TSTP Solution File: ANA031-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA031-1 : 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 19:21:48 EDT 2022
% Result : Timeout 300.06s 300.07s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA031-1 : 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 04:23:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.43/1.96 ============================== Prover9 ===============================
% 1.43/1.96 Prover9 (32) version 2009-11A, November 2009.
% 1.43/1.96 Process 27651 was started by sandbox on n004.cluster.edu,
% 1.43/1.96 Fri Jul 8 04:23:09 2022
% 1.43/1.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27498_n004.cluster.edu".
% 1.43/1.96 ============================== end of head ===========================
% 1.43/1.96
% 1.43/1.96 ============================== INPUT =================================
% 1.43/1.96
% 1.43/1.96 % Reading from file /tmp/Prover9_27498_n004.cluster.edu
% 1.43/1.96
% 1.43/1.96 set(prolog_style_variables).
% 1.43/1.96 set(auto2).
% 1.43/1.96 % set(auto2) -> set(auto).
% 1.43/1.96 % set(auto) -> set(auto_inference).
% 1.43/1.96 % set(auto) -> set(auto_setup).
% 1.43/1.96 % set(auto_setup) -> set(predicate_elim).
% 1.43/1.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.43/1.96 % set(auto) -> set(auto_limits).
% 1.43/1.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.43/1.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.43/1.96 % set(auto) -> set(auto_denials).
% 1.43/1.96 % set(auto) -> set(auto_process).
% 1.43/1.96 % set(auto2) -> assign(new_constants, 1).
% 1.43/1.96 % set(auto2) -> assign(fold_denial_max, 3).
% 1.43/1.96 % set(auto2) -> assign(max_weight, "200.000").
% 1.43/1.96 % set(auto2) -> assign(max_hours, 1).
% 1.43/1.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.43/1.96 % set(auto2) -> assign(max_seconds, 0).
% 1.43/1.96 % set(auto2) -> assign(max_minutes, 5).
% 1.43/1.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.43/1.96 % set(auto2) -> set(sort_initial_sos).
% 1.43/1.96 % set(auto2) -> assign(sos_limit, -1).
% 1.43/1.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.43/1.96 % set(auto2) -> assign(max_megs, 400).
% 1.43/1.96 % set(auto2) -> assign(stats, some).
% 1.43/1.96 % set(auto2) -> clear(echo_input).
% 1.43/1.96 % set(auto2) -> set(quiet).
% 1.43/1.96 % set(auto2) -> clear(print_initial_clauses).
% 1.43/1.96 % set(auto2) -> clear(print_given).
% 1.43/1.96 assign(lrs_ticks,-1).
% 1.43/1.96 assign(sos_limit,10000).
% 1.43/1.96 assign(order,kbo).
% 1.43/1.96 set(lex_order_vars).
% 1.43/1.96 clear(print_given).
% 1.43/1.96
% 1.43/1.96 % formulas(sos). % not echoed (2789 formulas)
% 1.43/1.96
% 1.43/1.96 ============================== end of input ==========================
% 1.43/1.96
% 1.43/1.96 % From the command line: assign(max_seconds, 300).
% 1.43/1.96
% 1.43/1.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.43/1.96
% 1.43/1.96 % Formulas that are not ordinary clauses:
% 1.43/1.96
% 1.43/1.96 ============================== end of process non-clausal formulas ===
% 1.43/1.96
% 1.43/1.96 ============================== PROCESS INITIAL CLAUSES ===============
% 1.43/1.96
% 1.43/1.96 ============================== PREDICATE ELIMINATION =================
% 1.43/1.96 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].
% 1.43/1.96 2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom). [assumption].
% 1.43/1.96 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)].
% 1.43/1.96 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].
% 1.43/1.96 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)].
% 1.43/1.96 4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 1.43/1.96 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4,a,1,a)].
% 1.43/1.96 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4,a,3,a)].
% 1.43/1.96 5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 1.43/1.96 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(5,a,1,a)].
% 1.43/1.96 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(5,a,3,a)].
% 1.43/1.96 6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 1.43/1.96 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 1.43/1.96 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 1.43/1.96 7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 1.43/1.98 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(7,b,1,a)].
% 1.43/1.98 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(7,b,3,a)].
% 1.43/1.98 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].
% 1.43/1.98 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)].
% 1.43/1.98 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)].
% 1.43/1.98 9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(9,a,2,a)].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(9,a,4,a)].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(9,a,5,a)].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(9,a,7,b)].
% 1.43/1.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 1.43/1.98 10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 1.43/1.98 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(10,a,2,a)].
% 1.43/1.98 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(10,a,4,a)].
% 1.43/1.98 Derived: class_HOL_Oplus(tc_nat). [resolve(10,a,5,a)].
