(1825,a,1766,b)].
% 12.11/12.26 1826 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1664,b,1653,a)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1826,a,1763,b)].
% 12.11/12.26 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1826,a,1764,b)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1826,a,1765,b)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1826,a,1766,b)].
% 12.34/12.48 1827 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1664,b,1654,a)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1827,a,1763,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1827,a,1764,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1827,a,1765,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1827,a,1766,b)].
% 12.34/12.48 1828 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1664,b,1655,a)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1828,a,1763,b)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1828,a,1764,b)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1828,a,1765,b)].
% 12.34/12.48 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1828,a,1766,b)].
% 12.34/12.48 1829 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1664,b,1656,a)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1829,a,1763,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1829,a,1764,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1829,a,1765,b)].
% 12.34/12.48 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1829,a,1766,b)].
% 12.34/12.48 1830 -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].
% 12.34/12.48 1831 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 12.34/12.48 1832 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 12.34/12.48 1833 -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].
% 12.34/12.48 1834 -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].
% 12.34/12.48 1835 -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].
% 12.34/12.48 1836 -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].
% 12.34/12.48 1837 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # label(axiom). [assumption].
% 12.34/12.48 1838 -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].
% 12.34/12.50 1839 -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].
% 12.34/12.50 1840 -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].
% 12.34/12.50 1841 -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].
% 12.34/12.50 1842 -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].
% 12.34/12.50 1843 -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].
% 12.34/12.50 1844 -class_OrderedGroup_Ocomm__monoid__add(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) # label(cls_OrderedGroup_Oadd__nonneg__nonneg_0) # label(axiom). [assumption].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1844,b,1831,a)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(1844,b,1832,a)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1844,b,1833,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1844,b,1834,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1844,b,1835,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1844,b,1836,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1844,b,1838,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1844,b,1839,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1844,b,1840,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1844,b,1841,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1844,b,1842,b)].
% 12.34/12.50 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1844,b,1843,b)].
% 12.34/12.50 1845 -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)].
% 12.58/12.76 1846 -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)].
% 12.58/12.76 1847 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 12.58/12.76 1848 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 12.58/12.76 1849 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(775,b,734,a)].
% 12.58/12.76 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1849,a,1839,b)].
% 12.58/12.76 1850 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(775,b,741,a)].
% 12.58/12.76 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1850,a,1839,b)].
% 12.58/12.76 1851 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1161,a,1121,a)].
% 12.58/12.76 1852 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1161,a,1146,a)].
% 12.58/12.76 1853 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1161,a,1147,b)].
% 12.58/12.76 1854 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1161,a,1148,b)].
% 12.58/12.76 1855 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1461,a)].
% 12.58/12.76 1856 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1474,a,1461,a)].
% 12.58/12.76 1857 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1475,a,1461,a)].
% 12.58/12.76 1858 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,a,1487,b)].
% 12.58/12.76 1859 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,a,1488,b)].
% 12.58/12.76 1860 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,a,1489,b)].
% 12.58/12.76 1861 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,a,1490,b)].
% 12.58/12.76 1862 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1572,b,1514,a)].
% 12.58/12.76 1863 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1572,b,1549,b)].
% 12.58/12.76 1864 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1572,b,1550,b)].
% 12.58/12.76 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1864,a,1845,a)].
% 12.58/12.76 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1864,a,1846,a)].
% 12.58/12.76 1865 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1572,b,1551,b)].
% 12.58/12.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1865,a,1845,a)].
% 12.58/12.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1865,a,1846,a)].
% 12.58/12.76 1866 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1600,b,1581,a)].
% 12.58/12.76 1867 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1582,a)].
% 12.58/12.76 1868 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1600,b,1583,a)].
% 12.58/12.76 1869 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1600,b,1584,a)].
% 12.58/12.76 1870 -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(1600,b,1585,a)].
% 12.73/12.84 1871 -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(1600,b,1586,a)].
% 12.73/12.84 1872 -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(1600,b,1587,a)].
% 12.73/12.84 1873 -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(1600,b,1588,a)].
% 12.73/12.84 1874 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1589,a)].
% 12.73/12.84 1875 -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(1600,b,1590,a)].
% 12.73/12.84 1876 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1600,b,1591,a)].
% 12.73/12.84 1877 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1600,b)].
% 12.73/12.84 1878 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1600,b)].
% 12.73/12.84 1879 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1637,a)].
% 12.73/12.84 1880 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1638,a)].
% 12.73/12.84 1881 -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(1665,b,1639,a)].
% 12.73/12.84 1882 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1640,a)].
% 12.73/12.84 1883 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1641,a)].
% 12.73/12.84 1884 -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(1665,b,1642,a)].
% 12.73/12.84 1885 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1643,a)].
% 12.73/12.84 1886 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1665,b,1644,a)].
% 12.73/12.84 1887 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1665,b,1645,a)].
% 12.73/12.84 1888 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1665,b,1646,a)].
% 12.73/12.84 1889 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1647,a)].
% 12.73/12.84 1890 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1648,a)].
% 12.73/12.84 1891 -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(1665,b,1649,a)].
% 12.73/12.84 1892 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1650,a)].
% 12.73/12.84 1893 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1651,a)].
% 12.73/12.84 1894 -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(1665,b,1652,a)].
% 13.01/13.13 1895 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1665,b,1653,a)].
% 13.01/13.13 1896 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1665,b,1654,a)].
% 13.01/13.13 1897 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1665,b,1655,a)].
% 13.01/13.13 1898 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1665,b,1656,a)].
% 13.01/13.13 1899 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1768,b)].
% 13.01/13.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1899,d,1831,a)].
% 13.01/13.13 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(1899,d,1832,a)].
% 13.01/13.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1899,d,1833,b)].
% 13.01/13.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1899,d,1834,b)].
% 13.01/13.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1899,d,1835,b)].
% 13.01/13.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1899,d,1836,b)].
% 13.01/13.13 1900 -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].
% 13.01/13.13 1901 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 13.01/13.13 1902 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 13.01/13.13 1903 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) # label(axiom). [assumption].
% 13.01/13.13 1904 -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].
% 13.01/13.13 1905 -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].
% 13.01/13.13 1906 -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].
% 13.01/13.13 1907 -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].
% 13.01/13.13 1908 -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)].
% 13.01/13.13 1909 -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)].
% 13.01/13.13 1910 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 13.01/13.13 1911 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 13.01/13.13 1912 -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(891,b,832,a)].
% 13.01/13.13 1913 -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(891,b,833,a)].
% 13.01/13.13 1914 -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(891,b,834,a)].
% 13.01/13.13 1915 -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(891,b,835,a)].
% 13.01/13.13 1916 -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(891,b,836,a)].
% 13.01/13.13 1917 -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(891,b,837,a)].
% 13.01/13.13 1918 -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(891,b,838,a)].
% 13.01/13.13 1919 -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(891,b,839,a)].
% 13.01/13.13 1920 -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(891,b,840,a)].
% 13.01/13.13 1921 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 13.01/13.13 1922 -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(891,b,842,a)].
% 13.01/13.13 1923 -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(891,b,843,a)].
% 13.01/13.13 1924 -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(891,b,844,a)].
% 13.01/13.13 1925 -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(891,b,845,a)].
% 13.01/13.13 1926 -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(891,b,846,a)].
% 13.01/13.13 1927 -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(891,b,847,a)].
% 13.01/13.13 1928 -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(891,b,848,a)].
% 13.01/13.13 1929 -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(891,b,849,a)].
% 13.01/13.13 1930 -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(891,b,850,a)].
% 13.01/13.13 1931 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,851,a)].
% 13.05/13.15 1932 -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(891,b,852,a)].
% 13.05/13.15 1933 -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(891,b,853,a)].
% 13.05/13.15 1934 -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(891,b,854,a)].
% 13.05/13.15 1935 -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(891,b,855,b)].
% 13.05/13.15 1936 -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(891,b,856,b)].
% 13.05/13.15 1937 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(891,b,857,a)].
% 13.05/13.15 1938 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(891,b,858,a)].
% 13.05/13.15 1939 -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(891,b,859,a)].
% 13.05/13.15 1940 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(891,b,860,a)].
% 13.05/13.15 1941 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(891,b,861,a)].
% 13.05/13.15 1942 -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(891,b,862,a)].
% 13.05/13.15 1943 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(891,b,863,a)].
% 13.05/13.15 1944 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(891,b,864,a)].
% 13.05/13.15 1945 -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(891,b,865,a)].
% 13.05/13.15 1946 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,866,a)].
% 13.05/13.15 1947 -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(891,b,867,a)].
% 13.05/13.15 1948 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(891,b,868,a)].
% 13.05/13.15 1949 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(891,b,869,a)].
% 13.05/13.15 1950 -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(891,b,870,a)].
% 13.05/13.15 1951 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,871,a)].
% 13.05/13.15 1952 -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(891,b,872,a)].
% 13.05/13.15 1953 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(891,b,873,a)].
% 13.05/13.15 1954 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(891,b,874,a)].
% 13.05/13.15 1955 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(891,b,875,a)].
% 13.15/13.28 1956 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(891,b,876,a)].
% 13.15/13.28 1957 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,877,a)].
% 13.15/13.28 1958 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,878,a)].
% 13.15/13.28 1959 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,879,a)].
% 13.15/13.28 1960 -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(891,b,880,a)].
% 13.15/13.28 1961 -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(891,b,881,a)].
% 13.15/13.28 1962 -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(891,b,882,a)].
% 13.15/13.28 1963 -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(891,b,883,a)].
% 13.15/13.28 1964 -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(891,b,884,a)].
% 13.15/13.28 1965 -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(891,b,885,a)].
% 13.15/13.28 1966 -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(891,b,886,a)].
% 13.15/13.28 1967 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,887,a)].
% 13.15/13.28 1968 -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(891,b,888,a)].
% 13.15/13.28 1969 -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(891,b,889,a)].
% 13.15/13.28 1970 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(904,a,891,b)].
% 13.15/13.28 1971 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(905,a,891,b)].
% 13.15/13.28 1972 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1076,a)].
% 13.15/13.28 1973 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1099,a)].
% 13.15/13.28 1974 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1121,a)].
% 13.15/13.28 1975 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1158,a,1146,a)].
% 13.15/13.28 1976 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1147,b)].
% 13.15/13.28 1977 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1148,b)].
% 13.15/13.28 1978 -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(1489,b,1477,a)].
% 13.15/13.28 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1978,a,1902,a)].
% 13.21/13.33 1979 -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(1489,b,1478,a)].
% 13.21/13.33 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1979,a,1902,a)].
% 13.21/13.33 1980 -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(1489,b,1479,a)].
% 13.21/13.33 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1980,a,1902,a)].
% 13.21/13.33 1981 -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(1489,b,1480,a)].
% 13.21/13.33 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1981,a,1902,a)].
% 13.21/13.33 1982 -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(1489,b,1481,a)].
% 13.21/13.33 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1982,a,1902,a)].
% 13.21/13.33 1983 -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(1489,b,1482,a)].
% 13.21/13.33 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1983,a,1902,a)].
% 13.21/13.33 1984 -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(1489,b,1483,a)].
% 13.21/13.33 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1984,a,1902,a)].
% 13.21/13.33 1985 -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(1489,b,1484,a)].
% 13.21/13.33 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1985,a,1902,a)].
% 13.21/13.33 1986 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1503,a,1489,b)].
% 13.21/13.33 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1986,c,1904,b)].
% 13.21/13.33 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1986,c,1907,b)].
% 13.21/13.33 1987 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1504,a,1489,b)].
% 13.21/13.33 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1987,c,1904,b)].
% 13.21/13.33 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1987,c,1907,b)].
% 13.21/13.33 1988 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1505,b,1489,b)].
% 13.21/13.33 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1988,b,1902,a)].
% 13.21/13.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1988,b,1907,b)].
% 13.21/13.33 1989 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1506,b,1489,b)].
% 13.21/13.33 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1989,b,1907,b)].
% 13.21/13.33 1990 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1597,b,1581,a)].
% 13.21/13.33 1991 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1582,a)].
% 13.21/13.33 1992 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1583,a)].
% 13.21/13.33 1993 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1584,a)].
% 13.21/13.33 1994 -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(1597,b,1585,a)].
% 13.21/13.33 1995 -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(1597,b,1586,a)].
% 13.27/13.38 1996 -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(1597,b,1587,a)].
% 13.27/13.38 1997 -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(1597,b,1588,a)].
% 13.27/13.38 1998 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1589,a)].
% 13.27/13.38 1999 -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(1597,b,1590,a)].
% 13.27/13.38 2000 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1597,b,1591,a)].
% 13.27/13.38 2001 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1597,b)].
% 13.27/13.38 2002 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1597,b)].
% 13.27/13.38 2003 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1637,a)].
% 13.27/13.38 2004 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1638,a)].
% 13.27/13.38 2005 -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(1662,b,1639,a)].
% 13.27/13.38 2006 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1640,a)].
% 13.27/13.38 2007 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1641,a)].
% 13.27/13.38 2008 -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(1662,b,1642,a)].
% 13.27/13.38 2009 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1643,a)].
% 13.27/13.38 2010 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1644,a)].
% 13.27/13.38 2011 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1645,a)].
% 13.27/13.38 2012 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1646,a)].
% 13.27/13.38 2013 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1647,a)].
% 13.27/13.38 2014 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1648,a)].
% 13.27/13.38 2015 -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(1662,b,1649,a)].
% 13.27/13.38 2016 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1650,a)].
% 13.27/13.38 2017 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1651,a)].
% 13.27/13.38 2018 -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(1662,b,1652,a)].
% 13.27/13.38 2019 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1653,a)].
% 13.27/13.45 2020 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1654,a)].
% 13.27/13.45 2021 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1655,a)].
% 13.27/13.45 2022 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1656,a)].
% 13.27/13.45 2023 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1765,b)].
% 13.27/13.45 2024 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1797,a,1765,b)].
% 13.27/13.45 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2024,b,1901,a)].
% 13.27/13.45 Derived: -c_less(A,A,tc_nat). [resolve(2024,b,1902,a)].
% 13.27/13.45 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2024,b,1904,b)].
% 13.27/13.45 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2024,b,1905,b)].
% 13.27/13.45 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2024,b,1906,b)].
% 13.27/13.45 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2024,b,1907,b)].
% 13.27/13.45 2025 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1798,a,1765,b)].
% 13.27/13.45 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2025,c,1901,a)].
% 13.27/13.45 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2025,c,1902,a)].
% 13.27/13.45 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2025,c,1904,b)].
% 13.27/13.45 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2025,c,1905,b)].
% 13.27/13.45 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2025,c,1906,b)].
% 13.27/13.45 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1907,b)].
% 13.27/13.45 2026 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1799,a,1765,b)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2026,b,1901,a)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2026,b,1902,a)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2026,b,1904,b)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2026,b,1905,b)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2026,b,1906,b)].
% 13.27/13.45 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2026,b,1907,b)].
% 13.27/13.45 2027 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1765,b)].
% 13.27/13.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2027,c,1901,a)].
% 13.27/13.45 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2027,c,1902,a)].
% 13.27/13.45 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2027,c,1904,b)].
% 13.27/13.45 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2027,c,1905,b)].
% 13.27/13.45 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2027,c,1906,b)].
% 13.27/13.45 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2027,c,1907,b)].
% 13.27/13.45 2028 -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(1801,a,1765,b)].
% 13.27/13.45 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(2028,c,1901,a)].
% 13.27/13.45 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(2028,c,1902,a)].
% 13.27/13.45 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(2028,c,1904,b)].
% 13.27/13.45 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(2028,c,1905,b)].
% 13.27/13.45 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(2028,c,1906,b)].
% 13.27/13.45 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(2028,c,1907,b)].
% 13.27/13.45 2029 -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(1802,a,1765,b)].
% 13.27/13.45 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(2029,c,1901,a)].
% 13.27/13.45 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(2029,c,1902,a)].
% 13.27/13.45 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(2029,c,1904,b)].
% 13.27/13.45 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(2029,c,1905,b)].
% 13.27/13.45 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(2029,c,1906,b)].
% 13.27/13.45 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(2029,c,1907,b)].
% 13.27/13.45 2030 -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(1803,a,1765,b)].
% 13.27/13.45 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(2030,c,1901,a)].
% 13.27/13.45 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(2030,c,1902,a)].
% 13.27/13.45 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(2030,c,1904,b)].
% 13.27/13.45 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(2030,c,1905,b)].
% 13.27/13.45 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(2030,c,1906,b)].
% 13.27/13.46 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(2030,c,1907,b)].
% 13.27/13.46 2031 -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(1804,a,1765,b)].
% 13.27/13.46 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(2031,c,1901,a)].
% 13.27/13.46 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(2031,c,1902,a)].
% 13.27/13.46 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(2031,c,1904,b)].
% 13.27/13.46 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(2031,c,1905,b)].
% 13.27/13.46 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(2031,c,1906,b)].
% 13.27/13.46 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(2031,c,1907,b)].
% 13.27/13.46 2032 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1765,b)].
% 13.27/13.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2032,c,1901,a)].
% 13.27/13.46 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2032,c,1902,a)].
% 13.27/13.46 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2032,c,1904,b)].
% 13.27/13.46 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2032,c,1905,b)].
% 13.27/13.46 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2032,c,1906,b)].
% 13.27/13.46 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1907,b)].
% 13.27/13.46 2033 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(1806,a,1765,b)].
% 13.27/13.46 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(2033,b,1901,a)].
% 13.27/13.46 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(2033,b,1902,a)].
% 13.27/13.46 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(2033,b,1904,b)].
% 13.27/13.46 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(2033,b,1905,b)].
% 13.27/13.46 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(2033,b,1906,b)].
% 13.27/13.46 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(2033,b,1907,b)].
% 13.27/13.46 2034 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1807,a,1765,b)].
% 13.27/13.46 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2034,b,1901,a)].
% 13.37/13.46 Derived: c_lessequals(A,A,tc_nat). [resolve(2034,b,1902,a)].
% 13.37/13.46 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2034,b,1904,b)].
% 13.37/13.46 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2034,b,1905,b)].
% 13.37/13.46 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2034,b,1906,b)].
% 13.37/13.46 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2034,b,1907,b)].
% 13.37/13.46 2035 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1808,d,1765,b)].
% 13.37/13.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2035,d,1901,a)].
% 13.37/13.46 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2035,d,1902,a)].
% 13.37/13.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2035,d,1904,b)].
% 13.37/13.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2035,d,1905,b)].
% 13.37/13.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2035,d,1906,b)].
% 13.37/13.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,d,1907,b)].
% 13.37/13.46 2036 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1809,d,1765,b)].
% 13.37/13.46 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2036,d,1901,a)].
% 13.37/13.46 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2036,d,1902,a)].
% 13.37/13.46 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2036,d,1904,b)].
% 13.37/13.46 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2036,d,1905,b)].
% 13.37/13.46 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2036,d,1906,b)].
% 13.37/13.46 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2036,d,1907,b)].
% 13.37/13.46 2037 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1810,a,1765,b)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2037,c,1901,a)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2037,c,1902,a)].
% 13.37/13.46 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(2037,c,1904,b)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2037,c,1905,b)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2037,c,1906,b)].
% 13.37/13.46 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(2037,c,1907,b)].
% 13.37/13.46 2038 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1811,a,1765,b)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2038,c,1901,a)].
% 13.37/13.46 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2038,c,1902,a)].
% 13.37/13.46 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(2038,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2038,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2038,c,1906,b)].
% 13.37/13.47 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(2038,c,1907,b)].
% 13.37/13.47 2039 -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(1812,a,1765,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2039,d,1901,a)].
% 13.37/13.47 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(2039,d,1902,a)].
% 13.37/13.47 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(2039,d,1904,b)].
% 13.37/13.47 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(2039,d,1905,b)].
% 13.37/13.47 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(2039,d,1906,b)].
% 13.37/13.47 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(2039,d,1907,b)].
% 13.37/13.47 2040 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1813,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2040,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2040,c,1902,a)].
% 13.37/13.47 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(2040,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2040,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2040,c,1906,b)].
% 13.37/13.47 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(2040,c,1907,b)].
% 13.37/13.47 2041 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1814,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2041,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2041,c,1902,a)].
% 13.37/13.47 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(2041,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2041,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2041,c,1906,b)].
% 13.37/13.47 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(2041,c,1907,b)].
% 13.37/13.47 2042 -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(1815,a,1765,b)].
% 13.37/13.47 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(2042,d,1901,a)].
% 13.37/13.47 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(2042,d,1902,a)].
% 13.37/13.47 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(2042,d,1904,b)].
% 13.37/13.47 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(2042,d,1905,b)].
% 13.37/13.47 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(2042,d,1906,b)].
% 13.37/13.47 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(2042,d,1907,b)].
% 13.37/13.47 2043 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1816,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2043,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2043,c,1902,a)].
% 13.37/13.47 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(2043,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2043,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2043,c,1906,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2043,c,1907,b)].
% 13.37/13.47 2044 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1817,a,1765,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2044,c,1901,a)].
% 13.37/13.47 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2044,c,1902,a)].
% 13.37/13.47 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(2044,c,1904,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2044,c,1905,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2044,c,1906,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2044,c,1907,b)].
% 13.37/13.47 2045 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1818,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2045,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2045,c,1902,a)].
% 13.37/13.47 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(2045,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2045,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2045,c,1906,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2045,c,1907,b)].
% 13.37/13.47 2046 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1819,a,1765,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2046,c,1901,a)].
% 13.37/13.47 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2046,c,1902,a)].
% 13.37/13.47 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(2046,c,1904,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2046,c,1905,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2046,c,1906,b)].
% 13.37/13.47 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2046,c,1907,b)].
% 13.37/13.47 2047 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1820,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2047,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2047,c,1902,a)].
% 13.37/13.47 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(2047,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2047,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2047,c,1906,b)].
% 13.37/13.47 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(2047,c,1907,b)].
% 13.37/13.47 2048 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1821,a,1765,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2048,c,1901,a)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2048,c,1902,a)].
% 13.37/13.47 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(2048,c,1904,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2048,c,1905,b)].
% 13.37/13.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2048,c,1906,b)].
% 13.37/13.47 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(2048,c,1907,b)].
% 13.37/13.47 2049 -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(1822,a,1765,b)].
% 13.37/13.47 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(2049,d,1901,a)].
% 13.37/13.47 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(2049,d,1902,a)].
% 13.37/13.47 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(2049,d,1904,b)].
% 13.37/13.47 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(2049,d,1905,b)].
% 13.37/13.47 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(2049,d,1906,b)].
% 13.37/13.47 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(2049,d,1907,b)].
% 13.37/13.48 2050 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1823,a,1765,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2050,c,1901,a)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2050,c,1902,a)].
% 13.37/13.48 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(2050,c,1904,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2050,c,1905,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2050,c,1906,b)].
% 13.37/13.48 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(2050,c,1907,b)].
% 13.37/13.48 2051 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1824,a,1765,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2051,c,1901,a)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2051,c,1902,a)].
% 13.37/13.48 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(2051,c,1904,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2051,c,1905,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2051,c,1906,b)].
% 13.37/13.48 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(2051,c,1907,b)].
% 13.37/13.48 2052 -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(1825,a,1765,b)].
% 13.37/13.48 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2052,d,1901,a)].
% 13.37/13.48 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(2052,d,1902,a)].
% 13.37/13.48 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(2052,d,1904,b)].
% 13.37/13.48 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(2052,d,1905,b)].
% 13.37/13.48 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(2052,d,1906,b)].
% 13.37/13.48 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(2052,d,1907,b)].
% 13.37/13.48 2053 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1826,a,1765,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2053,c,1901,a)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2053,c,1902,a)].
% 13.37/13.48 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(2053,c,1904,b)].
% 13.37/13.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2053,c,1905,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2053,c,1906,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2053,c,1907,b)].
% 13.37/13.49 2054 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1827,a,1765,b)].
% 13.37/13.49 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2054,c,1901,a)].
% 13.37/13.49 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2054,c,1902,a)].
% 13.37/13.49 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(2054,c,1904,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2054,c,1905,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2054,c,1906,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2054,c,1907,b)].
% 13.37/13.49 2055 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1828,a,1765,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2055,c,1901,a)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2055,c,1902,a)].
% 13.37/13.49 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(2055,c,1904,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2055,c,1905,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2055,c,1906,b)].
% 13.37/13.49 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2055,c,1907,b)].
% 13.37/13.49 2056 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1829,a,1765,b)].
% 13.37/13.49 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2056,c,1901,a)].
% 13.37/13.49 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2056,c,1902,a)].
% 13.37/13.49 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(2056,c,1904,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2056,c,1905,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2056,c,1906,b)].
% 13.37/13.49 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2056,c,1907,b)].
% 13.37/13.49 2057 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1844,b,1835,b)].
% 13.37/13.49 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2057,e,1901,a)].
% 13.37/13.49 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(2057,e,1902,a)].
% 13.37/13.49 2058 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1899,d,1835,b)].
% 13.57/13.66 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2058,d,1901,a)].
% 13.57/13.66 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2058,d,1902,a)].
% 13.57/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2058,d,1904,b)].
% 13.57/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2058,d,1905,b)].
% 13.57/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2058,d,1906,b)].
% 13.57/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2058,d,1907,b)].
% 13.57/13.66 2059 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 13.57/13.66 2060 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 13.57/13.66 2061 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 13.57/13.66 2062 -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].
% 13.57/13.66 2063 -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].
% 13.57/13.66 2064 -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].
% 13.57/13.66 2065 -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].
% 13.57/13.66 2066 -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].
% 13.57/13.66 2067 -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].
% 13.57/13.66 2068 -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].
% 13.57/13.66 2069 -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].
% 13.57/13.66 2070 -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].
% 13.57/13.66 2071 -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].
% 13.57/13.66 2072 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom). [assumption].
% 13.57/13.66 2073 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 13.57/13.66 2074 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 13.57/13.66 2075 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom). [assumption].
% 13.57/13.69 2076 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom). [assumption].
% 13.57/13.69 2077 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(c_0,D,A) | c_lessequals(c_times(B,D,A),c_times(C,D,A),A) # label(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) # label(axiom). [assumption].
% 13.57/13.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2077,a,2060,a)].
% 13.57/13.69 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2077,a,2061,a)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2062,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2077,a,2063,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2077,a,2064,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2077,a,2065,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2077,a,2066,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2067,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2068,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2077,a,2069,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2070,b)].
% 13.57/13.69 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2071,b)].
% 13.57/13.69 2078 -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)].
% 13.57/13.69 2079 -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)].
% 13.57/13.69 2080 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(163,a,159,b)].
% 13.57/13.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2080,b,2070,b)].
% 13.57/13.69 2081 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,159,b)].
% 13.57/13.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2081,b,2070,b)].
% 13.57/13.69 2082 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,159,b)].
% 13.57/13.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2082,b,2063,b)].
% 13.57/13.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2082,b,2066,b)].
% 13.57/13.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2082,b,2067,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2082,b,2068,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2082,b,2070,b)].
% 13.57/13.71 2083 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,159,b)].
% 13.57/13.71 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2083,b,2063,b)].
% 13.57/13.71 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2083,b,2066,b)].
% 13.57/13.71 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2083,b,2067,b)].
% 13.57/13.71 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2083,b,2068,b)].
% 13.57/13.71 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2083,b,2070,b)].
% 13.57/13.71 2084 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(171,a,159,b)].
% 13.57/13.71 2085 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(172,a,159,b)].
% 13.57/13.71 2086 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2086,b,2063,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2086,b,2066,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2086,b,2067,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2086,b,2068,b)].
% 13.57/13.71 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2086,b,2070,b)].
% 13.57/13.71 2087 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 13.57/13.71 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2087,b,2063,b)].
% 13.57/13.71 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2087,b,2066,b)].
% 13.57/13.71 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,b,2067,b)].
% 13.57/13.71 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2087,b,2068,b)].
% 13.57/13.71 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2087,b,2070,b)].
% 13.57/13.71 2088 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(247,b,233,b)].
% 13.57/13.71 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2088,b,2063,b)].
% 13.57/13.71 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2088,b,2066,b)].
% 13.57/13.71 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2088,b,2067,b)].
% 13.57/13.71 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2088,b,2068,b)].
% 13.57/13.71 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2088,b,2070,b)].
% 13.57/13.71 2089 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(248,b,233,b)].
% 13.57/13.71 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2089,b,2063,b)].
% 13.57/13.71 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2089,b,2066,b)].
% 13.85/13.94 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2089,b,2067,b)].
% 13.85/13.94 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,b,2068,b)].
% 13.85/13.94 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,b,2070,b)].
% 13.85/13.94 2090 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1165,a,1121,a)].
% 13.85/13.94 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2090,a,2059,a)].
% 13.85/13.94 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2090,a,2072,a)].
% 13.85/13.94 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(2090,a,2078,a)].
% 13.85/13.94 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(2090,a,2079,a)].
% 13.85/13.94 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2084,b)].
% 13.85/13.94 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2085,b)].
% 13.85/13.94 2091 class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1165,a,1146,a)].
% 13.85/13.94 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2091,a,2059,a)].
% 13.85/13.94 Derived: class_HOL_Otimes(tc_nat). [resolve(2091,a,2072,a)].
% 13.85/13.94 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2091,a,2073,a)].
% 13.85/13.94 Derived: class_HOL_Ozero(tc_nat). [resolve(2091,a,2076,a)].
% 13.85/13.94 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(2091,a,2078,a)].
% 13.85/13.94 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(2091,a,2079,a)].
% 13.85/13.94 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(2091,a,2084,b)].
% 13.85/13.94 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2091,a,2085,b)].
% 13.85/13.94 2092 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1165,a,1147,b)].
% 13.85/13.94 2093 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1165,a,1148,b)].
% 13.85/13.94 2094 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1612,b,1581,a)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2094,a,2062,b)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2094,a,2067,b)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2094,a,2068,b)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2094,a,2069,b)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2094,a,2070,b)].
% 13.85/13.94 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2094,a,2071,b)].
% 13.85/13.94 2095 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1582,a)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2095,a,2062,b)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2095,a,2067,b)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2095,a,2068,b)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2095,a,2069,b)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2095,a,2070,b)].
% 13.85/13.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2095,a,2071,b)].
% 13.85/13.95 2096 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1612,b,1583,a)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2096,a,2062,b)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2096,a,2067,b)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2096,a,2068,b)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2096,a,2069,b)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2096,a,2070,b)].
% 13.85/13.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2096,a,2071,b)].
% 13.85/13.95 2097 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1612,b,1584,a)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,a,2062,b)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,a,2067,b)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2097,a,2068,b)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2097,a,2069,b)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2097,a,2070,b)].
% 13.85/13.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2097,a,2071,b)].
% 13.85/13.95 2098 -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(1612,b,1585,a)].
% 13.85/13.95 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(2098,a,2062,b)].
% 13.85/13.95 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(2098,a,2067,b)].
% 13.85/13.95 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(2098,a,2068,b)].
% 13.85/13.95 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(2098,a,2069,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2098,a,2070,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2098,a,2071,b)].
% 13.85/13.96 2099 -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(1612,b,1586,a)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2099,a,2062,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2099,a,2067,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2099,a,2068,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2099,a,2069,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2099,a,2070,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2099,a,2071,b)].
% 13.85/13.96 2100 -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(1612,b,1587,a)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2100,a,2062,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2100,a,2067,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2100,a,2068,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2100,a,2069,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2100,a,2070,b)].
% 13.85/13.96 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2100,a,2071,b)].
% 13.85/13.96 2101 -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(1612,b,1588,a)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2101,a,2062,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2101,a,2067,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2101,a,2068,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2101,a,2069,b)].
% 13.85/13.96 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2101,a,2070,b)].
% 13.85/13.97 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(2101,a,2071,b)].
% 13.85/13.97 2102 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1589,a)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,a,2062,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,a,2067,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2102,a,2068,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2102,a,2069,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2102,a,2070,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2102,a,2071,b)].
% 13.85/13.97 2103 -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(1612,b,1590,a)].
% 13.85/13.97 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(2103,a,2062,b)].
% 13.85/13.97 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(2103,a,2067,b)].
% 13.85/13.97 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(2103,a,2068,b)].
% 13.85/13.97 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(2103,a,2069,b)].
% 13.85/13.97 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(2103,a,2070,b)].
% 13.85/13.97 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(2103,a,2071,b)].
% 13.85/13.97 2104 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1612,b,1591,a)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2104,a,2062,b)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2104,a,2067,b)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2104,a,2068,b)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2104,a,2069,b)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2104,a,2070,b)].
% 13.85/13.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2104,a,2071,b)].
% 13.85/13.97 2105 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1614,a,1612,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2062,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2067,b)].
% 13.85/13.97 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2105,d,2068,b)].
% 13.91/14.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2105,d,2069,b)].
% 13.91/14.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2105,d,2070,b)].
% 13.91/14.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2105,d,2071,b)].
% 13.91/14.03 2106 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1615,a,1612,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,d,2062,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,d,2067,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2106,d,2068,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2106,d,2069,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2106,d,2070,b)].
% 13.91/14.03 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2106,d,2071,b)].
% 13.91/14.03 2107 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1637,a)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2107,a,2062,b)].
% 13.91/14.03 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(2107,a,2067,b)].
% 13.91/14.03 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(2107,a,2068,b)].
% 13.91/14.03 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(2107,a,2069,b)].
% 13.91/14.03 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(2107,a,2070,b)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2107,a,2071,b)].
% 13.91/14.03 2108 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1638,a)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2108,a,2062,b)].
% 13.91/14.03 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(2108,a,2067,b)].
% 13.91/14.03 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(2108,a,2068,b)].
% 13.91/14.03 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(2108,a,2069,b)].
% 13.91/14.03 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(2108,a,2070,b)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2108,a,2071,b)].
% 13.91/14.03 2109 -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(1677,b,1639,a)].
% 13.91/14.03 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(2109,a,2062,b)].
% 13.91/14.03 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(2109,a,2067,b)].
% 13.91/14.03 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(2109,a,2068,b)].
% 13.91/14.03 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(2109,a,2069,b)].
% 13.91/14.03 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(2109,a,2070,b)].
% 13.91/14.03 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(2109,a,2071,b)].
% 13.91/14.03 2110 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1640,a)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,a,2062,b)].
% 13.91/14.03 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(2110,a,2067,b)].
% 13.91/14.03 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(2110,a,2068,b)].
% 13.91/14.03 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(2110,a,2069,b)].
% 13.91/14.03 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(2110,a,2070,b)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2110,a,2071,b)].
% 13.91/14.03 2111 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1641,a)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,a,2062,b)].
% 13.91/14.03 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(2111,a,2067,b)].
% 13.91/14.03 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(2111,a,2068,b)].
% 13.91/14.03 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(2111,a,2069,b)].
% 13.91/14.03 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(2111,a,2070,b)].
% 13.91/14.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2111,a,2071,b)].
% 13.91/14.03 2112 -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(1677,b,1642,a)].
% 13.91/14.03 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(2112,a,2062,b)].
% 13.91/14.03 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(2112,a,2067,b)].
% 13.91/14.03 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(2112,a,2068,b)].
% 13.91/14.03 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(2112,a,2069,b)].
% 13.91/14.03 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(2112,a,2070,b)].
% 13.91/14.04 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(2112,a,2071,b)].
% 13.91/14.04 2113 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1643,a)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2113,a,2062,b)].
% 13.91/14.04 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(2113,a,2067,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2113,a,2068,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2113,a,2069,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2113,a,2070,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2113,a,2071,b)].
% 13.91/14.04 2114 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1677,b,1644,a)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2114,a,2062,b)].
% 13.91/14.04 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(2114,a,2067,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2114,a,2068,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2114,a,2069,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2114,a,2070,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2114,a,2071,b)].
% 13.91/14.04 2115 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1677,b,1645,a)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,a,2062,b)].
% 13.91/14.04 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(2115,a,2067,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2115,a,2068,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2115,a,2069,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2115,a,2070,b)].
% 13.91/14.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2115,a,2071,b)].
% 13.91/14.04 2116 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1677,b,1646,a)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,a,2062,b)].
% 13.91/14.04 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(2116,a,2067,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2116,a,2068,b)].
% 13.91/14.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2116,a,2069,b)].
% 13.97/14.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2116,a,2070,b)].
% 13.97/14.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2116,a,2071,b)].
% 13.97/14.04 2117 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1647,a)].
% 13.97/14.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2117,a,2062,b)].
% 13.97/14.04 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(2117,a,2067,b)].
% 13.97/14.04 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(2117,a,2068,b)].
% 13.97/14.04 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(2117,a,2069,b)].
% 13.97/14.04 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(2117,a,2070,b)].
% 13.97/14.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2117,a,2071,b)].
% 13.97/14.04 2118 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1648,a)].
% 13.97/14.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2118,a,2062,b)].
% 13.97/14.04 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(2118,a,2067,b)].
% 13.97/14.04 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(2118,a,2068,b)].
% 13.97/14.04 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(2118,a,2069,b)].
% 13.97/14.04 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(2118,a,2070,b)].
% 13.97/14.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2118,a,2071,b)].
% 13.97/14.04 2119 -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(1677,b,1649,a)].
% 13.97/14.04 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(2119,a,2062,b)].
% 13.97/14.04 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(2119,a,2067,b)].
% 13.97/14.04 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(2119,a,2068,b)].
% 13.97/14.04 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(2119,a,2069,b)].
% 13.97/14.04 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(2119,a,2070,b)].
% 13.97/14.04 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(2119,a,2071,b)].
% 13.97/14.04 2120 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1650,a)].
% 13.97/14.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2120,a,2062,b)].
% 13.97/14.04 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(2120,a,2067,b)].
% 13.97/14.05 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(2120,a,2068,b)].
% 13.97/14.05 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(2120,a,2069,b)].
% 13.97/14.05 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(2120,a,2070,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2120,a,2071,b)].
% 13.97/14.05 2121 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1651,a)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2121,a,2062,b)].
% 13.97/14.05 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(2121,a,2067,b)].
% 13.97/14.05 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(2121,a,2068,b)].
% 13.97/14.05 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(2121,a,2069,b)].
% 13.97/14.05 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(2121,a,2070,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2121,a,2071,b)].
% 13.97/14.05 2122 -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(1677,b,1652,a)].
% 13.97/14.05 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(2122,a,2062,b)].
% 13.97/14.05 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(2122,a,2067,b)].
% 13.97/14.05 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(2122,a,2068,b)].
% 13.97/14.05 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(2122,a,2069,b)].
% 13.97/14.05 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(2122,a,2070,b)].
% 13.97/14.05 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(2122,a,2071,b)].
% 13.97/14.05 2123 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1677,b,1653,a)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2123,a,2062,b)].
% 13.97/14.05 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(2123,a,2067,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2123,a,2068,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2123,a,2069,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2123,a,2070,b)].
% 13.97/14.05 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2123,a,2071,b)].
% 13.98/14.07 2124 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1677,b,1654,a)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2124,a,2062,b)].
% 13.98/14.07 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(2124,a,2067,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2124,a,2068,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2124,a,2069,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2124,a,2070,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2124,a,2071,b)].
% 13.98/14.07 2125 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1677,b,1655,a)].
% 13.98/14.07 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2125,a,2062,b)].
% 13.98/14.07 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(2125,a,2067,b)].
% 13.98/14.07 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2125,a,2068,b)].
% 13.98/14.07 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2125,a,2069,b)].
% 13.98/14.07 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2125,a,2070,b)].
% 13.98/14.07 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2125,a,2071,b)].
% 13.98/14.07 2126 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1677,b,1656,a)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2126,a,2062,b)].
% 13.98/14.07 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(2126,a,2067,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2126,a,2068,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2126,a,2069,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2126,a,2070,b)].
% 13.98/14.07 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2126,a,2071,b)].
% 13.98/14.07 2127 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1780,a,1779,b)].
% 13.98/14.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2127,d,2062,b)].
% 13.98/14.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2127,d,2067,b)].
% 13.98/14.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2127,d,2068,b)].
% 13.98/14.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2127,d,2069,b)].
% 13.98/14.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2127,d,2070,b)].
% 14.21/14.33 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2127,d,2071,b)].
% 14.21/14.33 2128 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_10) # label(axiom). [assumption].
% 14.21/14.33 2129 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 14.21/14.33 2130 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 14.21/14.33 2131 -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].
% 14.21/14.33 2132 -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].
% 14.21/14.33 2133 -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].
% 14.21/14.33 2134 -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].
% 14.21/14.33 2135 -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].
% 14.21/14.33 2136 -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].
% 14.21/14.33 2137 -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].
% 14.21/14.33 2138 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_4) # label(axiom). [assumption].
% 14.21/14.33 2139 -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].
% 14.21/14.33 2140 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # label(axiom). [assumption].
% 14.21/14.33 2141 -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].
% 14.21/14.33 2142 -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].
% 14.21/14.33 2143 -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)].
% 14.21/14.33 2144 -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)].
% 14.21/14.33 2145 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 14.21/14.33 2146 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 14.21/14.33 2147 -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)].
% 14.21/14.33 2148 -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)].
% 14.21/14.33 2149 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(165,a,155,b)].
% 14.37/14.47 2150 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(166,a,155,b)].
% 14.37/14.47 2151 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(171,a,155,b)].
% 14.37/14.47 2152 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(172,a,155,b)].
% 14.37/14.47 2153 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 14.37/14.47 2154 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 14.37/14.47 2155 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(247,b,229,b)].
% 14.37/14.47 2156 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(248,b,229,b)].
% 14.37/14.47 2157 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,288,a)].
% 14.37/14.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2157,a,2132,b)].
% 14.37/14.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2157,a,2135,b)].
% 14.37/14.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2157,a,2136,b)].
% 14.37/14.47 2158 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,290,a)].
% 14.37/14.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2158,a,2132,b)].
% 14.37/14.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2158,a,2135,b)].
% 14.37/14.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2158,a,2136,b)].
% 14.37/14.47 2159 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(322,a,309,b)].
% 14.37/14.47 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2159,c,2136,b)].
% 14.37/14.47 2160 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(323,a,309,b)].
% 14.37/14.47 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2160,c,2136,b)].
% 14.37/14.47 2161 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(326,a,309,b)].
% 14.37/14.47 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,b,2136,b)].
% 14.37/14.47 2162 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(790,a,734,a)].
% 14.37/14.47 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,a,2136,b)].
% 14.37/14.47 2163 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1163,a,1121,a)].
% 14.37/14.47 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2163,a,2157,a)].
% 14.37/14.47 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2163,a,2158,a)].
% 14.37/14.47 2164 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1163,a,1146,a)].
% 14.37/14.47 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2164,a,2157,a)].
% 14.37/14.47 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2164,a,2158,a)].
% 14.37/14.47 2165 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1163,a,1147,b)].
% 14.37/14.47 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(2165,a,2157,a)].
% 14.37/14.47 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(2165,a,2158,a)].
% 14.37/14.47 2166 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1163,a,1148,b)].
% 14.37/14.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(2166,a,2157,a)].
% 14.37/14.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(2166,a,2158,a)].
% 14.56/14.66 2167 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1608,b,1581,a)].
% 14.56/14.66 2168 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1582,a)].
% 14.56/14.66 2169 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1608,b,1583,a)].
% 14.56/14.66 2170 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1608,b,1584,a)].
% 14.56/14.66 2171 -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(1608,b,1585,a)].
% 14.56/14.66 2172 -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(1608,b,1586,a)].
% 14.56/14.66 2173 -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(1608,b,1587,a)].
% 14.56/14.66 2174 -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(1608,b,1588,a)].
% 14.56/14.66 2175 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1589,a)].
% 14.56/14.66 2176 -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(1608,b,1590,a)].
% 14.56/14.66 2177 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1608,b,1591,a)].
% 14.56/14.66 2178 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1614,a,1608,b)].
% 14.56/14.66 2179 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1615,a,1608,b)].
% 14.56/14.66 2180 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1637,a)].
% 14.56/14.66 2181 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1638,a)].
% 14.56/14.66 2182 -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(1673,b,1639,a)].
% 14.56/14.66 2183 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1640,a)].
% 14.56/14.66 2184 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1641,a)].
% 14.56/14.66 2185 -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(1673,b,1642,a)].
% 14.56/14.66 2186 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1643,a)].
% 14.56/14.66 2187 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1673,b,1644,a)].
% 14.56/14.66 2188 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1673,b,1645,a)].
% 14.56/14.66 2189 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1673,b,1646,a)].
% 14.56/14.66 2190 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1647,a)].
% 14.56/14.66 2191 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1648,a)].
% 14.56/14.66 2192 -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(1673,b,1649,a)].
% 14.67/14.76 2193 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1650,a)].
% 14.67/14.76 2194 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1651,a)].
% 14.67/14.76 2195 -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(1673,b,1652,a)].
% 14.67/14.76 2196 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1673,b,1653,a)].
% 14.67/14.76 2197 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1673,b,1654,a)].
% 14.67/14.76 2198 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1673,b,1655,a)].
% 14.67/14.76 2199 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1673,b,1656,a)].
% 14.67/14.76 2200 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1780,a,1775,b)].
% 14.67/14.76 2201 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2068,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2201,d,2129,a)].
% 14.67/14.76 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2201,d,2130,a)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,d,2131,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,d,2132,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2201,d,2133,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2201,d,2134,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,d,2135,b)].
% 14.67/14.76 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2201,d,2136,b)].
% 14.67/14.76 2202 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2082,b,2068,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2202,b,2131,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2202,b,2132,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2202,b,2133,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2202,b,2134,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2202,b,2135,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2202,b,2136,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2202,b,2142,b)].
% 14.67/14.76 2203 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2083,b,2068,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2203,b,2131,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2203,b,2132,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2203,b,2133,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2203,b,2134,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2203,b,2135,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2203,b,2136,b)].
% 14.67/14.76 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2203,b,2142,b)].
% 14.67/14.76 2204 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2086,b,2068,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2204,b,2129,a)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2204,b,2131,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2204,b,2132,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2204,b,2133,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2204,b,2134,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2204,b,2135,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2204,b,2136,b)].
% 14.67/14.76 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2204,b,2142,b)].
% 14.67/14.76 2205 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2087,b,2068,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2205,b,2129,a)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2205,b,2131,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2205,b,2132,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2205,b,2133,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2205,b,2134,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2205,b,2135,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2205,b,2136,b)].
% 14.67/14.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2205,b,2142,b)].
% 14.67/14.76 2206 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2088,b,2068,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,b,2131,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2206,b,2132,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2206,b,2133,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2206,b,2134,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2206,b,2135,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2206,b,2136,b)].
% 14.67/14.76 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2206,b,2142,b)].
% 14.67/14.77 2207 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,b,2068,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2207,b,2131,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,b,2132,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2207,b,2133,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2207,b,2134,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2207,b,2135,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2207,b,2136,b)].
% 14.67/14.77 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2207,b,2142,b)].
% 14.67/14.77 2208 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2094,a,2068,b)].
% 14.67/14.77 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2208,b,2129,a)].
% 14.67/14.77 Derived: -c_less(A,A,tc_nat). [resolve(2208,b,2130,a)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2208,b,2131,b)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2208,b,2132,b)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2208,b,2133,b)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2208,b,2134,b)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2208,b,2135,b)].
% 14.67/14.77 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2208,b,2136,b)].
% 14.67/14.77 2209 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2095,a,2068,b)].
% 14.67/14.77 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2209,c,2129,a)].
% 14.67/14.77 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2209,c,2130,a)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2131,b)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2209,c,2132,b)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2209,c,2133,b)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2209,c,2134,b)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2135,b)].
% 14.67/14.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2209,c,2136,b)].
% 14.67/14.77 2210 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2096,a,2068,b)].
% 14.67/14.77 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2210,b,2129,a)].
% 14.67/14.77 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2210,b,2130,a)].
% 14.67/14.77 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2210,b,2131,b)].
% 14.67/14.77 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2210,b,2132,b)].
% 14.67/14.78 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2210,b,2133,b)].
% 14.67/14.78 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2210,b,2134,b)].
% 14.67/14.78 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2210,b,2135,b)].
% 14.67/14.78 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2210,b,2136,b)].
% 14.67/14.78 2211 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2097,a,2068,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2211,c,2129,a)].
% 14.67/14.78 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2211,c,2130,a)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2131,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2211,c,2132,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2211,c,2133,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2211,c,2134,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2135,b)].
% 14.67/14.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2211,c,2136,b)].
% 14.67/14.78 2212 -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(2098,a,2068,b)].
% 14.67/14.78 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(2212,c,2129,a)].
% 14.67/14.78 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(2212,c,2130,a)].
% 14.67/14.78 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(2212,c,2131,b)].
% 14.67/14.78 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(2212,c,2132,b)].
% 14.67/14.78 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(2212,c,2133,b)].
% 14.67/14.78 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(2212,c,2134,b)].
% 14.67/14.78 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(2212,c,2135,b)].
% 14.67/14.78 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(2212,c,2136,b)].
% 14.67/14.78 2213 -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(2099,a,2068,b)].
% 14.67/14.78 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(2213,c,2129,a)].
% 14.67/14.78 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(2213,c,2130,a)].
% 14.67/14.78 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(2213,c,2131,b)].
% 14.67/14.78 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(2213,c,2132,b)].
% 14.67/14.78 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(2213,c,2133,b)].
% 14.67/14.78 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(2213,c,2134,b)].
% 14.67/14.78 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(2213,c,2135,b)].
% 14.67/14.78 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(2213,c,2136,b)].
% 14.67/14.78 2214 -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(2100,a,2068,b)].
% 14.67/14.78 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(2214,c,2129,a)].
% 14.67/14.78 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(2214,c,2130,a)].
% 14.67/14.78 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(2214,c,2131,b)].
% 14.67/14.78 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(2214,c,2132,b)].
% 14.67/14.78 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(2214,c,2133,b)].
% 14.67/14.78 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(2214,c,2134,b)].
% 14.67/14.78 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(2214,c,2135,b)].
% 14.67/14.78 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(2214,c,2136,b)].
% 14.67/14.78 2215 -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(2101,a,2068,b)].
% 14.67/14.78 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(2215,c,2129,a)].
% 14.67/14.78 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(2215,c,2130,a)].
% 14.67/14.78 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(2215,c,2131,b)].
% 14.67/14.78 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(2215,c,2132,b)].
% 14.67/14.78 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(2215,c,2133,b)].
% 14.67/14.79 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(2215,c,2134,b)].
% 14.67/14.79 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(2215,c,2135,b)].
% 14.67/14.79 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(2215,c,2136,b)].
% 14.67/14.79 2216 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2102,a,2068,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2216,c,2129,a)].
% 14.67/14.79 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2216,c,2130,a)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2216,c,2131,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2216,c,2132,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2216,c,2133,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2216,c,2134,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2216,c,2135,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2216,c,2136,b)].
% 14.67/14.79 2217 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(2103,a,2068,b)].
% 14.67/14.79 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(2217,b,2129,a)].
% 14.67/14.79 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(2217,b,2130,a)].
% 14.67/14.79 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(2217,b,2131,b)].
% 14.67/14.79 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(2217,b,2132,b)].
% 14.67/14.79 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(2217,b,2133,b)].
% 14.67/14.79 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(2217,b,2134,b)].
% 14.67/14.79 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(2217,b,2135,b)].
% 14.67/14.79 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(2217,b,2136,b)].
% 14.67/14.79 2218 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2104,a,2068,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2218,b,2129,a)].
% 14.67/14.79 Derived: c_lessequals(A,A,tc_nat). [resolve(2218,b,2130,a)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2218,b,2131,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2218,b,2132,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2218,b,2133,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2218,b,2134,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2218,b,2135,b)].
% 14.67/14.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2218,b,2136,b)].
% 14.67/14.79 2219 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2105,d,2068,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2219,d,2129,a)].
% 14.67/14.79 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2219,d,2130,a)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2219,d,2131,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2219,d,2132,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2219,d,2133,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2219,d,2134,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2219,d,2135,b)].
% 14.67/14.79 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2219,d,2136,b)].
% 14.67/14.79 2220 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2106,d,2068,b)].
% 14.67/14.79 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2220,d,2129,a)].
% 14.67/14.79 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2220,d,2130,a)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2220,d,2131,b)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2220,d,2132,b)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2220,d,2133,b)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2220,d,2134,b)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2220,d,2135,b)].
% 14.67/14.79 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2220,d,2136,b)].
% 14.67/14.79 2221 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2107,a,2068,b)].
% 14.67/14.79 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2221,c,2129,a)].
% 14.67/14.79 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2221,c,2130,a)].
% 14.67/14.79 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2221,c,2131,b)].
% 14.67/14.79 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(2221,c,2132,b)].