% 1.43/1.98 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 1.43/1.98 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(10,a,7,b)].
% 1.43/1.98 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 1.43/1.98 11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 1.43/1.98 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 1.43/1.98 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 1.43/1.98 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].
% 1.43/1.98 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)].
% 1.43/1.98 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)].
% 1.43/1.98 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].
% 1.43/1.98 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)].
% 1.43/1.98 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)].
% 1.43/1.98 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].
% 1.43/1.98 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)].
% 1.43/1.98 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)].
% 1.43/1.98 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 1.43/2.00 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 1.43/2.00 19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 1.43/2.00 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(19,b,1,a)].
% 1.43/2.00 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(19,b,3,a)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.00 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 1.43/2.00 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].
% 1.43/2.00 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)].
% 1.43/2.00 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)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 1.43/2.06 24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 1.43/2.06 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(24,b,1,a)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(24,b,3,a)].
% 1.43/2.06 25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 1.43/2.06 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 1.43/2.06 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 1.43/2.06 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].
% 1.43/2.06 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)].
% 1.43/2.06 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)].
% 1.43/2.06 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 1.43/2.09 37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 1.43/2.09 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 1.43/2.09 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 1.43/2.09 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].
% 1.43/2.09 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)].
% 1.43/2.09 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)].
% 1.43/2.09 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].
% 1.94/2.22 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)].
% 1.94/2.22 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)].
% 1.94/2.22 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].
% 1.94/2.22 42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom). [assumption].
% 1.94/2.22 43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 1.94/2.22 44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 1.94/2.22 45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 1.94/2.22 46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 1.94/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 1.94/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 1.94/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 1.94/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 1.94/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 1.94/2.22 47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 1.94/2.22 48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 1.94/2.22 49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 1.94/2.22 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].
% 1.94/2.22 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 1.94/2.22 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 1.94/2.22 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 1.94/2.22 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].
% 1.94/2.22 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].
% 1.94/2.22 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].
% 1.94/2.22 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].
% 1.94/2.22 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].
% 1.94/2.22 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].
% 2.02/2.26 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 2.02/2.26 57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 2.02/2.26 62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 2.02/2.26 63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 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].
% 2.02/2.26 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 2.02/2.26 75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 2.02/2.27 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 2.02/2.27 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].
% 2.02/2.27 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 2.02/2.27 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].
% 2.02/2.27 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 2.02/2.27 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 2.02/2.27 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 2.02/2.27 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].
% 2.02/2.27 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)].
% 2.02/2.27 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)].
% 2.02/2.27 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(79,a,43,a)].
% 2.02/2.27 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(79,a,44,a)].
% 2.02/2.27 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 2.02/2.27 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(79,a,46,b)].
% 2.02/2.27 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)].
% 2.02/2.27 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)].
% 2.02/2.27 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(80,a,43,a)].
% 2.02/2.27 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(80,a,44,a)].
% 2.02/2.27 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 2.02/2.27 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(80,a,46,b)].
% 2.02/2.27 81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(81,b,42,a)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(81,b,43,a)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(81,b,44,a)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(81,b,46,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(81,b,54,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(81,b,57,b)].
% 2.02/2.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(81,b,59,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(81,b,62,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(81,b,66,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(81,b,67,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(81,b,73,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 2.18/2.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 2.18/2.42 82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(82,b,42,a)].
% 2.18/2.42 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(82,b,43,a)].
% 2.18/2.42 Derived: class_HOL_Oplus(tc_nat). [resolve(82,b,44,a)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(82,b,46,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(82,b,54,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(82,b,57,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(82,b,59,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(82,b,62,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(82,b,66,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(82,b,67,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(82,b,73,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 2.18/2.42 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 2.18/2.42 83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom). [assumption].
% 2.22/2.44 84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom). [assumption].
% 2.22/2.44 85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom). [assumption].
% 2.22/2.44 86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom). [assumption].
% 2.22/2.44 87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom). [assumption].
% 2.22/2.44 88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 2.22/2.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(83,a,84,a)].
% 2.22/2.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(83,a,85,a)].
% 2.22/2.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(83,a,86,a)].
% 2.22/2.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(83,a,87,a)].
% 2.22/2.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 2.22/2.44 89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom). [assumption].
% 2.22/2.44 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(89,a,84,a)].
% 2.22/2.44 Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(89,a,85,a)].
% 2.22/2.44 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(89,a,86,a)].
% 2.22/2.44 Derived: class_HOL_Otimes(tc_nat). [resolve(89,a,87,a)].
% 2.22/2.44 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 2.22/2.44 90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 2.22/2.44 91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom). [assumption].