% 14.67/14.79 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2221,c,2133,b)].
% 14.67/14.79 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2221,c,2134,b)].
% 14.67/14.80 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(2221,c,2135,b)].
% 14.67/14.80 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(2221,c,2136,b)].
% 14.67/14.80 2222 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2108,a,2068,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2222,c,2129,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2222,c,2130,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2222,c,2131,b)].
% 14.67/14.80 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(2222,c,2132,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2222,c,2133,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2222,c,2134,b)].
% 14.67/14.80 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(2222,c,2135,b)].
% 14.67/14.80 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(2222,c,2136,b)].
% 14.67/14.80 2223 -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(2109,a,2068,b)].
% 14.67/14.80 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(2223,d,2129,a)].
% 14.67/14.80 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(2223,d,2130,a)].
% 14.67/14.80 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(2223,d,2131,b)].
% 14.67/14.80 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(2223,d,2132,b)].
% 14.67/14.80 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(2223,d,2133,b)].
% 14.67/14.80 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(2223,d,2134,b)].
% 14.67/14.80 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(2223,d,2135,b)].
% 14.67/14.80 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(2223,d,2136,b)].
% 14.67/14.80 2224 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2110,a,2068,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2224,c,2129,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2224,c,2130,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2224,c,2131,b)].
% 14.67/14.80 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(2224,c,2132,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2224,c,2133,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2224,c,2134,b)].
% 14.67/14.80 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(2224,c,2135,b)].
% 14.67/14.80 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(2224,c,2136,b)].
% 14.67/14.80 2225 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2111,a,2068,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2225,c,2129,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2225,c,2130,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2225,c,2131,b)].
% 14.67/14.80 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(2225,c,2132,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2225,c,2133,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2225,c,2134,b)].
% 14.67/14.80 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(2225,c,2135,b)].
% 14.67/14.80 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(2225,c,2136,b)].
% 14.67/14.80 2226 -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(2112,a,2068,b)].
% 14.67/14.80 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(2226,d,2129,a)].
% 14.67/14.80 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(2226,d,2130,a)].
% 14.67/14.80 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(2226,d,2131,b)].
% 14.67/14.80 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(2226,d,2132,b)].
% 14.67/14.80 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(2226,d,2133,b)].
% 14.67/14.80 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(2226,d,2134,b)].
% 14.67/14.80 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(2226,d,2135,b)].
% 14.67/14.80 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(2226,d,2136,b)].
% 14.67/14.80 2227 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2113,a,2068,b)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2227,c,2129,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2227,c,2130,a)].
% 14.67/14.80 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2227,c,2131,b)].
% 14.67/14.81 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(2227,c,2132,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2227,c,2133,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2227,c,2134,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2227,c,2135,b)].
% 14.67/14.81 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(2227,c,2136,b)].
% 14.67/14.81 2228 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2114,a,2068,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2228,c,2129,a)].
% 14.67/14.81 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2228,c,2130,a)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2228,c,2131,b)].
% 14.67/14.81 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(2228,c,2132,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2228,c,2133,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2228,c,2134,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2228,c,2135,b)].
% 14.67/14.81 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(2228,c,2136,b)].
% 14.67/14.81 2229 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2115,a,2068,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2229,c,2129,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2229,c,2130,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2229,c,2131,b)].
% 14.67/14.81 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(2229,c,2132,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2229,c,2133,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2229,c,2134,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2229,c,2135,b)].
% 14.67/14.81 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(2229,c,2136,b)].
% 14.67/14.81 2230 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2116,a,2068,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2230,c,2129,a)].
% 14.67/14.81 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2230,c,2130,a)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2230,c,2131,b)].
% 14.67/14.81 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(2230,c,2132,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2230,c,2133,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2230,c,2134,b)].
% 14.67/14.81 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2230,c,2135,b)].
% 14.67/14.81 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(2230,c,2136,b)].
% 14.67/14.81 2231 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2117,a,2068,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2231,c,2129,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2231,c,2130,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2231,c,2131,b)].
% 14.67/14.81 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(2231,c,2132,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2231,c,2133,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2231,c,2134,b)].
% 14.67/14.81 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(2231,c,2135,b)].
% 14.67/14.81 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(2231,c,2136,b)].
% 14.67/14.81 2232 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2118,a,2068,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2232,c,2129,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2232,c,2130,a)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2232,c,2131,b)].
% 14.67/14.81 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(2232,c,2132,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2232,c,2133,b)].
% 14.67/14.81 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2232,c,2134,b)].
% 14.67/14.81 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(2232,c,2135,b)].
% 14.67/14.81 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(2232,c,2136,b)].
% 14.67/14.81 2233 -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(2119,a,2068,b)].
% 14.67/14.81 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(2233,d,2129,a)].
% 14.67/14.81 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(2233,d,2130,a)].
% 14.67/14.81 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(2233,d,2131,b)].
% 14.67/14.81 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(2233,d,2132,b)].
% 14.75/14.82 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(2233,d,2133,b)].
% 14.75/14.82 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(2233,d,2134,b)].
% 14.75/14.82 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(2233,d,2135,b)].
% 14.75/14.82 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(2233,d,2136,b)].
% 14.75/14.82 2234 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2120,a,2068,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2234,c,2129,a)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2234,c,2130,a)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2234,c,2131,b)].
% 14.75/14.82 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(2234,c,2132,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2234,c,2133,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2234,c,2134,b)].
% 14.75/14.82 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(2234,c,2135,b)].
% 14.75/14.82 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(2234,c,2136,b)].
% 14.75/14.82 2235 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2121,a,2068,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2235,c,2129,a)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2235,c,2130,a)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2235,c,2131,b)].
% 14.75/14.82 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(2235,c,2132,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2235,c,2133,b)].
% 14.75/14.82 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2235,c,2134,b)].
% 14.75/14.82 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(2235,c,2135,b)].
% 14.75/14.82 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(2235,c,2136,b)].
% 14.75/14.82 2236 -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(2122,a,2068,b)].
% 14.75/14.82 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(2236,d,2129,a)].
% 14.75/14.82 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(2236,d,2130,a)].
% 14.75/14.83 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(2236,d,2131,b)].
% 14.75/14.83 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(2236,d,2132,b)].
% 14.75/14.83 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(2236,d,2133,b)].
% 14.75/14.83 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(2236,d,2134,b)].
% 14.75/14.83 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(2236,d,2135,b)].
% 14.75/14.83 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(2236,d,2136,b)].
% 14.75/14.83 2237 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2123,a,2068,b)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2237,c,2129,a)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2237,c,2130,a)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2237,c,2131,b)].
% 14.75/14.83 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(2237,c,2132,b)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2237,c,2133,b)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2237,c,2134,b)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2237,c,2135,b)].
% 14.75/14.83 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(2237,c,2136,b)].
% 14.75/14.83 2238 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2124,a,2068,b)].
% 14.75/14.83 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2238,c,2129,a)].
% 14.75/14.83 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2238,c,2130,a)].
% 14.75/14.83 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2238,c,2131,b)].
% 14.75/14.83 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(2238,c,2132,b)].
% 14.75/14.83 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2238,c,2133,b)].
% 14.75/14.83 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2238,c,2134,b)].
% 14.75/14.83 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2238,c,2135,b)].
% 14.75/14.83 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(2238,c,2136,b)].
% 14.75/14.83 2239 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2125,a,2068,b)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2239,c,2129,a)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2239,c,2130,a)].
% 14.75/14.83 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,c,2131,b)].
% 14.97/15.04 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(2239,c,2132,b)].
% 14.97/15.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2239,c,2133,b)].
% 14.97/15.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2239,c,2134,b)].
% 14.97/15.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2239,c,2135,b)].
% 14.97/15.04 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(2239,c,2136,b)].
% 14.97/15.04 2240 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2126,a,2068,b)].
% 14.97/15.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2240,c,2129,a)].
% 14.97/15.04 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2240,c,2130,a)].
% 14.97/15.04 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,c,2131,b)].
% 14.97/15.04 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(2240,c,2132,b)].
% 14.97/15.04 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2240,c,2133,b)].
% 14.97/15.04 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2240,c,2134,b)].
% 14.97/15.04 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2240,c,2135,b)].
% 14.97/15.04 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(2240,c,2136,b)].
% 14.97/15.04 2241 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2127,d,2068,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2241,d,2129,a)].
% 14.97/15.04 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2241,d,2130,a)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2241,d,2131,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2241,d,2132,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2241,d,2133,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2241,d,2134,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2241,d,2135,b)].
% 14.97/15.04 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2241,d,2136,b)].
% 14.97/15.04 2242 -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].
% 14.97/15.04 2243 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 14.97/15.04 2244 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 14.97/15.07 2245 -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].
% 14.97/15.07 2246 -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].
% 14.97/15.07 2247 -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].
% 14.97/15.07 2248 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_3) # label(axiom). [assumption].
% 14.97/15.07 2249 -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].
% 14.97/15.07 2250 -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].
% 14.97/15.07 2251 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_7) # label(axiom). [assumption].
% 14.97/15.07 2252 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_8) # label(axiom). [assumption].
% 14.97/15.07 2253 -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)].
% 14.97/15.07 2254 -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)].
% 14.97/15.07 2255 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 14.97/15.07 2256 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 14.97/15.07 2257 -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)].
% 14.97/15.07 2258 -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)].
% 14.97/15.07 2259 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(165,a,153,b)].
% 14.97/15.07 2260 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(166,a,153,b)].
% 14.97/15.07 2261 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(171,a,153,b)].
% 14.97/15.07 2262 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(172,a,153,b)].
% 14.97/15.07 2263 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 14.97/15.07 2264 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 14.97/15.07 2265 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(247,b,227,b)].
% 14.97/15.07 2266 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(248,b,227,b)].
% 14.97/15.07 2267 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,288,a)].
% 14.97/15.07 2268 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,290,a)].
% 14.97/15.07 2269 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(322,a,307,b)].
% 14.97/15.07 2270 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(323,a,307,b)].
% 15.03/15.14 2271 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(789,a,734,a)].
% 15.03/15.14 2272 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(789,a,741,a)].
% 15.03/15.14 2273 -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(902,b,832,a)].
% 15.03/15.14 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(2273,a,2245,b)].
% 15.03/15.14 2274 -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(902,b,833,a)].
% 15.03/15.14 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(2274,a,2245,b)].
% 15.03/15.14 2275 -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(902,b,834,a)].
% 15.03/15.14 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(2275,a,2245,b)].
% 15.03/15.14 2276 -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(902,b,835,a)].
% 15.03/15.14 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(2276,a,2245,b)].
% 15.03/15.14 2277 -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(902,b,836,a)].
% 15.03/15.14 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(2277,a,2245,b)].
% 15.03/15.14 2278 -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(902,b,837,a)].
% 15.03/15.14 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(2278,a,2245,b)].
% 15.03/15.14 2279 -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(902,b,838,a)].
% 15.03/15.14 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(2279,a,2245,b)].
% 15.03/15.14 2280 -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(902,b,839,a)].
% 15.03/15.14 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(2280,a,2245,b)].
% 15.03/15.14 2281 -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(902,b,840,a)].
% 15.03/15.15 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(2281,a,2245,b)].
% 15.03/15.15 2282 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,841,a)].
% 15.03/15.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2245,b)].
% 15.03/15.15 2283 -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(902,b,842,a)].
% 15.03/15.15 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(2283,a,2245,b)].
% 15.03/15.15 2284 -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(902,b,843,a)].
% 15.03/15.15 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(2284,a,2245,b)].
% 15.03/15.15 2285 -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(902,b,844,a)].
% 15.03/15.15 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(2285,a,2245,b)].
% 15.03/15.15 2286 -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(902,b,845,a)].
% 15.03/15.15 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(2286,a,2245,b)].
% 15.03/15.15 2287 -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(902,b,846,a)].
% 15.03/15.15 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(2287,a,2245,b)].
% 15.03/15.15 2288 -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(902,b,847,a)].
% 15.03/15.15 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(2288,a,2245,b)].
% 15.03/15.15 2289 -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(902,b,848,a)].
% 15.03/15.15 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(2289,a,2245,b)].
% 15.03/15.15 2290 -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(902,b,849,a)].
% 15.03/15.15 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(2290,a,2245,b)].
% 15.03/15.16 2291 -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(902,b,850,a)].
% 15.03/15.16 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(2291,a,2245,b)].
% 15.03/15.16 2292 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,851,a)].
% 15.03/15.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,a,2245,b)].
% 15.03/15.16 2293 -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(902,b,852,a)].
% 15.03/15.16 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(2293,a,2245,b)].
% 15.03/15.16 2294 -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(902,b,853,a)].
% 15.03/15.16 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(2294,a,2245,b)].
% 15.03/15.16 2295 -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(902,b,854,a)].
% 15.03/15.16 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(2295,a,2245,b)].
% 15.03/15.16 2296 -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(902,b,855,b)].
% 15.03/15.16 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(2296,a,2245,b)].
% 15.03/15.16 2297 -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(902,b,856,b)].
% 15.03/15.16 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(2297,a,2245,b)].
% 15.03/15.16 2298 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(902,b,857,a)].
% 15.03/15.16 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(2298,a,2245,b)].
% 15.03/15.16 2299 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(902,b,858,a)].
% 15.03/15.16 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(2299,a,2245,b)].
% 15.03/15.16 2300 -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(902,b,859,a)].
% 15.03/15.16 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(2300,a,2245,b)].
% 15.03/15.16 2301 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(902,b,860,a)].
% 15.03/15.16 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(2301,a,2245,b)].
% 15.09/15.17 2302 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(902,b,861,a)].
% 15.09/15.17 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(2302,a,2245,b)].
% 15.09/15.17 2303 -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(902,b,862,a)].
% 15.09/15.17 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(2303,a,2245,b)].
% 15.09/15.17 2304 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(902,b,863,a)].
% 15.09/15.17 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(2304,a,2245,b)].
% 15.09/15.17 2305 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(902,b,864,a)].
% 15.09/15.17 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(2305,a,2245,b)].
% 15.09/15.17 2306 -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(902,b,865,a)].
% 15.09/15.17 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(2306,a,2245,b)].
% 15.09/15.17 2307 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(902,b,866,a)].
% 15.09/15.17 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2307,a,2245,b)].
% 15.09/15.17 2308 -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(902,b,867,a)].
% 15.09/15.17 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(2308,a,2245,b)].
% 15.09/15.17 2309 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(902,b,868,a)].
% 15.09/15.17 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(2309,a,2245,b)].
% 15.09/15.17 2310 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(902,b,869,a)].
% 15.09/15.17 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(2310,a,2245,b)].
% 15.09/15.17 2311 -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(902,b,870,a)].
% 15.09/15.17 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(2311,a,2245,b)].
% 15.09/15.17 2312 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(902,b,871,a)].
% 15.09/15.17 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2312,a,2245,b)].
% 15.09/15.17 2313 -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(902,b,872,a)].
% 15.09/15.17 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(2313,a,2245,b)].
% 15.09/15.17 2314 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(902,b,873,a)].
% 15.09/15.17 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(2314,a,2245,b)].
% 15.09/15.18 2315 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(902,b,874,a)].
% 15.09/15.18 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(2315,a,2245,b)].
% 15.09/15.18 2316 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(902,b,875,a)].
% 15.09/15.18 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(2316,a,2245,b)].
% 15.09/15.18 2317 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(902,b,876,a)].
% 15.09/15.18 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(2317,a,2245,b)].
% 15.09/15.18 2318 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(902,b,877,a)].
% 15.09/15.18 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2318,a,2245,b)].
% 15.09/15.18 2319 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(902,b,878,a)].
% 15.09/15.18 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2319,a,2245,b)].
% 15.09/15.18 2320 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(902,b,879,a)].
% 15.09/15.18 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2320,a,2245,b)].
% 15.09/15.18 2321 -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(902,b,880,a)].
% 15.09/15.18 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(2321,a,2245,b)].
% 15.09/15.18 2322 -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(902,b,881,a)].
% 15.09/15.18 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(2322,a,2245,b)].
% 15.09/15.18 2323 -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(902,b,882,a)].
% 15.09/15.18 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(2323,a,2245,b)].
% 15.09/15.18 2324 -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(902,b,883,a)].
% 15.09/15.18 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(2324,a,2245,b)].
% 15.09/15.18 2325 -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(902,b,884,a)].
% 15.09/15.18 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(2325,a,2245,b)].
% 15.22/15.30 2326 -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(902,b,885,a)].
% 15.22/15.30 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(2326,a,2245,b)].
% 15.22/15.30 2327 -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(902,b,886,a)].
% 15.22/15.30 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(2327,a,2245,b)].
% 15.22/15.30 2328 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(902,b,887,a)].
% 15.22/15.30 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,a,2245,b)].
% 15.22/15.30 2329 -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(902,b,888,a)].
% 15.22/15.30 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(2329,a,2245,b)].
% 15.22/15.30 2330 -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(902,b,889,a)].
% 15.22/15.30 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(2330,a,2245,b)].
% 15.22/15.30 2331 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(904,a,902,b)].
% 15.22/15.30 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2331,b,2245,b)].
% 15.22/15.30 2332 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(905,a,902,b)].
% 15.22/15.30 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2332,b,2245,b)].
% 15.22/15.30 2333 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1092,b,1076,a)].
% 15.22/15.30 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2333,a,2245,b)].
% 15.22/15.30 2334 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1115,b,1099,a)].
% 15.22/15.30 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2334,a,2245,b)].
% 15.22/15.30 2335 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1157,a,1121,a)].
% 15.22/15.30 2336 class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1157,a,1146,a)].
% 15.22/15.30 2337 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1147,b)].
% 15.22/15.30 2338 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1148,b)].
% 15.22/15.30 2339 -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(1501,b,1477,a)].
% 15.22/15.30 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(2339,a,2245,b)].
% 15.22/15.30 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(2339,a,2246,b)].
% 15.22/15.32 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(2339,a,2247,b)].
% 15.22/15.32 2340 -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(1501,b,1478,a)].
% 15.22/15.32 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(2340,a,2245,b)].
% 15.22/15.32 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(2340,a,2246,b)].
% 15.22/15.32 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(2340,a,2247,b)].
% 15.22/15.32 2341 -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(1501,b,1479,a)].
% 15.22/15.32 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(2341,a,2245,b)].
% 15.22/15.32 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(2341,a,2246,b)].
% 15.22/15.32 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(2341,a,2247,b)].
% 15.22/15.32 2342 -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(1501,b,1480,a)].
% 15.22/15.32 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(2342,a,2245,b)].
% 15.22/15.32 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(2342,a,2246,b)].
% 15.22/15.32 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(2342,a,2247,b)].
% 15.22/15.32 2343 -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(1501,b,1481,a)].
% 15.22/15.32 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(2343,a,2245,b)].
% 15.22/15.32 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(2343,a,2246,b)].
% 15.22/15.32 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(2343,a,2247,b)].
% 15.22/15.32 2344 -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(1501,b,1482,a)].
% 15.22/15.32 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(2344,a,2245,b)].
% 15.22/15.32 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(2344,a,2246,b)].
% 15.22/15.32 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(2344,a,2247,b)].
% 15.22/15.32 2345 -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(1501,b,1483,a)].
% 15.22/15.32 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(2345,a,2245,b)].
% 15.22/15.32 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(2345,a,2246,b)].
% 15.22/15.32 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(2345,a,2247,b)].
% 15.22/15.32 2346 -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(1501,b,1484,a)].
% 15.22/15.32 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(2346,a,2245,b)].
% 15.22/15.32 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(2346,a,2246,b)].
% 15.35/15.42 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(2346,a,2247,b)].
% 15.35/15.42 2347 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1606,b,1581,a)].
% 15.35/15.42 2348 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1582,a)].
% 15.35/15.42 2349 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1606,b,1583,a)].
% 15.35/15.42 2350 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1606,b,1584,a)].
% 15.35/15.42 2351 -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(1606,b,1585,a)].
% 15.35/15.42 2352 -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(1606,b,1586,a)].
% 15.35/15.42 2353 -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(1606,b,1587,a)].
% 15.35/15.42 2354 -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(1606,b,1588,a)].
% 15.35/15.42 2355 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1589,a)].
% 15.35/15.42 2356 -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(1606,b,1590,a)].
% 15.35/15.42 2357 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1606,b,1591,a)].
% 15.35/15.42 2358 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1614,a,1606,b)].
% 15.35/15.42 2359 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1615,a,1606,b)].
% 15.35/15.42 2360 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1637,a)].
% 15.35/15.42 2361 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1638,a)].
% 15.35/15.42 2362 -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(1671,b,1639,a)].
% 15.35/15.42 2363 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1640,a)].
% 15.35/15.42 2364 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1641,a)].
% 15.35/15.42 2365 -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(1671,b,1642,a)].
% 15.35/15.42 2366 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1643,a)].
% 15.35/15.42 2367 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1671,b,1644,a)].
% 15.35/15.42 2368 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1671,b,1645,a)].
% 15.35/15.42 2369 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1671,b,1646,a)].
% 15.35/15.42 2370 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1647,a)].
% 15.41/15.48 2371 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1648,a)].
% 15.41/15.48 2372 -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(1671,b,1649,a)].
% 15.41/15.48 2373 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1650,a)].
% 15.41/15.48 2374 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1651,a)].
% 15.41/15.48 2375 -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(1671,b,1652,a)].
% 15.41/15.48 2376 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1671,b,1653,a)].
% 15.41/15.48 2377 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1671,b,1654,a)].
% 15.41/15.48 2378 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1671,b,1655,a)].
% 15.41/15.48 2379 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1671,b,1656,a)].
% 15.41/15.48 2380 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1780,a,1773,b)].
% 15.41/15.48 2381 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1844,b,1842,b)].
% 15.41/15.48 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2381,e,2245,b)].
% 15.41/15.48 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2381,e,2246,b)].
% 15.41/15.48 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2381,e,2247,b)].
% 15.41/15.48 2382 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1986,c,1907,b)].
% 15.41/15.48 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2382,c,2243,a)].
% 15.41/15.48 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2382,c,2244,a)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2382,c,2245,b)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2382,c,2246,b)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2382,c,2247,b)].
% 15.41/15.48 2383 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1987,c,1907,b)].
% 15.41/15.48 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2383,c,2243,a)].
% 15.41/15.48 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2383,c,2244,a)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2383,c,2245,b)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2383,c,2246,b)].
% 15.41/15.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2383,c,2247,b)].
% 15.41/15.48 2384 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1988,b,1907,b)].
% 15.41/15.48 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2384,b,2243,a)].
% 15.41/15.48 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2384,b,2244,a)].
% 15.41/15.52 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2384,b,2245,b)].
% 15.41/15.52 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2384,b,2246,b)].
% 15.41/15.52 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2384,b,2247,b)].
% 15.41/15.52 2385 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1989,b,1907,b)].
% 15.41/15.52 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2385,b,2243,a)].
% 15.41/15.52 Derived: class_HOL_Oplus(tc_nat). [resolve(2385,b,2244,a)].
% 15.41/15.52 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2385,b,2245,b)].
% 15.41/15.52 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2385,b,2246,b)].
% 15.41/15.52 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2385,b,2247,b)].
% 15.41/15.52 2386 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2024,b,1907,b)].
% 15.41/15.52 2387 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1907,b)].
% 15.41/15.52 2388 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2026,b,1907,b)].
% 15.41/15.52 2389 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2027,c,1907,b)].
% 15.41/15.52 2390 -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(2028,c,1907,b)].
% 15.41/15.52 2391 -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(2029,c,1907,b)].
% 15.41/15.52 2392 -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(2030,c,1907,b)].
% 15.41/15.52 2393 -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(2031,c,1907,b)].
% 15.41/15.52 2394 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1907,b)].
% 15.41/15.52 2395 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(2033,b,1907,b)].
% 15.41/15.52 2396 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2034,b,1907,b)].
% 15.41/15.52 2397 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,d,1907,b)].
% 15.41/15.52 2398 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2036,d,1907,b)].
% 15.41/15.52 2399 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2037,c,1907,b)].
% 15.41/15.52 2400 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2038,c,1907,b)].
% 15.41/15.52 2401 -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(2039,d,1907,b)].
% 15.41/15.52 2402 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2040,c,1907,b)].
% 15.41/15.52 2403 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2041,c,1907,b)].
% 15.41/15.52 2404 -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(2042,d,1907,b)].
% 15.41/15.52 2405 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2043,c,1907,b)].
% 15.53/15.59 2406 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2044,c,1907,b)].
% 15.53/15.59 2407 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2045,c,1907,b)].
% 15.53/15.59 2408 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2046,c,1907,b)].
% 15.53/15.59 2409 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2047,c,1907,b)].
% 15.53/15.59 2410 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2048,c,1907,b)].
% 15.53/15.59 2411 -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(2049,d,1907,b)].
% 15.53/15.59 2412 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2050,c,1907,b)].
% 15.53/15.59 2413 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2051,c,1907,b)].
% 15.53/15.59 2414 -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(2052,d,1907,b)].
% 15.53/15.59 2415 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2053,c,1907,b)].
% 15.53/15.59 2416 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2054,c,1907,b)].
% 15.53/15.59 2417 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2055,c,1907,b)].
% 15.53/15.59 2418 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2056,c,1907,b)].
% 15.53/15.59 2419 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2058,d,1907,b)].
% 15.53/15.59 2420 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2077,a,2066,b)].
% 15.53/15.59 2421 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2082,b,2066,b)].
% 15.53/15.59 2422 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2083,b,2066,b)].
% 15.53/15.59 2423 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2086,b,2066,b)].
% 15.53/15.59 2424 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2087,b,2066,b)].
% 15.53/15.59 2425 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2088,b,2066,b)].
% 15.53/15.59 2426 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2089,b,2066,b)].
% 15.53/15.59 2427 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2157,a,2135,b)].
% 15.53/15.59 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2427,b,2245,b)].
% 15.53/15.59 2428 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2158,a,2135,b)].
% 15.53/15.59 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2428,b,2245,b)].
% 15.53/15.59 2429 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,d,2135,b)].
% 15.53/15.59 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2429,d,2243,a)].
% 15.53/15.60 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2429,d,2244,a)].
% 15.53/15.60 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2429,d,2245,b)].
% 15.53/15.60 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2429,d,2246,b)].
% 15.53/15.60 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2429,d,2247,b)].
% 15.53/15.60 2430 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2202,b,2135,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2430,b,2243,a)].
% 15.53/15.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2430,b,2244,a)].
% 15.53/15.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2430,b,2245,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2430,b,2246,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2430,b,2247,b)].
% 15.53/15.60 2431 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2203,b,2135,b)].
% 15.53/15.60 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2431,b,2243,a)].
% 15.53/15.60 Derived: class_HOL_Otimes(tc_nat). [resolve(2431,b,2244,a)].
% 15.53/15.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2431,b,2245,b)].
% 15.53/15.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2431,b,2246,b)].
% 15.53/15.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2431,b,2247,b)].
% 15.53/15.60 2432 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2204,b,2135,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2432,b,2243,a)].
% 15.53/15.60 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2432,b,2244,a)].
% 15.53/15.60 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2432,b,2245,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2432,b,2246,b)].
% 15.53/15.60 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2432,b,2247,b)].
% 15.53/15.60 2433 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2205,b,2135,b)].
% 15.53/15.60 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2433,b,2243,a)].
% 15.53/15.60 Derived: class_HOL_Ozero(tc_nat). [resolve(2433,b,2244,a)].
% 15.53/15.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2433,b,2245,b)].
% 15.53/15.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2433,b,2246,b)].
% 15.53/15.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2433,b,2247,b)].
% 15.53/15.60 2434 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2206,b,2135,b)].
% 15.53/15.60 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2434,b,2243,a)].
% 15.53/15.60 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(2434,b,2244,a)].
% 15.53/15.60 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2434,b,2245,b)].
% 15.53/15.60 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2434,b,2246,b)].
% 15.53/15.60 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2434,b,2247,b)].
% 15.53/15.61 2435 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2207,b,2135,b)].
% 15.53/15.61 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2435,b,2243,a)].
% 15.53/15.61 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2435,b,2244,a)].
% 15.53/15.61 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2435,b,2245,b)].
% 15.53/15.61 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2435,b,2246,b)].
% 15.53/15.61 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2435,b,2247,b)].
% 15.53/15.61 2436 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2208,b,2135,b)].
% 15.53/15.61 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2436,b,2243,a)].
% 15.53/15.61 Derived: -c_less(A,A,tc_nat). [resolve(2436,b,2244,a)].
% 15.53/15.61 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2436,b,2245,b)].
% 15.53/15.61 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2436,b,2246,b)].
% 15.53/15.61 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2436,b,2247,b)].
% 15.53/15.61 2437 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2135,b)].
% 15.53/15.61 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2437,c,2243,a)].
% 15.53/15.61 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2437,c,2244,a)].
% 15.53/15.61 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2437,c,2245,b)].
% 15.53/15.61 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2437,c,2246,b)].
% 15.53/15.61 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2437,c,2247,b)].
% 15.53/15.61 2438 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2210,b,2135,b)].
% 15.53/15.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2438,b,2243,a)].
% 15.53/15.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2438,b,2244,a)].
% 15.53/15.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2438,b,2245,b)].
% 15.53/15.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2438,b,2246,b)].
% 15.53/15.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2438,b,2247,b)].
% 15.53/15.61 2439 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2135,b)].
% 15.53/15.61 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2439,c,2243,a)].
% 15.53/15.61 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2439,c,2244,a)].
% 15.53/15.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2439,c,2245,b)].
% 15.53/15.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2439,c,2246,b)].
% 15.53/15.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2439,c,2247,b)].
% 15.56/15.62 2440 -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(2212,c,2135,b)].
% 15.56/15.62 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2440,c,2243,a)].
% 15.56/15.62 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2440,c,2244,a)].
% 15.56/15.62 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2440,c,2245,b)].
% 15.56/15.62 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2440,c,2246,b)].
% 15.56/15.62 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2440,c,2247,b)].
% 15.56/15.62 2441 -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(2213,c,2135,b)].
% 15.56/15.62 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2441,c,2243,a)].
% 15.56/15.62 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2441,c,2244,a)].
% 15.56/15.62 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2441,c,2245,b)].
% 15.56/15.62 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2441,c,2246,b)].
% 15.56/15.62 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2441,c,2247,b)].
% 15.56/15.62 2442 -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(2214,c,2135,b)].
% 15.56/15.62 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(2442,c,2243,a)].
% 15.56/15.62 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(2442,c,2244,a)].
% 15.56/15.62 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(2442,c,2245,b)].
% 15.56/15.62 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(2442,c,2246,b)].
% 15.56/15.62 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(2442,c,2247,b)].
% 15.56/15.62 2443 -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(2215,c,2135,b)].
% 15.56/15.62 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(2443,c,2243,a)].
% 15.56/15.62 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(2443,c,2244,a)].
% 15.56/15.62 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(2443,c,2245,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2443,c,2246,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2443,c,2247,b)].
% 15.56/15.63 2444 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2216,c,2135,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2444,c,2243,a)].
% 15.56/15.63 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2444,c,2244,a)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2444,c,2245,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2444,c,2246,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2444,c,2247,b)].
% 15.56/15.63 2445 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(2217,b,2135,b)].
% 15.56/15.63 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2445,b,2243,a)].
% 15.56/15.63 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2445,b,2244,a)].
% 15.56/15.63 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2445,b,2245,b)].
% 15.56/15.63 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2445,b,2246,b)].
% 15.56/15.63 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2445,b,2247,b)].
% 15.56/15.63 2446 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2218,b,2135,b)].
% 15.56/15.63 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2446,b,2243,a)].
% 15.56/15.63 Derived: c_lessequals(A,A,tc_nat). [resolve(2446,b,2244,a)].
% 15.56/15.63 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2446,b,2245,b)].
% 15.56/15.63 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2446,b,2246,b)].
% 15.56/15.63 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2446,b,2247,b)].
% 15.56/15.63 2447 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2219,d,2135,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2447,d,2243,a)].
% 15.56/15.63 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2447,d,2244,a)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2447,d,2245,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2447,d,2246,b)].
% 15.56/15.63 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2447,d,2247,b)].
% 15.56/15.63 2448 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2220,d,2135,b)].
% 15.56/15.63 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2448,d,2243,a)].
% 15.56/15.64 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2448,d,2244,a)].
% 15.56/15.64 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2448,d,2245,b)].
% 15.56/15.64 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2448,d,2246,b)].
% 15.56/15.64 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2448,d,2247,b)].
% 15.56/15.64 2449 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2221,c,2135,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2449,c,2243,a)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2449,c,2244,a)].
% 15.56/15.64 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(2449,c,2245,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2449,c,2246,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2449,c,2247,b)].
% 15.56/15.64 2450 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2222,c,2135,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2450,c,2243,a)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2450,c,2244,a)].
% 15.56/15.64 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(2450,c,2245,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2450,c,2246,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2450,c,2247,b)].
% 15.56/15.64 2451 -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(2223,d,2135,b)].
% 15.56/15.64 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(2451,d,2243,a)].
% 15.56/15.64 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(2451,d,2244,a)].
% 15.56/15.64 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2451,d,2245,b)].
% 15.56/15.64 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2451,d,2246,b)].
% 15.56/15.64 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2451,d,2247,b)].
% 15.56/15.64 2452 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2224,c,2135,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2452,c,2243,a)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2452,c,2244,a)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2452,c,2245,b)].
% 15.56/15.64 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2452,c,2246,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2452,c,2247,b)].
% 15.56/15.65 2453 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2225,c,2135,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2453,c,2243,a)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2453,c,2244,a)].
% 15.56/15.65 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(2453,c,2245,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2453,c,2246,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2453,c,2247,b)].
% 15.56/15.65 2454 -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(2226,d,2135,b)].
% 15.56/15.65 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(2454,d,2243,a)].
% 15.56/15.65 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(2454,d,2244,a)].
% 15.56/15.65 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(2454,d,2245,b)].
% 15.56/15.65 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(2454,d,2246,b)].
% 15.56/15.65 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(2454,d,2247,b)].
% 15.56/15.65 2455 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2227,c,2135,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2455,c,2243,a)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2455,c,2244,a)].
% 15.56/15.65 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(2455,c,2245,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2455,c,2246,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2455,c,2247,b)].
% 15.56/15.65 2456 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2228,c,2135,b)].
% 15.56/15.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2456,c,2243,a)].
% 15.56/15.65 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2456,c,2244,a)].
% 15.56/15.65 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(2456,c,2245,b)].
% 15.56/15.65 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2456,c,2246,b)].
% 15.56/15.65 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2456,c,2247,b)].
% 15.56/15.65 2457 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2229,c,2135,b)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2457,c,2243,a)].
% 15.56/15.65 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2457,c,2244,a)].
% 15.56/15.66 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(2457,c,2245,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2457,c,2246,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2457,c,2247,b)].
% 15.56/15.66 2458 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2230,c,2135,b)].
% 15.56/15.66 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2458,c,2243,a)].
% 15.56/15.66 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2458,c,2244,a)].
% 15.56/15.66 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(2458,c,2245,b)].
% 15.56/15.66 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2458,c,2246,b)].
% 15.56/15.66 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2458,c,2247,b)].
% 15.56/15.66 2459 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2231,c,2135,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2459,c,2243,a)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2459,c,2244,a)].
% 15.56/15.66 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(2459,c,2245,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2459,c,2246,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2459,c,2247,b)].
% 15.56/15.66 2460 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2232,c,2135,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2460,c,2243,a)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2460,c,2244,a)].
% 15.56/15.66 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(2460,c,2245,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2460,c,2246,b)].
% 15.56/15.66 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2460,c,2247,b)].
% 15.56/15.66 2461 -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(2233,d,2135,b)].
% 15.56/15.66 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(2461,d,2243,a)].
% 15.56/15.66 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(2461,d,2244,a)].
% 15.56/15.66 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(2461,d,2245,b)].
% 15.56/15.66 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(2461,d,2246,b)].
% 15.56/15.66 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(2461,d,2247,b)].
% 15.56/15.67 2462 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2234,c,2135,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2462,c,2243,a)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2462,c,2244,a)].
% 15.56/15.67 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(2462,c,2245,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2462,c,2246,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2462,c,2247,b)].
% 15.56/15.67 2463 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2235,c,2135,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2463,c,2243,a)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2463,c,2244,a)].
% 15.56/15.67 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(2463,c,2245,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2463,c,2246,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2463,c,2247,b)].
% 15.56/15.67 2464 -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(2236,d,2135,b)].
% 15.56/15.67 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(2464,d,2243,a)].
% 15.56/15.67 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(2464,d,2244,a)].
% 15.56/15.67 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(2464,d,2245,b)].
% 15.56/15.67 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(2464,d,2246,b)].
% 15.56/15.67 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(2464,d,2247,b)].
% 15.56/15.67 2465 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2237,c,2135,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2465,c,2243,a)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2465,c,2244,a)].
% 15.56/15.67 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(2465,c,2245,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2465,c,2246,b)].
% 15.56/15.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2465,c,2247,b)].
% 15.56/15.67 2466 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2238,c,2135,b)].
% 15.56/15.67 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2466,c,2243,a)].
% 15.56/15.67 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2466,c,2244,a)].
% 15.82/15.89 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(2466,c,2245,b)].
% 15.82/15.89 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2466,c,2246,b)].
% 15.82/15.89 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2466,c,2247,b)].
% 15.82/15.89 2467 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2239,c,2135,b)].
% 15.82/15.89 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2467,c,2243,a)].
% 15.82/15.89 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2467,c,2244,a)].
% 15.82/15.89 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(2467,c,2245,b)].
% 15.82/15.89 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2467,c,2246,b)].
% 15.82/15.89 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2467,c,2247,b)].
% 15.82/15.89 2468 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2240,c,2135,b)].
% 15.82/15.89 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2468,c,2243,a)].
% 15.82/15.89 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2468,c,2244,a)].
% 15.82/15.89 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(2468,c,2245,b)].
% 15.82/15.89 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2468,c,2246,b)].
% 15.82/15.89 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2468,c,2247,b)].
% 15.82/15.89 2469 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2241,d,2135,b)].
% 15.82/15.89 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2469,d,2243,a)].
% 15.82/15.89 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2469,d,2244,a)].
% 15.82/15.89 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2469,d,2245,b)].
% 15.82/15.89 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2469,d,2246,b)].
% 15.82/15.89 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2469,d,2247,b)].
% 15.82/15.89 2470 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_10) # label(axiom). [assumption].
% 15.82/15.89 2471 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 15.82/15.89 2472 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 15.82/15.89 2473 -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].
% 15.82/15.89 2474 -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].
% 15.82/15.89 2475 -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].
% 16.04/16.12 2476 -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].
% 16.04/16.12 2477 -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].
% 16.04/16.12 2478 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_11) # label(axiom). [assumption].
% 16.04/16.12 2479 -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].
% 16.04/16.12 2480 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_6) # label(axiom). [assumption].
% 16.04/16.12 2481 -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].
% 16.04/16.12 2482 -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].
% 16.04/16.12 2483 -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)].
% 16.04/16.12 2484 -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)].
% 16.04/16.12 2485 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(163,a,157,b)].
% 16.04/16.12 2486 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,157,b)].
% 16.04/16.12 2487 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,157,b)].
% 16.04/16.12 2488 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,157,b)].
% 16.04/16.12 2489 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(171,a,157,b)].
% 16.04/16.12 2490 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(172,a,157,b)].
% 16.04/16.12 2491 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 16.04/16.12 2492 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 16.04/16.12 2493 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(247,b,231,b)].
% 16.04/16.12 2494 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(248,b,231,b)].
% 16.04/16.12 2495 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1164,a,1121,a)].
% 16.04/16.12 2496 class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1164,a,1146,a)].
% 16.04/16.12 2497 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1164,a,1147,b)].
% 16.04/16.12 2498 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1164,a,1148,b)].
% 16.04/16.12 2499 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1610,b,1581,a)].
% 16.04/16.12 2500 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1582,a)].
% 16.04/16.12 2501 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1610,b,1583,a)].
% 16.04/16.12 2502 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1610,b,1584,a)].
% 16.13/16.19 2503 -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(1610,b,1585,a)].
% 16.13/16.19 2504 -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(1610,b,1586,a)].
% 16.13/16.19 2505 -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(1610,b,1587,a)].
% 16.13/16.19 2506 -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(1610,b,1588,a)].
% 16.13/16.19 2507 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1589,a)].
% 16.13/16.19 2508 -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(1610,b,1590,a)].
% 16.13/16.19 2509 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1610,b,1591,a)].
% 16.13/16.19 2510 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1614,a,1610,b)].
% 16.13/16.19 2511 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1615,a,1610,b)].
% 16.13/16.19 2512 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1637,a)].
% 16.13/16.19 2513 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1638,a)].
% 16.13/16.19 2514 -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(1675,b,1639,a)].
% 16.13/16.19 2515 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1640,a)].
% 16.13/16.19 2516 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1641,a)].
% 16.13/16.19 2517 -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(1675,b,1642,a)].
% 16.13/16.19 2518 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1643,a)].
% 16.13/16.19 2519 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1675,b,1644,a)].
% 16.13/16.19 2520 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1675,b,1645,a)].
% 16.13/16.19 2521 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1675,b,1646,a)].
% 16.13/16.19 2522 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1647,a)].
% 16.13/16.19 2523 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1648,a)].
% 16.13/16.19 2524 -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(1675,b,1649,a)].
% 16.13/16.19 2525 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1650,a)].
% 16.13/16.19 2526 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1651,a)].
% 16.13/16.19 2527 -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(1675,b,1652,a)].
% 16.17/16.28 2528 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1675,b,1653,a)].
% 16.17/16.28 2529 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1675,b,1654,a)].
% 16.17/16.28 2530 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1675,b,1655,a)].
% 16.17/16.28 2531 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1675,b,1656,a)].
% 16.17/16.28 2532 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1780,a,1777,b)].
% 16.17/16.28 2533 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2070,b)].
% 16.17/16.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2533,d,2477,b)].
% 16.17/16.28 2534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2080,b,2070,b)].
% 16.17/16.28 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2534,b,2477,b)].
% 16.17/16.28 2535 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2081,b,2070,b)].
% 16.17/16.28 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2535,b,2477,b)].
% 16.17/16.28 2536 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2082,b,2070,b)].
% 16.17/16.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2536,b,2477,b)].
% 16.17/16.28 2537 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2083,b,2070,b)].
% 16.17/16.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2537,b,2477,b)].
% 16.17/16.28 2538 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2086,b,2070,b)].
% 16.17/16.28 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2538,b,2477,b)].
% 16.17/16.28 2539 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2087,b,2070,b)].
% 16.17/16.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2539,b,2477,b)].
% 16.17/16.28 2540 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2088,b,2070,b)].
% 16.17/16.28 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2540,b,2477,b)].
% 16.17/16.28 2541 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,b,2070,b)].
% 16.17/16.28 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2541,b,2477,b)].
% 16.17/16.28 2542 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2094,a,2070,b)].
% 16.17/16.28 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2542,b,2477,b)].
% 16.17/16.28 2543 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2095,a,2070,b)].
% 16.17/16.28 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2543,c,2477,b)].
% 16.17/16.28 2544 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2096,a,2070,b)].
% 16.17/16.28 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2544,b,2477,b)].
% 16.17/16.30 2545 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2097,a,2070,b)].
% 16.17/16.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2545,c,2477,b)].
% 16.17/16.30 2546 -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(2098,a,2070,b)].
% 16.17/16.30 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(2546,c,2477,b)].
% 16.17/16.30 2547 -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(2099,a,2070,b)].
% 16.17/16.30 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(2547,c,2477,b)].
% 16.17/16.30 2548 -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(2100,a,2070,b)].
% 16.17/16.30 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(2548,c,2477,b)].
% 16.17/16.30 2549 -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(2101,a,2070,b)].
% 16.17/16.30 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(2549,c,2477,b)].
% 16.17/16.30 2550 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2102,a,2070,b)].
% 16.17/16.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2550,c,2477,b)].
% 16.17/16.30 2551 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(2103,a,2070,b)].
% 16.17/16.30 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(2551,b,2477,b)].
% 16.17/16.30 2552 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2104,a,2070,b)].
% 16.17/16.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2552,b,2477,b)].
% 16.17/16.30 2553 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2105,d,2070,b)].
% 16.17/16.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2553,d,2477,b)].
% 16.17/16.30 2554 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2106,d,2070,b)].
% 16.17/16.30 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2554,d,2477,b)].
% 16.17/16.30 2555 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2107,a,2070,b)].
% 16.17/16.30 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(2555,c,2477,b)].
% 16.17/16.30 2556 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2108,a,2070,b)].
% 16.17/16.30 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(2556,c,2477,b)].
% 16.17/16.30 2557 -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(2109,a,2070,b)].
% 16.26/16.32 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(2557,d,2477,b)].
% 16.26/16.32 2558 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2110,a,2070,b)].
% 16.26/16.32 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(2558,c,2477,b)].
% 16.26/16.32 2559 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2111,a,2070,b)].
% 16.26/16.32 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(2559,c,2477,b)].
% 16.26/16.32 2560 -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(2112,a,2070,b)].
% 16.26/16.32 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(2560,d,2477,b)].
% 16.26/16.32 2561 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2113,a,2070,b)].
% 16.26/16.32 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2561,c,2477,b)].
% 16.26/16.32 2562 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2114,a,2070,b)].
% 16.26/16.32 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2562,c,2477,b)].
% 16.26/16.32 2563 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2115,a,2070,b)].
% 16.26/16.32 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2563,c,2477,b)].
% 16.26/16.32 2564 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2116,a,2070,b)].
% 16.26/16.32 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2564,c,2477,b)].
% 16.26/16.32 2565 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2117,a,2070,b)].
% 16.26/16.32 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(2565,c,2477,b)].
% 16.26/16.32 2566 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2118,a,2070,b)].
% 16.26/16.32 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(2566,c,2477,b)].
% 16.26/16.32 2567 -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(2119,a,2070,b)].
% 16.26/16.32 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(2567,d,2477,b)].
% 16.26/16.32 2568 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2120,a,2070,b)].
% 16.26/16.32 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(2568,c,2477,b)].
% 16.26/16.32 2569 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2121,a,2070,b)].
% 16.26/16.32 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(2569,c,2477,b)].
% 16.26/16.32 2570 -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(2122,a,2070,b)].
% 16.48/16.60 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(2570,d,2477,b)].
% 16.48/16.60 2571 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2123,a,2070,b)].
% 16.48/16.60 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2571,c,2477,b)].
% 16.48/16.60 2572 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2124,a,2070,b)].
% 16.48/16.60 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2572,c,2477,b)].
% 16.48/16.60 2573 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2125,a,2070,b)].
% 16.48/16.60 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2573,c,2477,b)].
% 16.48/16.60 2574 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2126,a,2070,b)].
% 16.48/16.60 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2574,c,2477,b)].
% 16.48/16.60 2575 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2127,d,2070,b)].
% 16.48/16.60 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2575,d,2477,b)].
% 16.48/16.60 2576 -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].
% 16.48/16.60 2577 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 16.48/16.60 2578 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 16.48/16.60 2579 -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].
% 16.48/16.60 2580 -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].
% 16.48/16.60 2581 -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].
% 16.48/16.60 2582 -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].
% 16.48/16.60 2583 -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].
% 16.48/16.60 2584 -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].
% 16.48/16.60 2585 -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].
% 16.48/16.60 2586 -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].
% 16.48/16.60 2587 -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)].
% 16.48/16.60 2588 -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)].
% 16.76/16.83 2589 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 16.76/16.83 2590 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 16.76/16.83 2591 -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)].
% 16.76/16.83 2592 -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)].
% 16.76/16.83 2593 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(165,a,154,b)].
% 16.76/16.83 2594 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(166,a,154,b)].
% 16.76/16.83 2595 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(171,a,154,b)].
% 16.76/16.83 2596 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(172,a,154,b)].
% 16.76/16.83 2597 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(201,b,195,b)].
% 16.76/16.83 2598 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 16.76/16.83 2599 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 16.76/16.83 2600 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 16.76/16.83 2601 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(247,b,228,b)].
% 16.76/16.83 2602 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(248,b,228,b)].
% 16.76/16.83 2603 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,288,a)].
% 16.76/16.83 2604 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,290,a)].
% 16.76/16.83 2605 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(322,a,308,b)].
% 16.76/16.83 2606 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(323,a,308,b)].
% 16.76/16.83 2607 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1162,a,1121,a)].
% 16.76/16.83 2608 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1162,a,1146,a)].
% 16.76/16.83 2609 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1162,a,1147,b)].
% 16.76/16.83 2610 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1162,a,1148,b)].
% 16.76/16.83 2611 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1607,b,1581,a)].
% 16.76/16.83 2612 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1582,a)].
% 16.76/16.83 2613 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1607,b,1583,a)].
% 16.76/16.83 2614 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1607,b,1584,a)].
% 16.76/16.83 2615 -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(1607,b,1585,a)].
% 16.76/16.83 2616 -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(1607,b,1586,a)].
% 16.79/16.89 2617 -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(1607,b,1587,a)].
% 16.79/16.89 2618 -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(1607,b,1588,a)].
% 16.79/16.89 2619 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1589,a)].
% 16.79/16.89 2620 -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(1607,b,1590,a)].
% 16.79/16.89 2621 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1607,b,1591,a)].
% 16.79/16.89 2622 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1614,a,1607,b)].
% 16.79/16.89 2623 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1615,a,1607,b)].
% 16.79/16.89 2624 -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(1672,b,1637,a)].
% 16.79/16.89 2625 -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(1672,b,1638,a)].
% 16.79/16.89 2626 -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(1672,b,1639,a)].
% 16.79/16.89 2627 -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(1672,b,1640,a)].
% 16.79/16.89 2628 -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(1672,b,1641,a)].
% 16.79/16.89 2629 -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(1672,b,1642,a)].
% 16.79/16.89 2630 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1643,a)].
% 16.79/16.89 2631 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1672,b,1644,a)].
% 16.79/16.89 2632 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1672,b,1645,a)].
% 16.79/16.89 2633 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1672,b,1646,a)].
% 16.79/16.89 2634 -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(1672,b,1647,a)].
% 16.79/16.89 2635 -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(1672,b,1648,a)].
% 16.79/16.89 2636 -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(1672,b,1649,a)].
% 16.79/16.89 2637 -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(1672,b,1650,a)].
% 16.79/16.89 2638 -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(1672,b,1651,a)].
% 16.79/16.89 2639 -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(1672,b,1652,a)].
% 16.79/16.89 2640 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1672,b,1653,a)].
% 16.89/16.98 2641 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1672,b,1654,a)].
% 16.89/16.98 2642 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1672,b,1655,a)].
% 16.89/16.98 2643 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1672,b,1656,a)].
% 16.89/16.98 2644 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1780,a,1774,b)].
% 16.89/16.98 2645 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2067,b)].
% 16.89/16.98 2646 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2082,b,2067,b)].
% 16.89/16.98 2647 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2083,b,2067,b)].
% 16.89/16.98 2648 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2086,b,2067,b)].
% 16.89/16.98 2649 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,b,2067,b)].
% 16.89/16.98 2650 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2088,b,2067,b)].
% 16.89/16.98 2651 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2089,b,2067,b)].
% 16.89/16.98 2652 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2094,a,2067,b)].
% 16.89/16.98 2653 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2095,a,2067,b)].
% 16.89/16.98 2654 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2096,a,2067,b)].
% 16.89/16.98 2655 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,a,2067,b)].
% 16.89/16.98 2656 -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(2098,a,2067,b)].
% 16.89/16.98 2657 -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(2099,a,2067,b)].
% 16.89/16.98 2658 -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(2100,a,2067,b)].
% 16.89/16.98 2659 -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(2101,a,2067,b)].
% 16.89/16.98 2660 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,a,2067,b)].
% 16.89/16.98 2661 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(2103,a,2067,b)].
% 16.89/16.98 2662 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2104,a,2067,b)].
% 16.89/16.98 2663 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2067,b)].
% 16.89/16.98 2664 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,d,2067,b)].
% 16.89/16.98 2665 -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(2107,a,2067,b)].
% 16.89/16.98 2666 -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(2108,a,2067,b)].
% 16.96/17.01 2667 -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(2109,a,2067,b)].
% 16.96/17.01 2668 -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(2110,a,2067,b)].
% 16.96/17.01 2669 -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(2111,a,2067,b)].
% 16.96/17.01 2670 -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(2112,a,2067,b)].
% 16.96/17.01 2671 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2113,a,2067,b)].
% 16.96/17.01 2672 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2114,a,2067,b)].
% 16.96/17.01 2673 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2115,a,2067,b)].