% 2.22/2.44 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(91,b,83,a)].
% 2.22/2.44 Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A). [resolve(91,b,89,a)].
% 2.22/2.44 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].
% 2.22/2.44 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].
% 2.22/2.44 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(93,b,83,a)].
% 2.22/2.44 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A). [resolve(93,b,89,a)].
% 2.22/2.44 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].
% 2.22/2.44 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].
% 2.22/2.44 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].
% 2.22/2.44 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].
% 2.22/2.44 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].
% 2.22/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 2.22/2.44 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 2.22/2.44 99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom). [assumption].
% 2.22/2.50 100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 2.22/2.50 101 -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].
% 2.22/2.50 102 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_20) # label(axiom). [assumption].
% 2.22/2.50 103 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 2.22/2.50 104 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 2.22/2.50 105 -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].
% 2.22/2.50 106 -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].
% 2.22/2.50 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(106,b,83,a)].
% 2.22/2.50 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A). [resolve(106,b,89,a)].
% 2.22/2.50 107 -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].
% 2.22/2.50 108 -class_OrderedGroup_Oab__semigroup__mult(A) | c_times(B,C,A) = c_times(C,B,A) # label(cls_OrderedGroup_Omult__ac__2_0) # label(axiom). [assumption].
% 2.22/2.50 Derived: c_times(A,B,tc_fun(C,D)) = c_times(B,A,tc_fun(C,D)) | -class_OrderedGroup_Ocomm__monoid__mult(D). [resolve(108,a,84,a)].
% 2.22/2.50 Derived: c_times(A,B,tc_set(C)) = c_times(B,A,tc_set(C)) | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(108,a,85,a)].
% 2.22/2.50 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(108,a,86,a)].
% 2.22/2.50 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(108,a,87,a)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(108,a,88,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(108,a,90,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Power_Orecpower(C). [resolve(108,a,91,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(108,a,92,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(108,a,93,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(108,a,94,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(108,a,95,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(108,a,96,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(108,a,97,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(108,a,98,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(108,a,99,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(108,a,100,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(108,a,101,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(108,a,102,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(108,a,103,b)].
% 2.22/2.50 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(108,a,104,b)].
% 2.32/2.59 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(108,a,105,b)].
% 2.32/2.59 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(108,a,106,b)].
% 2.32/2.59 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(108,a,107,b)].
% 2.32/2.59 109 -class_OrderedGroup_Oab__semigroup__mult(A) | c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A) # label(cls_OrderedGroup_Omult__ac__3_0) # label(axiom). [assumption].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_times(B,c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_OrderedGroup_Ocomm__monoid__mult(E). [resolve(109,a,84,a)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,tc_set(D)),tc_set(D)) = c_times(B,c_times(A,C,tc_set(D)),tc_set(D)) | -class_OrderedGroup_Ocomm__monoid__mult(D). [resolve(109,a,85,a)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(109,a,86,a)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(109,a,87,a)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(109,a,88,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_OrderedGroup_Ocomm__monoid__mult(D). [resolve(109,a,90,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(109,a,91,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(109,a,92,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(109,a,93,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(109,a,94,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(109,a,95,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(109,a,96,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(109,a,97,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(109,a,98,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(109,a,99,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(109,a,100,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(109,a,101,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(109,a,102,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(109,a,103,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(109,a,104,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(109,a,105,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(109,a,106,b)].
% 2.32/2.59 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(109,a,107,b)].
% 2.32/2.59 110 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 2.32/2.59 111 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom). [assumption].
% 2.37/2.65 112 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom). [assumption].
% 2.37/2.65 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(110,a,111,a)].
% 2.37/2.65 Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(110,a,112,a)].
% 2.37/2.65 113 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 2.37/2.65 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(113,a,111,a)].
% 2.37/2.65 Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(113,a,112,a)].
% 2.37/2.65 114 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 2.37/2.65 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(114,a,110,a)].
% 2.37/2.65 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(114,a,113,a)].
% 2.37/2.65 115 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 2.37/2.65 Derived: c_times(c_1,A,tc_nat) = A. [resolve(115,a,110,a)].
% 2.37/2.65 Derived: c_times(A,c_1,tc_nat) = A. [resolve(115,a,113,a)].
% 2.37/2.65 116 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.37/2.65 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(116,b,110,a)].
% 2.37/2.65 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(116,b,113,a)].
% 2.37/2.65 117 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 2.37/2.65 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(117,b,110,a)].
% 2.37/2.65 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(117,b,113,a)].
% 2.37/2.65 118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.37/2.65 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(118,a,111,a)].
% 2.37/2.65 Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,112,a)].
% 2.37/2.65 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(118,a,114,a)].