% 16.96/17.01 2674 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2116,a,2067,b)].
% 16.96/17.01 2675 -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(2117,a,2067,b)].
% 16.96/17.01 2676 -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(2118,a,2067,b)].
% 16.96/17.01 2677 -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(2119,a,2067,b)].
% 16.96/17.01 2678 -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(2120,a,2067,b)].
% 16.96/17.01 2679 -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(2121,a,2067,b)].
% 16.96/17.01 2680 -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(2122,a,2067,b)].
% 16.96/17.01 2681 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2123,a,2067,b)].
% 16.96/17.01 2682 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2124,a,2067,b)].
% 16.96/17.01 2683 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2125,a,2067,b)].
% 16.96/17.01 2684 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2126,a,2067,b)].
% 16.96/17.01 2685 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2127,d,2067,b)].
% 16.96/17.01 2686 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2157,a,2136,b)].
% 16.96/17.01 2687 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2158,a,2136,b)].
% 16.96/17.01 2688 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2159,c,2136,b)].
% 16.96/17.01 2689 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2160,c,2136,b)].
% 16.96/17.01 2690 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,b,2136,b)].
% 16.96/17.01 2691 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,a,2136,b)].
% 16.96/17.01 2692 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2201,d,2136,b)].
% 16.96/17.05 2693 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2202,b,2136,b)].
% 16.96/17.05 2694 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2203,b,2136,b)].
% 16.96/17.05 2695 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2204,b,2136,b)].
% 16.96/17.05 2696 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2205,b,2136,b)].
% 16.96/17.05 2697 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2206,b,2136,b)].
% 16.96/17.05 2698 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2207,b,2136,b)].
% 16.96/17.05 2699 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2208,b,2136,b)].
% 16.96/17.05 2700 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2209,c,2136,b)].
% 16.96/17.05 2701 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2210,b,2136,b)].
% 16.96/17.05 2702 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2211,c,2136,b)].
% 16.96/17.05 2703 -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(2212,c,2136,b)].
% 16.96/17.05 2704 -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(2213,c,2136,b)].
% 16.96/17.05 2705 -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(2214,c,2136,b)].
% 16.96/17.05 2706 -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(2215,c,2136,b)].
% 16.96/17.05 2707 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2216,c,2136,b)].
% 16.96/17.05 2708 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(2217,b,2136,b)].
% 16.96/17.05 2709 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2218,b,2136,b)].
% 16.96/17.05 2710 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2219,d,2136,b)].
% 16.96/17.05 2711 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2220,d,2136,b)].
% 16.96/17.05 2712 -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(2221,c,2136,b)].
% 16.96/17.05 2713 -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(2222,c,2136,b)].
% 16.96/17.05 2714 -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(2223,d,2136,b)].
% 16.96/17.05 2715 -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(2224,c,2136,b)].
% 16.96/17.05 2716 -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(2225,c,2136,b)].
% 16.96/17.05 2717 -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(2226,d,2136,b)].
% 17.25/17.28 2718 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2227,c,2136,b)].
% 17.25/17.28 2719 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2228,c,2136,b)].
% 17.25/17.28 2720 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2229,c,2136,b)].
% 17.25/17.28 2721 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2230,c,2136,b)].
% 17.25/17.28 2722 -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(2231,c,2136,b)].
% 17.25/17.28 2723 -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(2232,c,2136,b)].
% 17.25/17.28 2724 -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(2233,d,2136,b)].
% 17.25/17.28 2725 -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(2234,c,2136,b)].
% 17.25/17.28 2726 -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(2235,c,2136,b)].
% 17.25/17.28 2727 -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(2236,d,2136,b)].
% 17.25/17.28 2728 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2237,c,2136,b)].
% 17.25/17.28 2729 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2238,c,2136,b)].
% 17.25/17.28 2730 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2239,c,2136,b)].
% 17.25/17.28 2731 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2240,c,2136,b)].
% 17.25/17.28 2732 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2241,d,2136,b)].
% 17.25/17.28 2733 -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].
% 17.25/17.28 2734 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 17.25/17.28 2735 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 17.25/17.28 2736 -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].
% 17.25/17.28 2737 -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].
% 17.25/17.28 2738 -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].
% 17.25/17.28 2739 -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].
% 17.25/17.28 2740 -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].
% 17.25/17.28 2741 -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].
% 17.31/17.35 2742 -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].
% 17.31/17.35 2743 -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)].
% 17.31/17.35 2744 -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)].
% 17.31/17.35 2745 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 17.31/17.35 2746 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 17.31/17.35 2747 -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)].
% 17.31/17.35 2748 -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)].
% 17.31/17.35 2749 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(165,a,148,b)].
% 17.31/17.35 2750 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(166,a,148,b)].
% 17.31/17.35 2751 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(171,a,148,b)].
% 17.31/17.35 2752 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(172,a,148,b)].
% 17.31/17.35 2753 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(201,b,191,b)].
% 17.31/17.35 2754 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(202,b,191,b)].
% 17.31/17.35 2755 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 17.31/17.35 2756 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 17.31/17.35 2757 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(247,b,222,b)].
% 17.31/17.35 2758 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(248,b,222,b)].
% 17.31/17.35 2759 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,288,a)].
% 17.31/17.35 2760 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,290,a)].
% 17.31/17.35 2761 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(322,a,302,b)].
% 17.31/17.35 2762 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(323,a,302,b)].
% 17.31/17.35 2763 -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(897,b,832,a)].
% 17.31/17.35 2764 -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(897,b,833,a)].
% 17.31/17.35 2765 -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(897,b,834,a)].
% 17.31/17.35 2766 -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(897,b,835,a)].
% 17.31/17.35 2767 -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(897,b,836,a)].
% 17.31/17.36 2768 -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(897,b,837,a)].
% 17.31/17.36 2769 -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(897,b,838,a)].
% 17.31/17.36 2770 -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(897,b,839,a)].
% 17.31/17.36 2771 -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(897,b,840,a)].
% 17.31/17.36 2772 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,841,a)].
% 17.31/17.36 2773 -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(897,b,842,a)].
% 17.31/17.36 2774 -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(897,b,843,a)].
% 17.31/17.36 2775 -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(897,b,844,a)].
% 17.31/17.36 2776 -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(897,b,845,a)].
% 17.31/17.36 2777 -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(897,b,846,a)].
% 17.31/17.36 2778 -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(897,b,847,a)].
% 17.31/17.36 2779 -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(897,b,848,a)].
% 17.31/17.36 2780 -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(897,b,849,a)].
% 17.31/17.36 2781 -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(897,b,850,a)].
% 17.31/17.36 2782 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,851,a)].
% 17.31/17.36 2783 -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(897,b,852,a)].
% 17.31/17.36 2784 -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(897,b,853,a)].
% 17.31/17.36 2785 -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(897,b,854,a)].
% 17.33/17.37 2786 -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(897,b,855,b)].
% 17.33/17.37 2787 -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(897,b,856,b)].
% 17.33/17.37 2788 -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(897,b,857,a)].
% 17.33/17.37 2789 -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(897,b,858,a)].
% 17.33/17.37 2790 -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(897,b,859,a)].
% 17.33/17.37 2791 -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(897,b,860,a)].
% 17.33/17.37 2792 -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(897,b,861,a)].
% 17.33/17.37 2793 -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(897,b,862,a)].
% 17.33/17.37 2794 -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(897,b,863,a)].
% 17.33/17.37 2795 -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(897,b,864,a)].
% 17.33/17.37 2796 -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(897,b,865,a)].
% 17.33/17.37 2797 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(897,b,866,a)].
% 17.33/17.37 2798 -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(897,b,867,a)].
% 17.33/17.37 2799 -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(897,b,868,a)].
% 17.33/17.37 2800 -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(897,b,869,a)].
% 17.33/17.37 2801 -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(897,b,870,a)].
% 17.33/17.37 2802 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(897,b,871,a)].
% 17.33/17.37 2803 -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(897,b,872,a)].
% 17.33/17.37 2804 -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(897,b,873,a)].
% 17.33/17.37 2805 -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(897,b,874,a)].
% 17.33/17.37 2806 -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(897,b,875,a)].
% 17.33/17.37 2807 -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(897,b,876,a)].
% 17.33/17.37 2808 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(897,b,877,a)].
% 17.33/17.37 2809 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(897,b,878,a)].
% 17.33/17.37 2810 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(897,b,879,a)].
% 17.33/17.37 2811 -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(897,b,880,a)].
% 17.42/17.49 2812 -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(897,b,881,a)].
% 17.42/17.49 2813 -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(897,b,882,a)].
% 17.42/17.49 2814 -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(897,b,883,a)].
% 17.42/17.49 2815 -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(897,b,884,a)].
% 17.42/17.49 2816 -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(897,b,885,a)].
% 17.42/17.49 2817 -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(897,b,886,a)].
% 17.42/17.49 2818 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(897,b,887,a)].
% 17.42/17.49 2819 -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(897,b,888,a)].
% 17.42/17.49 2820 -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(897,b,889,a)].
% 17.42/17.49 2821 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(904,a,897,b)].
% 17.42/17.49 2822 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(905,a,897,b)].
% 17.42/17.49 2823 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1087,b,1076,a)].
% 17.42/17.49 2824 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1110,b,1099,a)].
% 17.42/17.49 2825 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1156,a,1121,a)].
% 17.42/17.49 2826 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1156,a,1146,a)].
% 17.42/17.49 2827 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1147,b)].
% 17.42/17.49 2828 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1148,b)].
% 17.42/17.49 2829 -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(1498,b,1477,a)].
% 17.42/17.49 2830 -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(1498,b,1478,a)].
% 17.42/17.49 2831 -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(1498,b,1479,a)].
% 17.42/17.49 2832 -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(1498,b,1480,a)].
% 17.42/17.49 2833 -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(1498,b,1481,a)].
% 17.42/17.49 2834 -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(1498,b,1482,a)].
% 17.42/17.49 2835 -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(1498,b,1483,a)].
% 17.50/17.57 2836 -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(1498,b,1484,a)].
% 17.50/17.57 2837 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1603,b,1581,a)].
% 17.50/17.57 2838 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1582,a)].
% 17.50/17.57 2839 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1603,b,1583,a)].
% 17.50/17.57 2840 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1603,b,1584,a)].
% 17.50/17.57 2841 -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(1603,b,1585,a)].
% 17.50/17.57 2842 -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(1603,b,1586,a)].
% 17.50/17.57 2843 -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(1603,b,1587,a)].
% 17.50/17.57 2844 -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(1603,b,1588,a)].
% 17.50/17.57 2845 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1589,a)].
% 17.50/17.57 2846 -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(1603,b,1590,a)].
% 17.50/17.57 2847 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1603,b,1591,a)].
% 17.50/17.57 2848 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1614,a,1603,b)].
% 17.50/17.57 2849 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1615,a,1603,b)].
% 17.50/17.57 2850 -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(1668,b,1637,a)].
% 17.50/17.57 2851 -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(1668,b,1638,a)].
% 17.50/17.57 2852 -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(1668,b,1639,a)].
% 17.50/17.57 2853 -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(1668,b,1640,a)].
% 17.50/17.57 2854 -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(1668,b,1641,a)].
% 17.50/17.57 2855 -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(1668,b,1642,a)].
% 17.50/17.57 2856 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1643,a)].
% 17.50/17.57 2857 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1668,b,1644,a)].
% 17.50/17.57 2858 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1668,b,1645,a)].
% 17.50/17.57 2859 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1668,b,1646,a)].
% 17.50/17.57 2860 -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(1668,b,1647,a)].
% 17.55/17.63 2861 -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(1668,b,1648,a)].
% 17.55/17.63 2862 -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(1668,b,1649,a)].
% 17.55/17.63 2863 -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(1668,b,1650,a)].
% 17.55/17.63 2864 -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(1668,b,1651,a)].
% 17.55/17.63 2865 -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(1668,b,1652,a)].
% 17.55/17.63 2866 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1668,b,1653,a)].
% 17.55/17.63 2867 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1668,b,1654,a)].
% 17.55/17.63 2868 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1668,b,1655,a)].
% 17.55/17.63 2869 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1668,b,1656,a)].
% 17.55/17.63 2870 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1780,a,1770,b)].
% 17.55/17.63 2871 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1844,b,1839,b)].
% 17.55/17.63 2872 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1849,a,1839,b)].
% 17.55/17.63 2873 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1850,a,1839,b)].
% 17.55/17.63 2874 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1986,c,1904,b)].
% 17.55/17.63 2875 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1987,c,1904,b)].
% 17.55/17.63 2876 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2024,b,1904,b)].
% 17.55/17.63 2877 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2025,c,1904,b)].
% 17.55/17.63 2878 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2026,b,1904,b)].
% 17.55/17.63 2879 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2027,c,1904,b)].
% 17.55/17.63 2880 -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(2028,c,1904,b)].
% 17.55/17.63 2881 -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(2029,c,1904,b)].
% 17.55/17.63 2882 -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(2030,c,1904,b)].
% 17.55/17.63 2883 -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(2031,c,1904,b)].
% 17.55/17.63 2884 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2032,c,1904,b)].
% 17.55/17.63 2885 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(2033,b,1904,b)].
% 17.55/17.66 2886 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2034,b,1904,b)].
% 17.55/17.66 2887 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2035,d,1904,b)].
% 17.55/17.66 2888 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2036,d,1904,b)].
% 17.55/17.66 2889 -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(2037,c,1904,b)].
% 17.55/17.66 2890 -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(2038,c,1904,b)].
% 17.55/17.66 2891 -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(2039,d,1904,b)].
% 17.55/17.66 2892 -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(2040,c,1904,b)].
% 17.55/17.66 2893 -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(2041,c,1904,b)].
% 17.55/17.66 2894 -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(2042,d,1904,b)].
% 17.55/17.66 2895 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2043,c,1904,b)].
% 17.55/17.66 2896 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2044,c,1904,b)].
% 17.55/17.66 2897 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2045,c,1904,b)].
% 17.55/17.66 2898 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2046,c,1904,b)].
% 17.55/17.66 2899 -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(2047,c,1904,b)].
% 17.55/17.66 2900 -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(2048,c,1904,b)].
% 17.55/17.66 2901 -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(2049,d,1904,b)].
% 17.55/17.66 2902 -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(2050,c,1904,b)].
% 17.55/17.66 2903 -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(2051,c,1904,b)].
% 17.55/17.66 2904 -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(2052,d,1904,b)].
% 17.55/17.66 2905 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2053,c,1904,b)].
% 17.55/17.66 2906 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2054,c,1904,b)].
% 17.55/17.66 2907 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2055,c,1904,b)].
% 17.55/17.66 2908 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2056,c,1904,b)].
% 17.55/17.66 2909 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2058,d,1904,b)].
% 17.55/17.66 2910 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2077,a,2063,b)].
% 17.65/17.71 2911 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2082,b,2063,b)].
% 17.65/17.71 2912 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2083,b,2063,b)].
% 17.65/17.71 2913 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2086,b,2063,b)].
% 17.65/17.71 2914 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2087,b,2063,b)].
% 17.65/17.71 2915 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2088,b,2063,b)].
% 17.65/17.71 2916 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2089,b,2063,b)].
% 17.65/17.71 2917 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2157,a,2132,b)].
% 17.65/17.71 2918 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2158,a,2132,b)].
% 17.65/17.71 2919 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,d,2132,b)].
% 17.65/17.71 2920 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2202,b,2132,b)].
% 17.65/17.71 2921 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2203,b,2132,b)].
% 17.65/17.71 2922 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2204,b,2132,b)].
% 17.65/17.71 2923 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2205,b,2132,b)].
% 17.65/17.71 2924 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2206,b,2132,b)].
% 17.65/17.71 2925 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,b,2132,b)].
% 17.65/17.71 2926 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2208,b,2132,b)].
% 17.65/17.71 2927 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2209,c,2132,b)].
% 17.65/17.71 2928 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2210,b,2132,b)].
% 17.65/17.71 2929 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2211,c,2132,b)].
% 17.65/17.71 2930 -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(2212,c,2132,b)].
% 17.65/17.71 2931 -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(2213,c,2132,b)].
% 17.65/17.71 2932 -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(2214,c,2132,b)].
% 17.65/17.71 2933 -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(2215,c,2132,b)].
% 17.65/17.71 2934 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2216,c,2132,b)].
% 17.65/17.71 2935 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(2217,b,2132,b)].
% 17.65/17.71 2936 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2218,b,2132,b)].
% 17.70/17.74 2937 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2219,d,2132,b)].
% 17.70/17.74 2938 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2220,d,2132,b)].
% 17.70/17.74 2939 -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(2221,c,2132,b)].
% 17.70/17.74 2940 -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(2222,c,2132,b)].
% 17.70/17.74 2941 -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(2223,d,2132,b)].
% 17.70/17.74 2942 -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(2224,c,2132,b)].
% 17.70/17.74 2943 -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(2225,c,2132,b)].
% 17.70/17.74 2944 -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(2226,d,2132,b)].
% 17.70/17.74 2945 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2227,c,2132,b)].
% 17.70/17.74 2946 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2228,c,2132,b)].
% 17.70/17.74 2947 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2229,c,2132,b)].
% 17.70/17.74 2948 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2230,c,2132,b)].
% 17.70/17.74 2949 -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(2231,c,2132,b)].
% 17.70/17.74 2950 -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(2232,c,2132,b)].
% 17.70/17.74 2951 -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(2233,d,2132,b)].
% 17.70/17.74 2952 -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(2234,c,2132,b)].
% 17.70/17.74 2953 -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(2235,c,2132,b)].
% 17.70/17.74 2954 -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(2236,d,2132,b)].
% 17.70/17.74 2955 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2237,c,2132,b)].
% 17.70/17.74 2956 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2238,c,2132,b)].
% 17.70/17.74 2957 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2239,c,2132,b)].
% 17.70/17.74 2958 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2240,c,2132,b)].
% 17.70/17.74 2959 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2241,d,2132,b)].
% 17.70/17.74 2960 -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(2273,a,2245,b)].
% 17.70/17.74 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(2960,e,2734,a)].
% 17.70/17.74 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(2960,e,2735,a)].
% 17.70/17.74 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(2960,e,2741,b)].
% 17.70/17.74 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(2960,e,2742,b)].
% 17.70/17.74 2961 -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(2274,a,2245,b)].
% 17.70/17.74 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(2961,d,2734,a)].
% 17.70/17.74 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(2961,d,2735,a)].
% 17.70/17.74 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(2961,d,2741,b)].
% 17.70/17.74 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(2961,d,2742,b)].
% 17.70/17.74 2962 -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(2275,a,2245,b)].
% 17.70/17.74 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(2962,d,2734,a)].
% 17.70/17.74 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(2962,d,2735,a)].
% 17.70/17.74 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(2962,d,2741,b)].
% 17.70/17.74 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(2962,d,2742,b)].
% 17.70/17.74 2963 -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(2276,a,2245,b)].
% 17.70/17.74 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(2963,f,2734,a)].
% 17.70/17.74 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(2963,f,2735,a)].
% 17.70/17.74 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(2963,f,2741,b)].
% 17.70/17.74 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(2963,f,2742,b)].
% 17.70/17.74 2964 -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(2277,a,2245,b)].
% 17.70/17.74 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(2964,e,2734,a)].
% 17.70/17.74 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(2964,e,2735,a)].
% 17.70/17.74 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(2964,e,2741,b)].
% 17.70/17.74 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(2964,e,2742,b)].
% 17.70/17.74 2965 -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(2278,a,2245,b)].
% 17.70/17.74 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(2965,e,2734,a)].
% 17.70/17.74 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(2965,e,2735,a)].
% 17.70/17.74 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(2965,e,2741,b)].
% 17.70/17.74 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(2965,e,2742,b)].
% 17.70/17.74 2966 -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(2279,a,2245,b)].
% 17.70/17.74 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(2966,f,2734,a)].
% 17.70/17.74 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(2966,f,2735,a)].
% 17.70/17.74 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(2966,f,2741,b)].
% 17.70/17.74 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(2966,f,2742,b)].
% 17.70/17.74 2967 -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(2280,a,2245,b)].
% 17.70/17.74 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(2967,e,2734,a)].
% 17.70/17.74 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(2967,e,2735,a)].
% 17.70/17.74 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(2967,e,2741,b)].
% 17.70/17.74 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(2967,e,2742,b)].
% 17.70/17.75 2968 -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(2281,a,2245,b)].
% 17.70/17.75 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(2968,e,2734,a)].
% 17.70/17.75 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(2968,e,2735,a)].
% 17.70/17.75 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(2968,e,2741,b)].
% 17.70/17.75 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(2968,e,2742,b)].
% 17.70/17.75 2969 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2245,b)].
% 17.70/17.75 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2969,b,2734,a)].
% 17.70/17.75 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2969,b,2735,a)].
% 17.70/17.75 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2969,b,2741,b)].
% 17.70/17.75 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2969,b,2742,b)].
% 17.70/17.75 2970 -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(2283,a,2245,b)].
% 17.70/17.75 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(2970,f,2734,a)].
% 17.70/17.75 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(2970,f,2735,a)].
% 17.70/17.75 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(2970,f,2741,b)].
% 17.70/17.75 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(2970,f,2742,b)].
% 17.70/17.75 2971 -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(2284,a,2245,b)].
% 17.70/17.75 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(2971,e,2734,a)].
% 17.70/17.75 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(2971,e,2735,a)].
% 17.70/17.75 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(2971,e,2741,b)].
% 17.70/17.75 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(2971,e,2742,b)].
% 17.72/17.75 2972 -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(2285,a,2245,b)].
% 17.72/17.75 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(2972,e,2734,a)].
% 17.72/17.75 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(2972,e,2735,a)].
% 17.72/17.75 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(2972,e,2741,b)].
% 17.72/17.75 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(2972,e,2742,b)].
% 17.72/17.75 2973 -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(2286,a,2245,b)].
% 17.72/17.75 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(2973,f,2734,a)].
% 17.72/17.75 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(2973,f,2735,a)].
% 17.72/17.75 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(2973,f,2741,b)].
% 17.72/17.75 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(2973,f,2742,b)].
% 17.72/17.75 2974 -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(2287,a,2245,b)].
% 17.72/17.75 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(2974,e,2734,a)].
% 17.72/17.75 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(2974,e,2735,a)].
% 17.72/17.75 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(2974,e,2741,b)].
% 17.72/17.75 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(2974,e,2742,b)].
% 17.72/17.75 2975 -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(2288,a,2245,b)].
% 17.72/17.75 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(2975,e,2734,a)].
% 17.72/17.75 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(2975,e,2735,a)].
% 17.72/17.75 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(2975,e,2741,b)].
% 17.72/17.75 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(2975,e,2742,b)].
% 17.72/17.75 2976 -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(2289,a,2245,b)].
% 17.72/17.75 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(2976,d,2734,a)].
% 17.72/17.75 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(2976,d,2735,a)].
% 17.72/17.75 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(2976,d,2741,b)].
% 17.72/17.75 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(2976,d,2742,b)].
% 17.72/17.75 2977 -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(2290,a,2245,b)].
% 17.72/17.75 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(2977,d,2734,a)].
% 17.72/17.75 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(2977,d,2735,a)].
% 17.72/17.76 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(2977,d,2741,b)].
% 17.72/17.76 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(2977,d,2742,b)].
% 17.72/17.76 2978 -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(2291,a,2245,b)].
% 17.72/17.76 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(2978,e,2734,a)].
% 17.72/17.76 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(2978,e,2735,a)].
% 17.72/17.76 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(2978,e,2741,b)].
% 17.72/17.76 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(2978,e,2742,b)].
% 17.72/17.76 2979 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,a,2245,b)].
% 17.72/17.76 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2979,b,2734,a)].
% 17.72/17.76 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2979,b,2735,a)].
% 17.72/17.76 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2979,b,2741,b)].
% 17.72/17.76 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2979,b,2742,b)].
% 17.72/17.76 2980 -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(2293,a,2245,b)].
% 17.72/17.76 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(2980,d,2734,a)].
% 17.72/17.76 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(2980,d,2735,a)].
% 17.72/17.76 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(2980,d,2741,b)].
% 17.72/17.76 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(2980,d,2742,b)].
% 17.72/17.76 2981 -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(2294,a,2245,b)].
% 17.72/17.76 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(2981,e,2734,a)].
% 17.72/17.76 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(2981,e,2735,a)].
% 17.72/17.76 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(2981,e,2741,b)].
% 17.72/17.76 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(2981,e,2742,b)].
% 17.72/17.76 2982 -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(2295,a,2245,b)].
% 17.72/17.76 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(2982,e,2734,a)].
% 17.72/17.76 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(2982,e,2735,a)].
% 17.72/17.76 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(2982,e,2741,b)].
% 17.72/17.76 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(2982,e,2742,b)].
% 17.72/17.76 2983 -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(2296,a,2245,b)].
% 17.72/17.76 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(2983,d,2734,a)].
% 17.72/17.76 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(2983,d,2735,a)].
% 17.72/17.76 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(2983,d,2741,b)].
% 17.72/17.76 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(2983,d,2742,b)].
% 17.72/17.76 2984 -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(2297,a,2245,b)].
% 17.72/17.76 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(2984,d,2734,a)].
% 17.72/17.76 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(2984,d,2735,a)].
% 17.72/17.76 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(2984,d,2741,b)].
% 17.72/17.76 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(2984,d,2742,b)].
% 17.72/17.76 2985 -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(2298,a,2245,b)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2985,c,2734,a)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2985,c,2735,a)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2985,c,2741,b)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2985,c,2742,b)].
% 17.72/17.76 2986 -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(2299,a,2245,b)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2986,c,2734,a)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2986,c,2735,a)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2986,c,2741,b)].
% 17.72/17.76 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2986,c,2742,b)].
% 17.72/17.76 2987 -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(2300,a,2245,b)].
% 17.72/17.76 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(2987,d,2734,a)].
% 17.72/17.76 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(2987,d,2735,a)].
% 17.72/17.76 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(2987,d,2741,b)].
% 17.72/17.76 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(2987,d,2742,b)].
% 17.72/17.76 2988 -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(2301,a,2245,b)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2988,c,2734,a)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2988,c,2735,a)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2988,c,2741,b)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2988,c,2742,b)].
% 17.72/17.76 2989 -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(2302,a,2245,b)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2989,c,2734,a)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2989,c,2735,a)].
% 17.72/17.76 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2989,c,2741,b)].
% 17.72/17.77 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2989,c,2742,b)].
% 17.72/17.77 2990 -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(2303,a,2245,b)].
% 17.72/17.77 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(2990,d,2734,a)].
% 17.72/17.77 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(2990,d,2735,a)].
% 17.72/17.77 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(2990,d,2741,b)].
% 17.72/17.77 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(2990,d,2742,b)].
% 17.72/17.77 2991 -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(2304,a,2245,b)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2991,c,2734,a)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2991,c,2735,a)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2991,c,2741,b)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2991,c,2742,b)].
% 17.72/17.77 2992 -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(2305,a,2245,b)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2992,c,2734,a)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2992,c,2735,a)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2992,c,2741,b)].
% 17.72/17.77 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2992,c,2742,b)].
% 17.72/17.77 2993 -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(2306,a,2245,b)].
% 17.72/17.77 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(2993,d,2734,a)].
% 17.72/17.77 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(2993,d,2735,a)].
% 17.72/17.77 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(2993,d,2741,b)].
% 17.72/17.77 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(2993,d,2742,b)].
% 17.72/17.77 2994 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2307,a,2245,b)].
% 17.72/17.77 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2994,b,2734,a)].
% 17.72/17.77 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2994,b,2735,a)].
% 17.72/17.77 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2994,b,2741,b)].
% 17.72/17.77 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2742,b)].
% 17.72/17.77 2995 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(2308,a,2245,b)].
% 17.72/17.77 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(2995,b,2734,a)].
% 17.72/17.77 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2995,b,2735,a)].
% 17.72/17.77 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(2995,b,2741,b)].
% 17.72/17.77 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(2995,b,2742,b)].
% 17.72/17.77 2996 -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(2309,a,2245,b)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2996,c,2734,a)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2996,c,2735,a)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2996,c,2741,b)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2996,c,2742,b)].
% 17.72/17.77 2997 -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(2310,a,2245,b)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2997,c,2734,a)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2997,c,2735,a)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2997,c,2741,b)].
% 17.72/17.77 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2997,c,2742,b)].
% 17.72/17.77 2998 -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(2311,a,2245,b)].
% 17.72/17.77 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(2998,d,2734,a)].
% 17.72/17.77 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(2998,d,2735,a)].
% 17.72/17.77 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(2998,d,2741,b)].
% 17.72/17.77 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(2998,d,2742,b)].
% 17.72/17.77 2999 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2312,a,2245,b)].
% 17.72/17.77 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2999,b,2734,a)].
% 17.72/17.77 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2999,b,2735,a)].
% 17.72/17.77 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2999,b,2741,b)].
% 17.72/17.77 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2999,b,2742,b)].
% 17.72/17.77 3000 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(2313,a,2245,b)].
% 17.72/17.77 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(3000,b,2734,a)].
% 17.72/17.77 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(3000,b,2735,a)].
% 17.72/17.77 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(3000,b,2741,b)].
% 17.72/17.77 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(3000,b,2742,b)].
% 17.72/17.77 3001 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(2314,a,2245,b)].
% 17.72/17.77 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(3001,b,2734,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(3001,b,2735,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3001,b,2741,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3001,b,2742,b)].
% 17.72/17.78 3002 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(2315,a,2245,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(3002,b,2734,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(3002,b,2735,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3002,b,2741,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3002,b,2742,b)].
% 17.72/17.78 3003 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(2316,a,2245,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(3003,b,2734,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(3003,b,2735,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3003,b,2741,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3003,b,2742,b)].
% 17.72/17.78 3004 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(2317,a,2245,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(3004,b,2734,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(3004,b,2735,a)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3004,b,2741,b)].
% 17.72/17.78 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3004,b,2742,b)].
% 17.72/17.78 3005 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2318,a,2245,b)].
% 17.72/17.78 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(3005,c,2734,a)].
% 17.72/17.78 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(3005,c,2735,a)].
% 17.72/17.78 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3005,c,2741,b)].
% 17.72/17.78 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3005,c,2742,b)].
% 17.72/17.78 3006 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2319,a,2245,b)].
% 17.72/17.78 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(3006,c,2734,a)].
% 17.72/17.78 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(3006,c,2735,a)].
% 17.72/17.78 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3006,c,2741,b)].
% 17.72/17.78 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3006,c,2742,b)].
% 17.72/17.78 3007 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2320,a,2245,b)].
% 17.72/17.78 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(3007,c,2734,a)].
% 17.72/17.78 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(3007,c,2735,a)].
% 17.72/17.78 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3007,c,2741,b)].
% 17.72/17.78 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,c,2742,b)].
% 17.72/17.78 3008 -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(2321,a,2245,b)].
% 17.72/17.78 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(3008,c,2734,a)].
% 17.72/17.78 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(3008,c,2735,a)].
% 17.72/17.78 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(3008,c,2741,b)].
% 17.72/17.78 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(3008,c,2742,b)].
% 17.72/17.78 3009 -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(2322,a,2245,b)].
% 17.72/17.78 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(3009,c,2734,a)].
% 17.72/17.78 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(3009,c,2735,a)].
% 17.72/17.78 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(3009,c,2741,b)].
% 17.72/17.78 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(3009,c,2742,b)].
% 17.72/17.78 3010 -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(2323,a,2245,b)].
% 17.72/17.78 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(3010,c,2734,a)].
% 17.72/17.78 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(3010,c,2735,a)].
% 17.72/17.78 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(3010,c,2741,b)].
% 17.72/17.78 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(3010,c,2742,b)].
% 17.72/17.78 3011 -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(2324,a,2245,b)].
% 17.72/17.78 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(3011,d,2734,a)].
% 17.72/17.78 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(3011,d,2735,a)].
% 17.72/17.78 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(3011,d,2741,b)].
% 17.72/17.78 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(3011,d,2742,b)].
% 17.72/17.78 3012 -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(2325,a,2245,b)].
% 17.72/17.78 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(3012,d,2734,a)].
% 17.72/17.78 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(3012,d,2735,a)].
% 17.72/17.78 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(3012,d,2741,b)].
% 17.72/17.78 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(3012,d,2742,b)].
% 17.72/17.78 3013 -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(2326,a,2245,b)].
% 17.72/17.78 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(3013,c,2734,a)].
% 17.72/17.78 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(3013,c,2735,a)].
% 17.72/17.78 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(3013,c,2741,b)].
% 17.72/17.78 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(3013,c,2742,b)].
% 17.72/17.78 3014 -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(2327,a,2245,b)].
% 17.72/17.78 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(3014,d,2734,a)].
% 17.72/17.78 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(3014,d,2735,a)].
% 17.72/17.78 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(3014,d,2741,b)].
% 17.72/17.79 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(3014,d,2742,b)].
% 17.72/17.79 3015 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,a,2245,b)].
% 17.72/17.79 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(3015,c,2734,a)].
% 17.72/17.79 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(3015,c,2735,a)].
% 17.72/17.79 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3015,c,2741,b)].
% 17.72/17.79 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3015,c,2742,b)].
% 17.72/17.79 3016 -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(2329,a,2245,b)].
% 17.72/17.79 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(3016,c,2734,a)].
% 17.72/17.79 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(3016,c,2735,a)].
% 17.72/17.79 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(3016,c,2741,b)].
% 17.72/17.79 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(3016,c,2742,b)].
% 17.72/17.79 3017 -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(2330,a,2245,b)].
% 17.72/17.79 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(3017,c,2734,a)].
% 17.72/17.79 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(3017,c,2735,a)].
% 17.72/17.79 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(3017,c,2741,b)].
% 17.72/17.79 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(3017,c,2742,b)].
% 17.72/17.79 3018 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2331,b,2245,b)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3018,b,2734,a)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(3018,b,2735,a)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3018,b,2741,b)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3018,b,2742,b)].
% 17.72/17.79 3019 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2332,b,2245,b)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3019,b,2734,a)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(3019,b,2735,a)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3019,b,2741,b)].
% 17.72/17.79 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3019,b,2742,b)].
% 17.72/17.79 3020 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2333,a,2245,b)].
% 17.72/17.80 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(3020,b,2734,a)].
% 17.72/17.80 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(3020,b,2735,a)].
% 17.72/17.80 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3020,b,2741,b)].
% 17.72/17.80 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3020,b,2742,b)].
% 17.72/17.80 3021 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2334,a,2245,b)].
% 17.72/17.80 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(3021,b,2734,a)].
% 17.72/17.80 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(3021,b,2735,a)].
% 17.72/17.80 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3021,b,2741,b)].
% 17.72/17.80 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3021,b,2742,b)].
% 17.72/17.80 3022 -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(2339,a,2245,b)].
% 17.72/17.80 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(3022,c,2734,a)].
% 17.72/17.80 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(3022,c,2735,a)].
% 17.72/17.80 3023 -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(2340,a,2245,b)].
% 17.72/17.80 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(3023,c,2734,a)].
% 17.72/17.80 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(3023,c,2735,a)].
% 17.72/17.80 3024 -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(2341,a,2245,b)].
% 17.72/17.80 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(3024,c,2734,a)].
% 17.72/17.80 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3024,c,2735,a)].
% 17.72/17.80 3025 -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(2342,a,2245,b)].
% 17.72/17.80 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(3025,c,2734,a)].
% 17.72/17.80 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(3025,c,2735,a)].
% 17.72/17.80 3026 -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(2343,a,2245,b)].
% 17.72/17.80 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(3026,c,2734,a)].
% 17.72/17.80 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(3026,c,2735,a)].
% 17.72/17.80 3027 -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(2344,a,2245,b)].
% 17.72/17.80 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(3027,c,2734,a)].
% 17.72/17.80 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(3027,c,2735,a)].
% 17.72/17.80 3028 -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(2345,a,2245,b)].
% 17.72/17.80 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(3028,c,2734,a)].
% 17.72/17.80 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3028,c,2735,a)].
% 17.72/17.80 3029 -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(2346,a,2245,b)].
% 17.72/17.80 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(3029,c,2734,a)].
% 17.72/17.81 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(3029,c,2735,a)].
% 17.72/17.81 3030 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2381,e,2245,b)].
% 17.72/17.81 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3030,e,2734,a)].
% 17.72/17.81 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(3030,e,2735,a)].
% 17.72/17.81 3031 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2382,c,2245,b)].
% 17.72/17.81 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(3031,c,2734,a)].
% 17.72/17.81 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(3031,c,2735,a)].
% 17.72/17.81 3032 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2383,c,2245,b)].
% 17.72/17.81 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(3032,c,2734,a)].
% 17.72/17.81 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(3032,c,2735,a)].
% 17.72/17.81 3033 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2384,b,2245,b)].
% 17.72/17.81 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3033,b,2734,a)].
% 17.72/17.81 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(3033,b,2735,a)].
% 17.72/17.81 3034 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2385,b,2245,b)].
% 17.72/17.81 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3034,b,2734,a)].
% 17.72/17.81 Derived: class_HOL_Oplus(tc_nat). [resolve(3034,b,2735,a)].
% 17.72/17.81 3035 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2427,b,2245,b)].
% 17.72/17.81 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3035,b,2734,a)].
% 17.72/17.81 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(3035,b,2735,a)].
% 17.72/17.81 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3035,b,2741,b)].
% 17.72/17.81 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3035,b,2742,b)].
% 17.72/17.81 3036 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2428,b,2245,b)].
% 17.72/17.81 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3036,b,2734,a)].
% 17.72/17.81 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(3036,b,2735,a)].
% 17.72/17.81 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3036,b,2741,b)].
% 17.72/17.81 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3036,b,2742,b)].
% 17.72/17.81 3037 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2429,d,2245,b)].
% 17.72/17.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3037,d,2734,a)].
% 17.72/17.81 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(3037,d,2735,a)].
% 17.72/17.81 3038 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2430,b,2245,b)].
% 17.72/17.81 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3038,b,2734,a)].
% 17.72/17.81 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(3038,b,2735,a)].
% 17.72/17.81 3039 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2431,b,2245,b)].
% 17.72/17.81 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3039,b,2734,a)].
% 17.72/17.81 Derived: class_HOL_Otimes(tc_nat). [resolve(3039,b,2735,a)].
% 17.72/17.81 3040 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2432,b,2245,b)].
% 17.79/17.82 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3040,b,2734,a)].
% 17.79/17.82 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(3040,b,2735,a)].
% 17.79/17.82 3041 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2433,b,2245,b)].
% 17.79/17.82 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3041,b,2734,a)].
% 17.79/17.82 Derived: class_HOL_Ozero(tc_nat). [resolve(3041,b,2735,a)].
% 17.79/17.82 3042 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2434,b,2245,b)].
% 17.79/17.82 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3042,b,2734,a)].
% 17.79/17.82 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(3042,b,2735,a)].
% 17.79/17.82 3043 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2435,b,2245,b)].
% 17.79/17.82 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3043,b,2734,a)].
% 17.79/17.82 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(3043,b,2735,a)].
% 17.79/17.82 3044 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2436,b,2245,b)].
% 17.79/17.82 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(3044,b,2734,a)].
% 17.79/17.82 Derived: -c_less(A,A,tc_nat). [resolve(3044,b,2735,a)].
% 17.79/17.82 3045 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2437,c,2245,b)].
% 17.79/17.82 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3045,c,2734,a)].
% 17.79/17.82 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(3045,c,2735,a)].
% 17.79/17.82 3046 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2438,b,2245,b)].
% 17.79/17.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3046,b,2734,a)].
% 17.79/17.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(3046,b,2735,a)].
% 17.79/17.82 3047 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2439,c,2245,b)].
% 17.79/17.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3047,c,2734,a)].
% 17.79/17.82 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(3047,c,2735,a)].
% 17.79/17.82 3048 -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(2440,c,2245,b)].
% 17.79/17.82 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(3048,c,2734,a)].
% 17.79/17.82 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(3048,c,2735,a)].
% 17.79/17.82 3049 -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(2441,c,2245,b)].
% 17.79/17.82 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(3049,c,2734,a)].
% 17.79/17.82 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(3049,c,2735,a)].
% 17.79/17.82 3050 -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(2442,c,2245,b)].
% 17.79/17.83 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(3050,c,2734,a)].
% 17.79/17.83 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(3050,c,2735,a)].
% 17.79/17.83 3051 -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(2443,c,2245,b)].
% 17.79/17.83 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(3051,c,2734,a)].
% 17.79/17.83 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(3051,c,2735,a)].
% 17.79/17.83 3052 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2444,c,2245,b)].
% 17.79/17.83 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3052,c,2734,a)].
% 17.79/17.83 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(3052,c,2735,a)].
% 17.79/17.83 3053 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(2445,b,2245,b)].
% 17.79/17.83 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(3053,b,2734,a)].
% 17.79/17.83 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(3053,b,2735,a)].
% 17.79/17.83 3054 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2446,b,2245,b)].
% 17.79/17.83 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3054,b,2734,a)].
% 17.79/17.83 Derived: c_lessequals(A,A,tc_nat). [resolve(3054,b,2735,a)].
% 17.79/17.83 3055 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2447,d,2245,b)].
% 17.79/17.83 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(3055,d,2734,a)].
% 17.79/17.83 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(3055,d,2735,a)].
% 17.79/17.83 3056 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2448,d,2245,b)].
% 17.79/17.83 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3056,d,2734,a)].
% 17.79/17.83 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(3056,d,2735,a)].
% 17.79/17.83 3057 -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(2449,c,2245,b)].
% 17.79/17.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3057,c,2734,a)].
% 17.79/17.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3057,c,2735,a)].
% 17.79/17.83 3058 -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(2450,c,2245,b)].
% 17.79/17.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3058,c,2734,a)].
% 17.79/17.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3058,c,2735,a)].
% 17.79/17.83 3059 -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(2451,d,2245,b)].
% 17.79/17.83 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(3059,d,2734,a)].
% 17.79/17.85 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(3059,d,2735,a)].
% 17.79/17.85 3060 -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(2452,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3060,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3060,c,2735,a)].
% 17.79/17.85 3061 -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(2453,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3061,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3061,c,2735,a)].
% 17.79/17.85 3062 -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(2454,d,2245,b)].
% 17.79/17.85 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(3062,d,2734,a)].
% 17.79/17.85 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(3062,d,2735,a)].
% 17.79/17.85 3063 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2455,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3063,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3063,c,2735,a)].
% 17.79/17.85 3064 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2456,c,2245,b)].
% 17.79/17.85 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3064,c,2734,a)].
% 17.79/17.85 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3064,c,2735,a)].
% 17.79/17.85 3065 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2457,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3065,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3065,c,2735,a)].
% 17.79/17.85 3066 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2458,c,2245,b)].
% 17.79/17.85 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3066,c,2734,a)].
% 17.79/17.85 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3066,c,2735,a)].
% 17.79/17.85 3067 -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(2459,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3067,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3067,c,2735,a)].
% 17.79/17.85 3068 -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(2460,c,2245,b)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3068,c,2734,a)].
% 17.79/17.85 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3068,c,2735,a)].
% 18.03/18.08 3069 -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(2461,d,2245,b)].
% 18.03/18.08 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(3069,d,2734,a)].
% 18.03/18.08 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(3069,d,2735,a)].
% 18.03/18.08 3070 -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(2462,c,2245,b)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3070,c,2734,a)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3070,c,2735,a)].
% 18.03/18.08 3071 -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(2463,c,2245,b)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3071,c,2734,a)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3071,c,2735,a)].
% 18.03/18.08 3072 -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(2464,d,2245,b)].
% 18.03/18.08 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(3072,d,2734,a)].
% 18.03/18.08 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(3072,d,2735,a)].
% 18.03/18.08 3073 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2465,c,2245,b)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3073,c,2734,a)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3073,c,2735,a)].
% 18.03/18.08 3074 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2466,c,2245,b)].
% 18.03/18.08 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3074,c,2734,a)].
% 18.03/18.08 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3074,c,2735,a)].
% 18.03/18.08 3075 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2467,c,2245,b)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(3075,c,2734,a)].
% 18.03/18.08 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3075,c,2735,a)].
% 18.03/18.08 3076 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2468,c,2245,b)].
% 18.03/18.08 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3076,c,2734,a)].
% 18.03/18.08 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3076,c,2735,a)].
% 18.03/18.08 3077 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2469,d,2245,b)].
% 18.03/18.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3077,d,2734,a)].
% 18.03/18.08 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(3077,d,2735,a)].
% 18.03/18.08 3078 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_0) # label(axiom). [assumption].
% 18.61/18.67 3079 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 18.61/18.67 3080 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_2) # label(axiom). [assumption].
% 18.61/18.67 3081 -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].
% 18.61/18.67 3082 -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].
% 18.61/18.67 3083 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1321,a,1277,a)].
% 18.61/18.67 3084 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1321,a,1303,b)].
% 18.61/18.67 3085 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1321,a,1304,b)].
% 18.61/18.67 3086 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1637,a)].
% 18.61/18.67 3087 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1638,a)].
% 18.61/18.67 3088 -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(1666,b,1639,a)].
% 18.61/18.67 3089 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1640,a)].
% 18.61/18.67 3090 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1641,a)].
% 18.61/18.67 3091 -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(1666,b,1642,a)].
% 18.61/18.67 3092 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1643,a)].
% 18.61/18.67 3093 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1666,b,1644,a)].
% 18.61/18.67 3094 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1666,b,1645,a)].
% 18.61/18.67 3095 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1666,b,1646,a)].
% 18.61/18.67 3096 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1647,a)].
% 18.61/18.67 3097 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1648,a)].
% 18.61/18.67 3098 -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(1666,b,1649,a)].
% 18.61/18.67 3099 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1650,a)].
% 18.61/18.67 3100 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1651,a)].
% 18.61/18.67 3101 -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(1666,b,1652,a)].
% 18.61/18.67 3102 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1666,b,1653,a)].
% 18.61/18.67 3103 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1666,b,1654,a)].
% 18.61/18.67 3104 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1666,b,1655,a)].
% 18.61/18.67 3105 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1666,b,1656,a)].
% 18.61/18.67 3106 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 18.61/18.69 3107 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 18.61/18.69 3108 -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].
% 18.61/18.69 3109 -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].
% 18.61/18.69 3110 -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].
% 18.61/18.69 3111 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 18.61/18.69 3112 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 18.61/18.69 3113 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom). [assumption].
% 18.61/18.69 3114 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom). [assumption].
% 18.61/18.69 3115 -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].
% 18.61/18.69 3116 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom). [assumption].
% 18.61/18.69 3117 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 18.61/18.69 3118 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom). [assumption].
% 18.61/18.69 3119 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(36,b,1,a)].
% 18.61/18.69 3120 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(36,b,3,a)].
% 18.61/18.69 3121 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 18.61/18.69 3122 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 18.61/18.69 3123 -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)].
% 18.61/18.69 3124 -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)].
% 18.61/18.69 3125 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(165,a,158,b)].
% 18.61/18.69 3126 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(166,a,158,b)].
% 18.61/18.69 3127 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(171,a,158,b)].
% 18.61/18.69 3128 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(172,a,158,b)].
% 18.61/18.69 3129 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 18.61/18.69 3130 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 18.61/18.69 3131 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(247,b,232,b)].
% 18.61/18.69 3132 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(248,b,232,b)].
% 18.61/18.69 3133 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,288,a)].
% 18.61/18.69 3134 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,290,a)].
% 18.61/18.72 3135 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(322,a,311,b)].
% 18.61/18.72 3136 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(323,a,311,b)].
% 18.61/18.72 3137 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(325,a,311,b)].
% 18.61/18.72 3138 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(326,a,311,b)].
% 18.61/18.72 3139 -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(348,b,331,b)].
% 18.61/18.72 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(3139,a,3108,b)].
% 18.61/18.72 3140 -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(348,b,333,b)].
% 18.61/18.72 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(3140,a,3108,b)].
% 18.61/18.72 3141 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(348,b,334,a)].
% 18.61/18.72 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(3141,a,3108,b)].
% 18.61/18.72 3142 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,335,a)].
% 18.61/18.72 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(3142,a,3108,b)].
% 18.61/18.72 3143 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,336,a)].
% 18.61/18.72 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(3143,a,3108,b)].
% 18.61/18.72 3144 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,a,348,b)].
% 18.61/18.72 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3108,b)].
% 18.61/18.72 3145 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(355,a,348,b)].
% 18.61/18.72 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3108,b)].
% 18.61/18.72 3146 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,b,348,b)].
% 18.61/18.72 3147 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,b,348,b)].
% 18.61/18.72 3148 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(370,b,348,b)].
% 18.61/18.72 3149 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(371,b,348,b)].
% 18.61/18.72 3150 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(372,b,348,b)].
% 18.61/18.72 3151 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(373,b,348,b)].
% 18.61/18.72 3152 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(374,a,348,b)].
% 18.61/18.72 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3152,b,3108,b)].
% 18.61/18.72 3153 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(375,a,348,b)].
% 18.61/18.72 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3153,b,3108,b)].
% 18.61/18.72 3154 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(376,c,348,b)].
% 18.61/18.72 3155 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(377,c,348,b)].
% 18.80/18.86 3156 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,734,a)].
% 18.80/18.86 3157 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(814,a,741,a)].
% 18.80/18.86 3158 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1325,a,1277,a)].
% 18.80/18.86 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(3158,a,3139,a)].
% 18.80/18.86 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(3158,a,3140,a)].
% 18.80/18.86 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(3158,a,3141,a)].
% 18.80/18.86 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(3158,a,3142,a)].
% 18.80/18.86 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(3158,a,3143,a)].
% 18.80/18.86 3159 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1325,a,1303,b)].
% 18.80/18.86 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(3159,a,3139,a)].
% 18.80/18.86 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(3159,a,3140,a)].
% 18.80/18.86 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(3159,a,3141,a)].
% 18.80/18.86 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(3159,a,3142,a)].
% 18.80/18.86 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(3159,a,3143,a)].
% 18.80/18.86 3160 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1325,a,1304,b)].
% 18.80/18.86 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(3160,a,3139,a)].
% 18.80/18.86 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(3160,a,3140,a)].
% 18.80/18.86 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(3160,a,3141,a)].
% 18.80/18.86 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(3160,a,3142,a)].
% 18.80/18.86 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(3160,a,3143,a)].
% 18.80/18.86 3161 -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(1502,b,1477,a)].
% 18.80/18.86 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(3161,a,3108,b)].
% 18.80/18.86 3162 -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(1502,b,1478,a)].
% 18.80/18.86 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(3162,a,3108,b)].
% 18.90/18.95 3163 -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(1502,b,1479,a)].
% 18.90/18.95 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(3163,a,3108,b)].
% 18.90/18.95 3164 -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(1502,b,1480,a)].
% 18.90/18.95 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(3164,a,3108,b)].
% 18.90/18.95 3165 -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(1502,b,1481,a)].
% 18.90/18.95 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(3165,a,3108,b)].
% 18.90/18.95 3166 -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(1502,b,1482,a)].
% 18.90/18.95 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(3166,a,3108,b)].
% 18.90/18.95 3167 -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(1502,b,1483,a)].
% 18.90/18.95 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(3167,a,3108,b)].
% 18.90/18.95 3168 -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(1502,b,1484,a)].
% 18.90/18.95 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(3168,a,3108,b)].
% 18.90/18.95 3169 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1611,b,1581,a)].
% 18.90/18.95 3170 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1582,a)].
% 18.90/18.95 3171 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1611,b,1583,a)].
% 18.90/18.95 3172 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1611,b,1584,a)].
% 18.90/18.95 3173 -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(1611,b,1585,a)].
% 18.90/18.95 3174 -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(1611,b,1586,a)].
% 18.90/18.95 3175 -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(1611,b,1587,a)].
% 18.90/18.95 3176 -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(1611,b,1588,a)].
% 18.90/18.95 3177 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1589,a)].
% 18.90/18.95 3178 -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(1611,b,1590,a)].
% 18.90/18.95 3179 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1611,b,1591,a)].
% 18.90/18.95 3180 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1614,a,1611,b)].
% 18.90/18.95 3181 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1615,a,1611,b)].
% 18.90/18.95 3182 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1637,a)].
% 18.90/18.95 3183 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1638,a)].
% 18.90/18.95 3184 -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(1676,b,1639,a)].
% 19.00/19.02 3185 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1640,a)].
% 19.00/19.02 3186 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1641,a)].
% 19.00/19.02 3187 -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(1676,b,1642,a)].
% 19.00/19.02 3188 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1643,a)].
% 19.00/19.02 3189 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1676,b,1644,a)].
% 19.00/19.02 3190 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1676,b,1645,a)].
% 19.00/19.02 3191 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1676,b,1646,a)].
% 19.00/19.02 3192 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1647,a)].
% 19.00/19.02 3193 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1648,a)].
% 19.00/19.02 3194 -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(1676,b,1649,a)].
% 19.00/19.02 3195 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1650,a)].
% 19.00/19.02 3196 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1651,a)].
% 19.00/19.02 3197 -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(1676,b,1652,a)].
% 19.00/19.02 3198 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1676,b,1653,a)].
% 19.00/19.02 3199 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1676,b,1654,a)].
% 19.00/19.02 3200 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1676,b,1655,a)].
% 19.00/19.02 3201 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1676,b,1656,a)].
% 19.00/19.02 3202 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1780,a,1778,b)].
% 19.00/19.02 3203 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1792,b,1760,a)].
% 19.00/19.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3203,a,3108,b)].
% 19.00/19.02 3204 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1792,b,1767,a)].
% 19.00/19.02 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3204,a,3108,b)].
% 19.00/19.02 3205 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1844,b,1843,b)].
% 19.00/19.02 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3205,e,3108,b)].
% 19.00/19.02 3206 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2071,b)].
% 19.00/19.02 3207 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2094,a,2071,b)].
% 19.00/19.02 3208 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2095,a,2071,b)].
% 19.00/19.02 3209 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2096,a,2071,b)].
% 19.00/19.02 3210 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2097,a,2071,b)].
% 19.00/19.04 3211 -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(2098,a,2071,b)].
% 19.00/19.04 3212 -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(2099,a,2071,b)].
% 19.00/19.04 3213 -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(2100,a,2071,b)].
% 19.00/19.04 3214 -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(2101,a,2071,b)].
% 19.00/19.04 3215 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2102,a,2071,b)].
% 19.00/19.04 3216 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(2103,a,2071,b)].
% 19.00/19.04 3217 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2104,a,2071,b)].
% 19.00/19.04 3218 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2105,d,2071,b)].
% 19.00/19.04 3219 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2106,d,2071,b)].
% 19.00/19.04 3220 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2107,a,2071,b)].
% 19.00/19.04 3221 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2108,a,2071,b)].
% 19.00/19.04 3222 -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(2109,a,2071,b)].
% 19.00/19.04 3223 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2110,a,2071,b)].
% 19.00/19.04 3224 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2111,a,2071,b)].
% 19.00/19.04 3225 -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(2112,a,2071,b)].
% 19.00/19.04 3226 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2113,a,2071,b)].
% 19.00/19.04 3227 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2114,a,2071,b)].
% 19.00/19.04 3228 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2115,a,2071,b)].
% 19.00/19.04 3229 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2116,a,2071,b)].
% 19.00/19.04 3230 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2117,a,2071,b)].
% 19.00/19.04 3231 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2118,a,2071,b)].
% 19.00/19.04 3232 -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(2119,a,2071,b)].
% 19.00/19.04 3233 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2120,a,2071,b)].
% 19.00/19.04 3234 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2121,a,2071,b)].
% 19.00/19.04 3235 -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(2122,a,2071,b)].
% 19.00/19.04 3236 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2123,a,2071,b)].
% 19.00/19.04 3237 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2124,a,2071,b)].
% 19.20/19.33 3238 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2125,a,2071,b)].
% 19.20/19.33 3239 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2126,a,2071,b)].
% 19.20/19.33 3240 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2127,d,2071,b)].
% 19.20/19.33 3241 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2202,b,2142,b)].
% 19.20/19.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3241,b,3108,b)].
% 19.20/19.33 3242 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2203,b,2142,b)].
% 19.20/19.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3242,b,3108,b)].
% 19.20/19.33 3243 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2204,b,2142,b)].
% 19.20/19.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3243,b,3108,b)].
% 19.20/19.33 3244 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2205,b,2142,b)].
% 19.20/19.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3244,b,3108,b)].
% 19.20/19.33 3245 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2206,b,2142,b)].
% 19.20/19.33 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(3245,b,3108,b)].
% 19.20/19.33 3246 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2207,b,2142,b)].
% 19.20/19.33 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3246,b,3108,b)].
% 19.20/19.33 3247 -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].
% 19.20/19.33 3248 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 19.20/19.33 3249 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 19.20/19.33 3250 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 19.20/19.33 3251 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom). [assumption].
% 19.20/19.33 3252 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom). [assumption].
% 19.20/19.33 3253 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 19.20/19.33 3254 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom). [assumption].
% 19.20/19.33 3255 -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].
% 19.20/19.33 3256 -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].
% 19.20/19.33 3257 -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].
% 19.20/19.33 3258 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(14,b,1,a)].
% 19.20/19.33 3259 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(14,b,3,a)].
% 19.48/19.50 3260 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 19.48/19.50 3261 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 19.48/19.50 3262 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1076,a)].
% 19.48/19.50 3263 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1099,a)].
% 19.48/19.50 3264 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1327,a,1277,a)].
% 19.48/19.50 3265 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1327,a,1303,b)].
% 19.48/19.50 3266 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1327,a,1304,b)].
% 19.48/19.50 3267 -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(1488,b,1477,a)].
% 19.48/19.50 3268 -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(1488,b,1478,a)].
% 19.48/19.50 3269 -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(1488,b,1479,a)].
% 19.48/19.50 3270 -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(1488,b,1480,a)].
% 19.48/19.50 3271 -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(1488,b,1481,a)].
% 19.48/19.50 3272 -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(1488,b,1482,a)].
% 19.48/19.50 3273 -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(1488,b,1483,a)].
% 19.48/19.50 3274 -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(1488,b,1484,a)].
% 19.48/19.50 3275 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1503,a,1488,b)].
% 19.48/19.50 3276 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1504,a,1488,b)].
% 19.48/19.50 3277 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1505,b,1488,b)].
% 19.48/19.50 3278 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1506,b,1488,b)].
% 19.48/19.50 3279 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1548,b,1515,a)].
% 19.48/19.50 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3279,a,3248,a)].
% 19.48/19.50 3280 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1548,b,1516,a)].
% 19.48/19.50 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3280,a,3248,a)].
% 19.48/19.50 3281 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1517,a)].
% 19.48/19.50 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3281,a,3248,a)].
% 19.48/19.50 3282 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1518,a)].
% 19.48/19.50 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3282,a,3248,a)].
% 19.48/19.50 3283 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1519,a)].
% 19.48/19.50 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3283,a,3248,a)].
% 19.48/19.50 3284 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1520,a)].
% 19.48/19.50 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3284,a,3248,a)].
% 19.48/19.50 3285 -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(1548,b,1521,a)].
% 19.48/19.51 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(3285,a,3248,a)].
% 19.48/19.51 3286 -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(1548,b,1522,a)].
% 19.48/19.51 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(3286,a,3248,a)].
% 19.48/19.51 3287 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1548,b,1523,a)].
% 19.48/19.51 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3287,a,3248,a)].
% 19.48/19.51 3288 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1548,b,1524,a)].
% 19.48/19.51 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(3288,a,3248,a)].
% 19.48/19.51 3289 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1548,b,1525,a)].
% 19.48/19.51 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(3289,a,3248,a)].
% 19.48/19.51 3290 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1548,b,1526,a)].
% 19.48/19.51 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3290,a,3248,a)].
% 19.48/19.51 3291 -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(1548,b,1527,a)].
% 19.48/19.51 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(3291,a,3248,a)].
% 19.48/19.51 3292 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1548,b,1528,a)].
% 19.48/19.51 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3292,a,3248,a)].
% 19.48/19.51 3293 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1548,b,1529,a)].
% 19.48/19.51 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(3293,a,3248,a)].
% 19.48/19.51 3294 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1548,b,1530,a)].
% 19.48/19.51 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(3294,a,3248,a)].
% 19.48/19.51 3295 -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(1548,b,1531,a)].
% 19.48/19.51 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(3295,a,3248,a)].
% 19.48/19.51 3296 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1548,b,1532,a)].
% 19.48/19.51 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3296,a,3248,a)].
% 19.48/19.51 3297 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1548,b,1533,a)].
% 19.48/19.51 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3297,a,3248,a)].
% 19.48/19.51 3298 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1548,b,1534,a)].
% 19.48/19.51 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3298,a,3248,a)].
% 19.48/19.51 3299 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1548,b,1535,a)].
% 19.48/19.51 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3299,a,3248,a)].
% 19.48/19.51 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3299,a,3255,b)].
% 19.48/19.55 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3299,a,3256,b)].
% 19.48/19.55 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3299,a,3257,b)].
% 19.48/19.55 3300 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1536,a)].
% 19.48/19.55 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(3300,a,3248,a)].
% 19.48/19.55 3301 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1596,b,1581,a)].
% 19.48/19.55 3302 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1582,a)].
% 19.48/19.55 3303 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1583,a)].
% 19.48/19.55 3304 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1584,a)].
% 19.48/19.55 3305 -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(1596,b,1585,a)].
% 19.48/19.55 3306 -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(1596,b,1586,a)].
% 19.48/19.55 3307 -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(1596,b,1587,a)].
% 19.48/19.55 3308 -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(1596,b,1588,a)].
% 19.48/19.55 3309 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1589,a)].
% 19.48/19.55 3310 -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(1596,b,1590,a)].
% 19.48/19.55 3311 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1596,b,1591,a)].
% 19.48/19.55 3312 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1614,a,1596,b)].
% 19.48/19.55 3313 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1615,a,1596,b)].
% 19.48/19.55 3314 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1637,a)].
% 19.48/19.55 3315 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1638,a)].
% 19.48/19.55 3316 -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(1661,b,1639,a)].
% 19.48/19.55 3317 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1640,a)].
% 19.48/19.55 3318 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1641,a)].
% 19.48/19.55 3319 -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(1661,b,1642,a)].
% 19.48/19.55 3320 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1643,a)].
% 19.48/19.55 3321 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1644,a)].
% 19.48/19.55 3322 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1645,a)].
% 19.48/19.55 3323 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1646,a)].
% 19.57/19.59 3324 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1647,a)].
% 19.57/19.59 3325 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1648,a)].
% 19.57/19.59 3326 -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(1661,b,1649,a)].
% 19.57/19.59 3327 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1650,a)].
% 19.57/19.59 3328 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1651,a)].
% 19.57/19.59 3329 -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(1661,b,1652,a)].
% 19.57/19.59 3330 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1653,a)].
% 19.57/19.59 3331 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1654,a)].
% 19.57/19.59 3332 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1655,a)].
% 19.57/19.59 3333 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1656,a)].
% 19.57/19.59 3334 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1764,b)].
% 19.57/19.59 3335 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1797,a,1764,b)].
% 19.57/19.59 3336 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1798,a,1764,b)].
% 19.57/19.59 3337 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1799,a,1764,b)].
% 19.57/19.59 3338 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1764,b)].
% 19.57/19.59 3339 -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(1801,a,1764,b)].
% 19.57/19.59 3340 -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(1802,a,1764,b)].
% 19.57/19.59 3341 -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(1803,a,1764,b)].
% 19.57/19.59 3342 -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(1804,a,1764,b)].
% 19.57/19.59 3343 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1764,b)].
% 19.57/19.59 3344 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(1806,a,1764,b)].
% 19.57/19.59 3345 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1807,a,1764,b)].
% 19.57/19.59 3346 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1808,d,1764,b)].
% 19.57/19.59 3347 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1809,d,1764,b)].
% 19.57/19.59 3348 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1810,a,1764,b)].
% 19.57/19.59 3349 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1811,a,1764,b)].
% 19.90/19.93 3350 -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(1812,a,1764,b)].
% 19.90/19.93 3351 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1813,a,1764,b)].
% 19.90/19.93 3352 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1814,a,1764,b)].
% 19.90/19.93 3353 -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(1815,a,1764,b)].
% 19.90/19.93 3354 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1816,a,1764,b)].
% 19.90/19.93 3355 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1817,a,1764,b)].
% 19.90/19.93 3356 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1818,a,1764,b)].
% 19.90/19.93 3357 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1819,a,1764,b)].
% 19.90/19.93 3358 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1820,a,1764,b)].
% 19.90/19.93 3359 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1821,a,1764,b)].
% 19.90/19.93 3360 -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(1822,a,1764,b)].
% 19.90/19.93 3361 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1823,a,1764,b)].
% 19.90/19.93 3362 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1824,a,1764,b)].
% 19.90/19.93 3363 -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(1825,a,1764,b)].
% 19.90/19.93 3364 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1826,a,1764,b)].
% 19.90/19.93 3365 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1827,a,1764,b)].
% 19.90/19.93 3366 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1828,a,1764,b)].
% 19.90/19.93 3367 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1829,a,1764,b)].
% 19.90/19.93 3368 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1844,b,1834,b)].
% 19.90/19.93 3369 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1899,d,1834,b)].
% 19.90/19.93 3370 -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].
% 19.90/19.93 3371 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 19.90/19.93 3372 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 19.90/19.93 3373 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 19.90/19.93 3374 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom). [assumption].
% 19.90/19.93 3375 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom). [assumption].
% 20.08/20.09 3376 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 20.08/20.09 3377 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom). [assumption].
% 20.08/20.09 3378 -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].
% 20.08/20.09 3379 -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].
% 20.08/20.09 3380 -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].
% 20.08/20.09 3381 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(13,b,1,a)].
% 20.08/20.09 3382 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(13,b,3,a)].
% 20.08/20.09 3383 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 20.08/20.09 3384 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 20.08/20.09 3385 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1076,a)].
% 20.08/20.09 3386 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1099,a)].
% 20.08/20.09 3387 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1328,a,1277,a)].
% 20.08/20.09 3388 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1328,a,1303,b)].
% 20.08/20.09 3389 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1328,a,1304,b)].
% 20.08/20.09 3390 -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(1487,b,1477,a)].
% 20.08/20.09 3391 -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(1487,b,1478,a)].
% 20.08/20.09 3392 -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(1487,b,1479,a)].
% 20.08/20.09 3393 -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(1487,b,1480,a)].
% 20.08/20.09 3394 -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(1487,b,1481,a)].
% 20.08/20.09 3395 -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(1487,b,1482,a)].
% 20.08/20.09 3396 -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(1487,b,1483,a)].
% 20.08/20.09 3397 -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(1487,b,1484,a)].
% 20.08/20.09 3398 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1503,a,1487,b)].
% 20.08/20.09 3399 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1504,a,1487,b)].
% 20.08/20.09 3400 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1505,b,1487,b)].
% 20.08/20.09 3401 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1506,b,1487,b)].
% 20.08/20.09 3402 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1547,b,1515,a)].
% 20.08/20.09 3403 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1547,b,1516,a)].
% 20.08/20.09 3404 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1517,a)].
% 20.08/20.12 3405 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1518,a)].
% 20.08/20.12 3406 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1519,a)].
% 20.08/20.12 3407 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1520,a)].
% 20.08/20.12 3408 -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(1547,b,1521,a)].
% 20.08/20.12 3409 -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(1547,b,1522,a)].
% 20.08/20.12 3410 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1547,b,1523,a)].
% 20.08/20.12 3411 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1547,b,1524,a)].
% 20.08/20.12 3412 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1547,b,1525,a)].
% 20.08/20.12 3413 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1547,b,1526,a)].
% 20.08/20.12 3414 -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(1547,b,1527,a)].
% 20.08/20.12 3415 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1547,b,1528,a)].
% 20.08/20.12 3416 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1547,b,1529,a)].
% 20.08/20.12 3417 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1547,b,1530,a)].
% 20.08/20.12 3418 -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(1547,b,1531,a)].
% 20.08/20.12 3419 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1547,b,1532,a)].
% 20.08/20.12 3420 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1547,b,1533,a)].
% 20.08/20.12 3421 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1547,b,1534,a)].
% 20.08/20.12 3422 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1547,b,1535,a)].
% 20.08/20.12 3423 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1536,a)].
% 20.08/20.12 3424 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1595,b,1581,a)].
% 20.08/20.12 3425 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1582,a)].
% 20.08/20.12 3426 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1583,a)].
% 20.08/20.12 3427 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1584,a)].
% 20.08/20.12 3428 -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(1595,b,1585,a)].
% 20.08/20.12 3429 -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(1595,b,1586,a)].
% 20.08/20.12 3430 -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(1595,b,1587,a)].
% 20.08/20.12 3431 -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(1595,b,1588,a)].
% 20.08/20.12 3432 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1589,a)].
% 20.15/20.18 3433 -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(1595,b,1590,a)].
% 20.15/20.18 3434 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1595,b,1591,a)].
% 20.15/20.18 3435 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1614,a,1595,b)].
% 20.15/20.18 3436 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1615,a,1595,b)].
% 20.15/20.18 3437 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1637,a)].
% 20.15/20.18 3438 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1638,a)].
% 20.15/20.18 3439 -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(1660,b,1639,a)].
% 20.15/20.18 3440 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1640,a)].
% 20.15/20.18 3441 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1641,a)].
% 20.15/20.18 3442 -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(1660,b,1642,a)].
% 20.15/20.18 3443 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1643,a)].
% 20.15/20.18 3444 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1644,a)].
% 20.15/20.18 3445 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1645,a)].
% 20.15/20.18 3446 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1646,a)].
% 20.15/20.18 3447 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1647,a)].
% 20.15/20.18 3448 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1648,a)].
% 20.15/20.18 3449 -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(1660,b,1649,a)].
% 20.15/20.18 3450 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1650,a)].
% 20.15/20.18 3451 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1651,a)].
% 20.15/20.18 3452 -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(1660,b,1652,a)].
% 20.15/20.18 3453 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1653,a)].
% 20.15/20.18 3454 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1654,a)].
% 20.15/20.18 3455 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1655,a)].
% 20.15/20.18 3456 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1656,a)].
% 20.15/20.18 3457 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1763,b)].
% 20.15/20.18 3458 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1797,a,1763,b)].
% 20.15/20.18 3459 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1798,a,1763,b)].
% 20.15/20.19 3460 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1799,a,1763,b)].
% 20.15/20.19 3461 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1763,b)].
% 20.15/20.19 3462 -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(1801,a,1763,b)].
% 20.15/20.19 3463 -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(1802,a,1763,b)].
% 20.15/20.19 3464 -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(1803,a,1763,b)].
% 20.15/20.19 3465 -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(1804,a,1763,b)].
% 20.15/20.19 3466 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1763,b)].
% 20.15/20.19 3467 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(1806,a,1763,b)].
% 20.15/20.19 3468 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1807,a,1763,b)].
% 20.15/20.19 3469 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1808,d,1763,b)].
% 20.15/20.19 3470 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1809,d,1763,b)].
% 20.15/20.19 3471 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1810,a,1763,b)].
% 20.15/20.19 3472 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1811,a,1763,b)].
% 20.15/20.19 3473 -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(1812,a,1763,b)].
% 20.15/20.19 3474 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1813,a,1763,b)].
% 20.15/20.19 3475 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1814,a,1763,b)].
% 20.15/20.19 3476 -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(1815,a,1763,b)].
% 20.15/20.19 3477 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1816,a,1763,b)].
% 20.15/20.19 3478 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1817,a,1763,b)].
% 20.15/20.19 3479 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1818,a,1763,b)].
% 20.15/20.19 3480 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1819,a,1763,b)].
% 20.15/20.19 3481 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1820,a,1763,b)].
% 20.15/20.19 3482 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1821,a,1763,b)].
% 20.15/20.19 3483 -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(1822,a,1763,b)].
% 20.15/20.19 3484 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1823,a,1763,b)].
% 20.15/20.19 3485 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1824,a,1763,b)].
% 20.46/20.51 3486 -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(1825,a,1763,b)].
% 20.46/20.51 3487 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1826,a,1763,b)].
% 20.46/20.51 3488 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1827,a,1763,b)].
% 20.46/20.51 3489 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1828,a,1763,b)].
% 20.46/20.51 3490 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1829,a,1763,b)].
% 20.46/20.51 3491 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1844,b,1833,b)].
% 20.46/20.51 3492 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1899,d,1833,b)].
% 20.46/20.51 3493 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 20.46/20.51 3494 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 20.46/20.51 3495 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom). [assumption].
% 20.46/20.51 3496 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 20.46/20.51 3497 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom). [assumption].
% 20.46/20.51 3498 -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].
% 20.46/20.51 3499 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 20.46/20.51 3500 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom). [assumption].
% 20.46/20.51 3501 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 20.46/20.51 3502 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom). [assumption].
% 20.46/20.51 3503 -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].
% 20.46/20.51 3504 -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].
% 20.46/20.51 3505 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(26,b,1,a)].
% 20.46/20.51 3506 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(26,b,3,a)].
% 20.46/20.51 3507 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 20.46/20.51 3508 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 20.46/20.51 3509 -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)].
% 20.46/20.51 3510 -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)].
% 20.53/20.55 3511 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(165,a,147,b)].
% 20.53/20.55 3512 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(166,a,147,b)].
% 20.53/20.55 3513 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(171,a,147,b)].
% 20.53/20.55 3514 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(172,a,147,b)].
% 20.53/20.55 3515 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 20.53/20.55 3516 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 20.53/20.55 3517 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(247,b,221,b)].
% 20.53/20.55 3518 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(248,b,221,b)].
% 20.53/20.55 3519 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,288,a)].
% 20.53/20.55 3520 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,290,a)].
% 20.53/20.55 3521 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(322,a,301,b)].
% 20.53/20.55 3522 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(323,a,301,b)].
% 20.53/20.55 3523 -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(343,b,331,b)].
% 20.53/20.55 3524 -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(343,b,333,b)].
% 20.53/20.55 3525 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(343,b,334,a)].
% 20.53/20.55 3526 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,335,a)].
% 20.53/20.55 3527 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,336,a)].
% 20.53/20.55 3528 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,a,343,b)].
% 20.53/20.55 3529 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(355,a,343,b)].
% 20.53/20.55 3530 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,343,b)].
% 20.53/20.55 3531 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,343,b)].
% 20.53/20.55 3532 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,b,343,b)].
% 20.53/20.55 3533 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,b,343,b)].
% 20.53/20.55 3534 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(370,b,343,b)].
% 20.53/20.55 3535 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(371,b,343,b)].
% 20.53/20.55 3536 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(372,b,343,b)].
% 20.53/20.55 3537 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(373,b,343,b)].
% 20.53/20.55 3538 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(374,a,343,b)].
% 20.53/20.55 3539 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(375,a,343,b)].
% 20.53/20.55 3540 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(376,c,343,b)].
% 20.53/20.55 3541 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(377,c,343,b)].
% 20.53/20.55 3542 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,734,a)].
% 20.53/20.55 3543 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(809,a,741,a)].
% 20.61/20.67 3544 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1086,b,1076,a)].
% 20.61/20.67 3545 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1109,b,1099,a)].
% 20.61/20.67 3546 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1324,a,1277,a)].
% 20.61/20.67 3547 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1324,a,1303,b)].
% 20.61/20.67 3548 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1324,a,1304,b)].
% 20.61/20.67 3549 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1463,b,1434,a)].
% 20.61/20.67 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3549,a,3494,a)].
% 20.61/20.67 3550 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1463,b,1435,a)].
% 20.61/20.67 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3550,a,3494,a)].
% 20.61/20.67 3551 -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(1463,b,1436,a)].
% 20.61/20.67 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(3551,a,3494,a)].
% 20.61/20.67 3552 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1463,b,1437,a)].
% 20.61/20.67 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3552,a,3494,a)].
% 20.61/20.67 3553 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1463,b,1438,a)].
% 20.61/20.67 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3553,a,3494,a)].
% 20.61/20.67 3554 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1463,b,1439,a)].
% 20.61/20.67 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3554,a,3494,a)].
% 20.61/20.67 3555 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1440,a)].
% 20.61/20.67 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3555,a,3494,a)].
% 20.61/20.67 3556 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1463,b,1441,a)].
% 20.61/20.67 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3556,a,3494,a)].
% 20.61/20.67 3557 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1463,b,1442,a)].
% 20.61/20.67 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3557,a,3494,a)].
% 20.61/20.67 3558 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1443,a)].
% 20.61/20.67 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3558,a,3494,a)].
% 20.61/20.67 3559 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1463,b,1444,a)].
% 20.61/20.67 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3559,a,3494,a)].
% 20.61/20.67 3560 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1463,b,1445,a)].
% 20.61/20.67 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3560,a,3494,a)].
% 20.61/20.67 3561 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1463,b,1446,a)].
% 20.61/20.67 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3561,a,3494,a)].
% 20.61/20.67 3562 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1463,b,1447,a)].
% 20.61/20.67 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3562,a,3494,a)].
% 20.61/20.67 3563 -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1463,b,1448,a)].
% 20.61/20.67 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3563,a,3494,a)].
% 20.61/20.67 3564 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1463,b,1450,a)].
% 20.67/20.70 3565 c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1466,a,1463,b)].
% 20.67/20.70 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,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),tc_IntDef_Oint). [resolve(3565,b,3494,a)].
% 20.67/20.70 3566 -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(1497,b,1477,a)].
% 20.67/20.70 3567 -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(1497,b,1478,a)].
% 20.67/20.70 3568 -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(1497,b,1479,a)].
% 20.67/20.70 3569 -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(1497,b,1480,a)].
% 20.67/20.70 3570 -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(1497,b,1481,a)].
% 20.67/20.70 3571 -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(1497,b,1482,a)].
% 20.67/20.70 3572 -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(1497,b,1483,a)].
% 20.67/20.70 3573 -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(1497,b,1484,a)].
% 20.67/20.70 3574 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1549,b,1515,a)].
% 20.67/20.70 3575 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1549,b,1516,a)].
% 20.67/20.70 3576 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1517,a)].
% 20.67/20.70 3577 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1518,a)].
% 20.67/20.70 3578 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1519,a)].
% 20.67/20.70 3579 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1520,a)].
% 20.67/20.70 3580 -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(1549,b,1521,a)].
% 20.67/20.70 3581 -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(1549,b,1522,a)].
% 20.67/20.70 3582 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1549,b,1523,a)].
% 20.67/20.70 3583 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1549,b,1524,a)].
% 20.67/20.70 3584 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1549,b,1525,a)].
% 20.67/20.70 3585 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1549,b,1526,a)].
% 20.67/20.70 3586 -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(1549,b,1527,a)].
% 20.67/20.70 3587 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1549,b,1528,a)].
% 20.67/20.70 3588 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1549,b,1529,a)].
% 20.67/20.70 3589 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1549,b,1530,a)].
% 20.67/20.70 3590 -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(1549,b,1531,a)].
% 20.67/20.70 3591 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1549,b,1532,a)].
% 20.67/20.70 3592 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1549,b,1533,a)].
% 20.67/20.70 3593 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1549,b,1534,a)].
% 20.67/20.73 3594 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1576,c,1549,b)].
% 20.67/20.73 3595 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1577,c,1549,b)].
% 20.67/20.73 3596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1578,b,1549,b)].
% 20.67/20.73 3597 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1579,b,1549,b)].
% 20.67/20.73 3598 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1602,b,1581,a)].
% 20.67/20.73 3599 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1582,a)].
% 20.67/20.73 3600 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1602,b,1583,a)].
% 20.67/20.73 3601 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1602,b,1584,a)].
% 20.67/20.73 3602 -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(1602,b,1585,a)].
% 20.67/20.73 3603 -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(1602,b,1586,a)].
% 20.67/20.73 3604 -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(1602,b,1587,a)].
% 20.67/20.73 3605 -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(1602,b,1588,a)].
% 20.67/20.73 3606 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1589,a)].
% 20.67/20.73 3607 -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(1602,b,1590,a)].
% 20.67/20.73 3608 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1602,b,1591,a)].
% 20.67/20.73 3609 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1614,a,1602,b)].
% 20.67/20.73 3610 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1615,a,1602,b)].
% 20.67/20.73 3611 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1637,a)].
% 20.67/20.73 3612 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1638,a)].
% 20.67/20.73 3613 -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(1667,b,1639,a)].
% 20.67/20.73 3614 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1640,a)].
% 20.67/20.73 3615 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1641,a)].
% 20.67/20.73 3616 -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(1667,b,1642,a)].
% 20.67/20.73 3617 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1643,a)].
% 20.67/20.73 3618 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1667,b,1644,a)].
% 20.67/20.73 3619 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1667,b,1645,a)].
% 20.67/20.73 3620 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1667,b,1646,a)].
% 20.67/20.73 3621 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1647,a)].
% 20.77/20.79 3622 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1648,a)].
% 20.77/20.79 3623 -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(1667,b,1649,a)].
% 20.77/20.79 3624 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1650,a)].
% 20.77/20.79 3625 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1651,a)].
% 20.77/20.79 3626 -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(1667,b,1652,a)].
% 20.77/20.79 3627 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1667,b,1653,a)].
% 20.77/20.79 3628 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1667,b,1654,a)].
% 20.77/20.79 3629 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1667,b,1655,a)].
% 20.77/20.79 3630 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1667,b,1656,a)].
% 20.77/20.79 3631 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1780,a,1769,b)].
% 20.77/20.79 3632 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1844,b,1838,b)].
% 20.77/20.79 3633 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2062,b)].
% 20.77/20.79 3634 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2094,a,2062,b)].
% 20.77/20.79 3635 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2095,a,2062,b)].
% 20.77/20.79 3636 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2096,a,2062,b)].
% 20.77/20.79 3637 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,a,2062,b)].
% 20.77/20.79 3638 -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(2098,a,2062,b)].
% 20.77/20.79 3639 -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(2099,a,2062,b)].
% 20.77/20.79 3640 -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(2100,a,2062,b)].
% 20.77/20.79 3641 -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(2101,a,2062,b)].
% 20.77/20.79 3642 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,a,2062,b)].
% 20.77/20.79 3643 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(2103,a,2062,b)].
% 20.77/20.79 3644 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2104,a,2062,b)].
% 20.77/20.79 3645 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2062,b)].
% 20.77/20.79 3646 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,d,2062,b)].
% 20.77/20.79 3647 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2107,a,2062,b)].
% 20.77/20.79 3648 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2108,a,2062,b)].
% 20.77/20.81 3649 -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(2109,a,2062,b)].
% 20.77/20.81 3650 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,a,2062,b)].
% 20.77/20.81 3651 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,a,2062,b)].
% 20.77/20.81 3652 -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(2112,a,2062,b)].
% 20.77/20.81 3653 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2113,a,2062,b)].
% 20.77/20.81 3654 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2114,a,2062,b)].
% 20.77/20.81 3655 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,a,2062,b)].
% 20.77/20.81 3656 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,a,2062,b)].
% 20.77/20.81 3657 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2117,a,2062,b)].
% 20.77/20.81 3658 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2118,a,2062,b)].
% 20.77/20.81 3659 -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(2119,a,2062,b)].
% 20.77/20.81 3660 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2120,a,2062,b)].
% 20.77/20.81 3661 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2121,a,2062,b)].
% 20.77/20.81 3662 -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(2122,a,2062,b)].
% 20.77/20.81 3663 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2123,a,2062,b)].
% 20.77/20.81 3664 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2124,a,2062,b)].
% 20.77/20.81 3665 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2125,a,2062,b)].
% 20.77/20.81 3666 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2126,a,2062,b)].
% 20.77/20.81 3667 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2127,d,2062,b)].
% 20.77/20.81 3668 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,d,2131,b)].
% 20.77/20.81 3669 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2202,b,2131,b)].
% 20.77/20.81 3670 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2203,b,2131,b)].
% 20.77/20.81 3671 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2204,b,2131,b)].
% 20.77/20.81 3672 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2205,b,2131,b)].
% 20.77/20.81 3673 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,b,2131,b)].
% 20.77/20.81 3674 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2207,b,2131,b)].
% 20.77/20.81 3675 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2208,b,2131,b)].
% 20.77/20.81 3676 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2131,b)].
% 20.77/20.81 3677 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2210,b,2131,b)].
% 20.82/20.84 3678 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2131,b)].
% 20.82/20.84 3679 -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(2212,c,2131,b)].
% 20.82/20.84 3680 -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(2213,c,2131,b)].
% 20.82/20.84 3681 -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(2214,c,2131,b)].
% 20.82/20.84 3682 -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(2215,c,2131,b)].
% 20.82/20.84 3683 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2216,c,2131,b)].
% 20.82/20.84 3684 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(2217,b,2131,b)].
% 20.82/20.84 3685 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2218,b,2131,b)].
% 20.82/20.84 3686 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2219,d,2131,b)].
% 20.82/20.84 3687 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2220,d,2131,b)].
% 20.82/20.84 3688 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2221,c,2131,b)].
% 20.82/20.84 3689 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2222,c,2131,b)].
% 20.82/20.84 3690 -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(2223,d,2131,b)].
% 20.82/20.84 3691 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2224,c,2131,b)].
% 20.82/20.84 3692 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2225,c,2131,b)].
% 20.82/20.84 3693 -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(2226,d,2131,b)].
% 20.82/20.84 3694 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2227,c,2131,b)].
% 20.82/20.84 3695 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2228,c,2131,b)].
% 20.82/20.84 3696 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2229,c,2131,b)].
% 20.82/20.84 3697 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2230,c,2131,b)].
% 20.82/20.84 3698 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2231,c,2131,b)].
% 20.82/20.84 3699 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2232,c,2131,b)].
% 20.82/20.84 3700 -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(2233,d,2131,b)].
% 20.82/20.84 3701 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2234,c,2131,b)].
% 20.82/20.84 3702 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2235,c,2131,b)].
% 20.82/20.84 3703 -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(2236,d,2131,b)].
% 20.82/20.84 3704 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2237,c,2131,b)].
% 20.93/20.95 3705 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2238,c,2131,b)].
% 20.93/20.95 3706 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,c,2131,b)].
% 20.93/20.95 3707 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,c,2131,b)].
% 20.93/20.95 3708 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2241,d,2131,b)].
% 20.93/20.95 3709 -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(3139,a,3108,b)].
% 20.93/20.95 3710 -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(3140,a,3108,b)].
% 20.93/20.95 3711 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3141,a,3108,b)].
% 20.93/20.95 3712 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3142,a,3108,b)].
% 20.93/20.95 3713 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3143,a,3108,b)].
% 20.93/20.95 3714 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3108,b)].
% 20.93/20.95 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3714,b,3503,b)].
% 20.93/20.95 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3714,b,3504,b)].
% 20.93/20.95 3715 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3108,b)].
% 20.93/20.95 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(3715,b,3494,a)].
% 20.93/20.95 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3715,b,3503,b)].
% 20.93/20.95 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3715,b,3504,b)].
% 20.93/20.95 3716 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3152,b,3108,b)].
% 20.93/20.95 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3716,b,3494,a)].
% 20.93/20.95 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3716,b,3503,b)].
% 20.93/20.95 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3716,b,3504,b)].
% 20.93/20.95 3717 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3153,b,3108,b)].
% 20.93/20.95 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3717,b,3494,a)].
% 20.93/20.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3717,b,3503,b)].
% 20.93/20.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3717,b,3504,b)].
% 20.93/20.95 3718 -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(3161,a,3108,b)].
% 20.93/20.95 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(3718,c,3494,a)].
% 20.93/20.95 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(3718,c,3503,b)].
% 20.93/20.95 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(3718,c,3504,b)].
% 20.93/20.95 3719 -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(3162,a,3108,b)].
% 20.93/20.95 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(3719,c,3494,a)].
% 20.93/20.95 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(3719,c,3503,b)].
% 20.93/20.95 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(3719,c,3504,b)].
% 20.93/20.95 3720 -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(3163,a,3108,b)].
% 20.93/20.95 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(3720,c,3494,a)].
% 20.93/20.95 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(3720,c,3503,b)].
% 20.93/20.95 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(3720,c,3504,b)].
% 20.93/20.95 3721 -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(3164,a,3108,b)].
% 20.93/20.95 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(3721,c,3494,a)].
% 20.93/20.95 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(3721,c,3503,b)].
% 20.93/20.95 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(3721,c,3504,b)].
% 20.93/20.95 3722 -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(3165,a,3108,b)].
% 20.93/20.95 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(3722,c,3494,a)].
% 20.93/20.95 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(3722,c,3503,b)].
% 20.93/20.95 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(3722,c,3504,b)].
% 20.93/20.95 3723 -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(3166,a,3108,b)].
% 20.93/20.95 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(3723,c,3494,a)].
% 20.93/20.95 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(3723,c,3503,b)].
% 20.93/20.95 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(3723,c,3504,b)].
% 20.93/20.95 3724 -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(3167,a,3108,b)].
% 20.93/20.95 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(3724,c,3494,a)].
% 20.93/20.95 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(3724,c,3503,b)].
% 20.93/20.95 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(3724,c,3504,b)].
% 20.93/20.95 3725 -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(3168,a,3108,b)].
% 20.93/20.95 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(3725,c,3494,a)].
% 20.93/20.95 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(3725,c,3503,b)].
% 20.93/20.95 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(3725,c,3504,b)].
% 20.93/20.95 3726 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3203,a,3108,b)].
% 20.93/20.95 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3726,b,3494,a)].
% 20.93/20.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3726,b,3503,b)].
% 20.93/20.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3726,b,3504,b)].
% 20.93/20.95 3727 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3204,a,3108,b)].
% 20.93/20.95 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3727,b,3494,a)].
% 20.93/20.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3727,b,3503,b)].
% 20.93/20.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3727,b,3504,b)].
% 20.93/20.96 3728 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3205,e,3108,b)].
% 20.93/20.96 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3728,e,3494,a)].
% 20.93/20.96 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3728,e,3503,b)].
% 20.93/20.96 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3728,e,3504,b)].
% 20.93/20.96 3729 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3241,b,3108,b)].
% 20.93/20.96 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3729,b,3494,a)].
% 20.93/20.96 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3729,b,3503,b)].
% 20.93/20.96 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3729,b,3504,b)].
% 20.93/20.96 3730 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3242,b,3108,b)].
% 20.93/20.96 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3730,b,3494,a)].
% 20.93/20.96 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3730,b,3503,b)].
% 20.93/20.96 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3504,b)].
% 20.93/20.96 3731 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3243,b,3108,b)].
% 20.93/20.96 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3731,b,3494,a)].
% 20.93/20.96 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3731,b,3503,b)].
% 20.93/20.96 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3731,b,3504,b)].
% 20.93/20.96 3732 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3244,b,3108,b)].
% 20.93/20.96 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3732,b,3494,a)].
% 20.93/20.96 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3732,b,3503,b)].
% 20.93/20.96 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3732,b,3504,b)].
% 20.93/20.96 3733 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(3245,b,3108,b)].
% 20.93/20.96 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3733,b,3494,a)].
% 20.93/20.96 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3733,b,3503,b)].
% 20.93/20.96 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3733,b,3504,b)].
% 20.93/20.96 3734 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3246,b,3108,b)].
% 20.93/20.96 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3734,b,3494,a)].
% 20.93/20.96 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3734,b,3503,b)].
% 20.93/20.96 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3734,b,3504,b)].
% 20.93/20.96 3735 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3299,a,3255,b)].
% 21.58/21.58 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3735,b,3494,a)].
% 21.58/21.58 3736 -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].
% 21.58/21.58 3737 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom). [assumption].
% 21.58/21.58 3738 -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].
% 21.58/21.58 3739 -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].
% 21.58/21.58 3740 -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].
% 21.58/21.58 3741 -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].
% 21.58/21.58 3742 -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].
% 21.58/21.58 3743 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1329,a,1277,a)].
% 21.58/21.58 3744 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1329,a,1303,b)].
% 21.58/21.58 3745 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1329,a,1304,b)].
% 21.58/21.58 3746 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 21.58/21.58 3747 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 21.58/21.58 3748 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 21.58/21.58 Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A). [resolve(3746,a,3748,b)].
% 21.58/21.58 3749 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 21.58/21.58 3750 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 21.58/21.58 3751 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom). [assumption].
% 21.58/21.58 3752 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 21.58/21.58 3753 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom). [assumption].
% 21.58/21.58 3754 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 21.58/21.58 3755 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom). [assumption].
% 21.58/21.58 3756 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 21.58/21.58 3757 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom). [assumption].
% 21.58/21.58 3758 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 21.58/21.58 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3758,a,3748,b)].
% 21.58/21.58 3759 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 21.58/21.58 3760 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 21.58/21.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A). [resolve(3760,b,3746,a)].
% 21.58/21.60 3761 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 21.58/21.60 3762 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 21.58/21.60 3763 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 21.58/21.60 3764 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 21.58/21.60 3765 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(124,b,108,a)].
% 21.58/21.60 3766 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(124,b,111,a)].
% 21.58/21.60 3767 -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)].
% 21.58/21.60 3768 -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)].
% 21.58/21.61 3769 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(165,a,146,b)].
% 21.58/21.61 3770 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(166,a,146,b)].
% 21.58/21.61 3771 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(171,a,146,b)].
% 21.58/21.61 3772 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(172,a,146,b)].
% 21.58/21.61 3773 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(201,b,190,b)].
% 21.58/21.61 3774 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(202,b,190,b)].
% 21.58/21.61 3775 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 21.58/21.61 3776 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 21.58/21.61 3777 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(247,b,220,b)].
% 21.58/21.61 3778 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(248,b,220,b)].
% 21.58/21.61 3779 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,288,a)].
% 21.58/21.61 3780 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,290,a)].
% 21.58/21.61 3781 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(322,a,300,b)].
% 21.58/21.61 3782 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(323,a,300,b)].
% 21.58/21.61 3783 -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(342,b,331,b)].
% 21.58/21.61 3784 -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(342,b,333,b)].
% 21.58/21.61 3785 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(342,b,334,a)].
% 21.58/21.61 3786 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,335,a)].
% 21.58/21.61 3787 -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,336,a)].
% 21.58/21.61 3788 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,a,342,b)].
% 21.58/21.61 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3788,b,3748,b)].
% 21.58/21.61 3789 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(355,a,342,b)].
% 21.58/21.61 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3789,b,3748,b)].
% 21.58/21.61 3790 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(366,b,342,b)].
% 21.58/21.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3790,b,3748,b)].
% 21.58/21.63 3791 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(367,b,342,b)].
% 21.58/21.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3748,b)].
% 21.58/21.63 3792 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(370,b,342,b)].
% 21.58/21.63 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3792,b,3748,b)].
% 21.58/21.63 3793 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(371,b,342,b)].
% 21.58/21.63 3794 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(372,b,342,b)].
% 21.58/21.63 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(3794,b,3748,b)].
% 21.58/21.63 3795 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(373,b,342,b)].
% 21.58/21.63 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3795,b,3748,b)].
% 21.58/21.63 3796 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(374,a,342,b)].
% 21.58/21.63 3797 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(375,a,342,b)].
% 21.58/21.63 3798 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(376,c,342,b)].
% 21.58/21.63 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3798,c,3748,b)].
% 21.58/21.63 3799 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(377,c,342,b)].
% 21.58/21.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3799,c,3748,b)].
% 21.58/21.63 3800 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(479,b,435,b)].
% 21.58/21.63 3801 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(480,b,435,b)].
% 21.58/21.63 3802 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(517,a,511,b)].
% 21.58/21.63 3803 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(524,a,511,b)].
% 21.58/21.63 3804 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(525,a,511,b)].
% 21.58/21.63 3805 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(571,b,549,b)].
% 21.58/21.63 3806 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(572,b,549,b)].
% 21.58/21.63 3807 -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(654,a,618,b)].
% 21.58/21.63 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(3807,c,3748,b)].
% 21.58/21.63 3808 -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(655,a,618,b)].
% 21.58/21.63 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(3808,c,3748,b)].
% 21.58/21.63 3809 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(656,a,618,b)].
% 21.58/21.63 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3809,b,3748,b)].
% 21.58/21.63 3810 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(657,a,618,b)].
% 21.58/21.63 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3810,b,3748,b)].
% 21.58/21.63 3811 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(658,a,618,b)].
% 21.58/21.63 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3811,b,3748,b)].
% 21.58/21.63 3812 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(659,b,618,b)].
% 21.58/21.63 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(3812,b,3748,b)].
% 23.53/23.60 3813 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(660,b,618,b)].
% 23.53/23.60 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3813,b,3748,b)].
% 23.53/23.60 3814 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(661,b,618,b)].
% 23.53/23.60 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3814,b,3748,b)].
% 23.53/23.60 3815 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(663,b,618,b)].
% 23.53/23.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3815,b,3748,b)].
% 23.53/23.60 3816 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(664,b,618,b)].
% 23.53/23.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3816,b,3748,b)].
% 23.53/23.60 3817 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(666,b,618,b)].
% 23.53/23.60 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3817,b,3748,b)].
% 23.53/23.60 3818 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(667,b,618,b)].
% 23.53/23.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(3818,b,3748,b)].
% 23.53/23.60 3819 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(694,b,668,a)].
% 23.53/23.60 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3819,a,3748,b)].
% 23.53/23.60 3820 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(694,b,670,a)].
% 23.53/23.60 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3820,a,3748,b)].
% 23.53/23.60 3821 -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(694,b,671,a)].
% 23.53/23.60 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(3821,a,3748,b)].
% 23.53/23.60 3822 -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(694,b,672,a)].
% 23.53/23.60 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(3822,a,3748,b)].
% 23.53/23.60 3823 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(694,b,673,a)].
% 23.53/23.60 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3823,a,3748,b)].
% 23.53/23.60 3824 -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(694,b,674,a)].
% 23.53/23.60 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(3824,a,3748,b)].
% 23.53/23.60 3825 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(694,b,675,a)].
% 23.53/23.60 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3825,a,3748,b)].
% 23.53/23.60 3826 -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(694,b,676,a)].
% 23.53/23.60 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(3826,a,3748,b)].
% 23.53/23.60 3827 -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(694,b,677,a)].
% 23.53/23.60 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(3827,a,3748,b)].
% 23.53/23.60 3828 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(694,b,678,a)].
% 23.53/23.60 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3828,a,3748,b)].
% 23.53/23.60 3829 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(826,a,734,a)].
% 23.53/23.60 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3829,a,3748,b)].
% 23.53/23.60 3830 -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(903,b,832,a)].
% 23.53/23.60 3831 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 23.53/23.60 3832 -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(903,b,833,a)].
% 23.53/23.60 3833 -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(903,b,834,a)].
% 23.53/23.60 3834 -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(903,b,835,a)].
% 23.53/23.60 3835 -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(903,b,836,a)].
% 23.53/23.60 3836 -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(903,b,837,a)].
% 23.53/23.60 3837 -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(903,b,838,a)].
% 23.53/23.60 3838 -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(903,b,839,a)].
% 23.53/23.60 3839 -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(903,b,840,a)].
% 23.53/23.60 3840 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,841,a)].
% 23.53/23.60 3841 -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(903,b,842,a)].
% 23.53/23.60 3842 -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(903,b,843,a)].
% 23.53/23.60 3843 -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(903,b,844,a)].
% 23.53/23.60 3844 -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(903,b,845,a)].
% 23.53/23.60 3845 -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(903,b,846,a)].
% 23.53/23.60 3846 -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(903,b,847,a)].
% 23.53/23.60 3847 -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(903,b,848,a)].
% 23.53/23.60 3848 -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(903,b,849,a)].
% 23.53/23.60 3849 -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(903,b,850,a)].
% 23.53/23.60 3850 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,851,a)].
% 23.53/23.61 3851 -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(903,b,852,a)].
% 23.53/23.61 3852 -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(903,b,853,a)].
% 23.53/23.61 3853 -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(903,b,854,a)].
% 23.53/23.61 3854 -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(903,b,855,b)].
% 23.53/23.61 3855 -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(903,b,856,b)].
% 23.53/23.61 3856 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(903,b,857,a)].
% 23.53/23.61 3857 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(903,b,858,a)].
% 23.53/23.61 3858 -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(903,b,859,a)].
% 23.53/23.61 3859 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(903,b,860,a)].
% 23.53/23.61 3860 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(903,b,861,a)].
% 23.53/23.61 3861 -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(903,b,862,a)].
% 23.53/23.61 3862 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(903,b,863,a)].
% 23.53/23.61 3863 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(903,b,864,a)].
% 23.53/23.61 3864 -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(903,b,865,a)].
% 23.53/23.61 3865 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(903,b,866,a)].
% 23.53/23.61 3866 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(903,b,867,a)].
% 23.53/23.61 3867 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(903,b,868,a)].
% 23.53/23.61 3868 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(903,b,869,a)].
% 23.53/23.61 3869 -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(903,b,870,a)].
% 23.53/23.61 3870 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(903,b,871,a)].
% 23.53/23.61 3871 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(903,b,872,a)].
% 23.53/23.61 3872 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(903,b,873,a)].
% 23.53/23.61 3873 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(903,b,874,a)].
% 23.53/23.61 3874 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(903,b,875,a)].
% 23.53/23.61 3875 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(903,b,876,a)].
% 23.53/23.61 3876 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(903,b,877,a)].
% 23.53/23.61 3877 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(903,b,878,a)].
% 23.70/23.70 3878 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(903,b,879,a)].
% 23.70/23.70 3879 -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(903,b,880,a)].
% 23.70/23.70 3880 -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(903,b,881,a)].
% 23.70/23.70 3881 -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(903,b,882,a)].
% 23.70/23.70 3882 -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(903,b,883,a)].
% 23.70/23.70 3883 -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(903,b,884,a)].
% 23.70/23.70 3884 -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(903,b,885,a)].
% 23.70/23.70 3885 -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(903,b,886,a)].
% 23.70/23.70 3886 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(903,b,887,a)].
% 23.70/23.70 3887 -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(903,b,888,a)].
% 23.70/23.70 3888 -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(903,b,889,a)].
% 23.70/23.70 3889 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(904,a,903,b)].
% 23.70/23.70 3890 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(905,a,903,b)].
% 23.70/23.70 3891 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1093,b,1076,a)].
% 23.70/23.70 3892 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1116,b,1099,a)].
% 23.70/23.70 3893 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1613,b,1581,a)].
% 23.70/23.70 3894 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1582,a)].
% 23.70/23.70 3895 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1613,b,1583,a)].
% 23.70/23.70 3896 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1613,b,1584,a)].
% 23.70/23.70 3897 -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(1613,b,1585,a)].
% 23.70/23.70 3898 -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(1613,b,1586,a)].
% 23.70/23.70 3899 -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(1613,b,1587,a)].
% 23.70/23.70 3900 -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(1613,b,1588,a)].
% 23.70/23.70 3901 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1589,a)].
% 23.70/23.70 3902 -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(1613,b,1590,a)].
% 25.70/25.70 3903 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1613,b,1591,a)].
% 25.70/25.70 3904 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1614,a,1613,b)].
% 25.70/25.70 3905 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1615,a,1613,b)].
% 25.70/25.70 3906 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1637,a)].
% 25.70/25.70 3907 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1638,a)].
% 25.70/25.70 3908 -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(1678,b,1639,a)].
% 25.70/25.70 3909 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1640,a)].
% 25.70/25.70 3910 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1641,a)].
% 25.70/25.70 3911 -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(1678,b,1642,a)].
% 25.70/25.70 3912 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1643,a)].
% 25.70/25.70 3913 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1678,b,1644,a)].
% 25.70/25.70 3914 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1678,b,1645,a)].
% 25.70/25.70 3915 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1678,b,1646,a)].
% 25.70/25.70 3916 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1647,a)].
% 25.70/25.70 3917 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1648,a)].
% 25.70/25.70 3918 -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(1678,b,1649,a)].
% 25.70/25.70 3919 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1650,a)].
% 25.70/25.70 3920 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1651,a)].
% 25.70/25.70 3921 -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(1678,b,1652,a)].
% 25.70/25.70 3922 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1678,b,1653,a)].
% 25.70/25.70 3923 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1678,b,1654,a)].
% 25.70/25.70 3924 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1678,b,1655,a)].
% 25.70/25.70 3925 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1678,b,1656,a)].
% 25.70/25.70
% 25.70/25.70 ============================== end predicate elimination =============
% 25.70/25.70
% 25.70/25.70 Auto_denials: (non-Horn, no changes).
% 25.70/25.70
% 25.70/25.70 Term ordering decisions:
% 25.70/25.70 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. t_b=1. tc_List_Onibble=1. c_Relation_OId=1. c_IntDef_OInts=1. v_xa=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. v_c=1. v_ca=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_HOL_Oabs=1. c_Numeral_OBit=1. tc_Datatype__Universe_Onode=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. v_a=1. v_b=1. v_f=1. v_g=1. c_IntDef_ORep__Integ=1. c_times=1. c_plus=1. c_SetInterval_OatLeastLessThan=1. c_minus=1. c_insert=1. c_Orderings_Omax=1. c_divide=1. c_Orderings_Omin=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=Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------