% 2.37/2.65 Derived: class_HOL_Oone(tc_nat). [resolve(118,a,115,a)].
% 2.37/2.65 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(118,a,116,b)].
% 2.37/2.65 Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,117,b)].
% 2.37/2.65 119 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 2.37/2.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(119,a,117,b)].
% 2.37/2.65 120 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 2.37/2.65 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(120,a,117,b)].
% 2.37/2.65 121 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 2.37/2.65 Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B. [resolve(121,b,110,a)].
% 2.37/2.65 Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B. [resolve(121,b,113,a)].
% 2.37/2.65 122 -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].
% 2.37/2.65 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B. [resolve(122,b,110,a)].
% 2.37/2.65 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B. [resolve(122,b,113,a)].
% 2.37/2.65 123 -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].
% 2.37/2.65 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(123,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(123,b,113,a)].
% 2.54/2.77 124 -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].
% 2.54/2.77 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(124,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(124,b,113,a)].
% 2.54/2.77 125 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 2.54/2.77 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B. [resolve(125,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B. [resolve(125,b,113,a)].
% 2.54/2.77 126 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(126,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(126,b,113,a)].
% 2.54/2.77 127 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B. [resolve(127,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B. [resolve(127,b,113,a)].
% 2.54/2.77 128 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B. [resolve(128,b,110,a)].
% 2.54/2.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B. [resolve(128,b,113,a)].
% 2.54/2.77 129 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(129,b,110,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(129,b,113,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(129,b,119,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(129,b,120,a)].
% 2.54/2.78 130 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(130,b,110,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(130,b,113,a)].
% 2.54/2.78 131 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(131,b,110,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(131,b,113,a)].
% 2.54/2.78 132 -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].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(132,b,110,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(132,b,113,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(132,b,118,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(132,b,119,a)].
% 2.54/2.78 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(132,b,120,a)].
% 2.54/2.78 133 -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].
% 2.54/2.85 134 class_Ring__and__Field_Osemiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_17) # label(axiom). [assumption].
% 2.54/2.85 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(133,b,134,a)].
% 2.54/2.85 135 -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].
% 2.54/2.85 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(135,b,134,a)].
% 2.54/2.85 136 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.54/2.85 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(136,a,133,b)].
% 2.54/2.85 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(136,a,135,b)].
% 2.54/2.85 137 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.54/2.85 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(137,a,133,b)].
% 2.54/2.85 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(137,a,135,b)].
% 2.54/2.85 138 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.54/2.85 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(138,b,133,b)].
% 2.54/2.85 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(138,b,135,b)].
% 2.54/2.85 139 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.54/2.85 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(139,b,133,b)].
% 2.54/2.85 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(139,b,135,b)].
% 2.54/2.85 140 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 2.54/2.85 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(140,b,133,b)].
% 2.63/2.86 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(140,b,135,b)].
% 2.63/2.86 141 -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].
% 2.63/2.86 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(141,b,133,b)].
% 2.63/2.86 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(141,b,135,b)].
% 2.63/2.86 142 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 2.63/2.86 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(142,b,133,b)].
% 2.63/2.86 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(142,b,135,b)].
% 2.63/2.86 143 -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].
% 2.63/2.86 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(143,b,133,b)].
% 2.63/2.86 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(143,b,135,b)].
% 2.63/2.86 144 -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].
% 2.63/2.86 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(144,b,133,b)].
% 2.63/2.86 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(144,b,135,b)].
% 2.63/2.86 145 -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].
% 2.63/2.86 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(145,b,133,b)].
% 2.63/2.86 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(145,b,135,b)].
% 2.63/2.86 146 -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].
% 2.63/2.86 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(146,b,133,b)].
% 2.63/2.88 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(146,b,135,b)].
% 2.63/2.88 147 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.63/2.88 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(147,b,133,b)].
% 2.63/2.88 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(147,b,135,b)].
% 2.63/2.88 148 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.63/2.88 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(148,b,133,b)].
% 2.63/2.88 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(148,b,135,b)].
% 2.63/2.88 149 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 2.63/2.88 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(149,b,133,b)].
% 2.63/2.88 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(149,b,135,b)].
% 2.63/2.88 150 -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].
% 2.63/2.88 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(150,b,133,b)].
% 2.63/2.88 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(150,b,135,b)].
% 2.63/2.88 151 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 2.63/2.88 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(151,b,133,b)].
% 2.63/2.88 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(151,b,135,b)].
% 2.63/2.88 152 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 2.63/2.88 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(152,b,133,b)].
% 2.67/2.89 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(152,b,135,b)].
% 2.67/2.89 153 -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].
% 2.67/2.89 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(153,b,133,b)].
% 2.67/2.89 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(153,b,135,b)].
% 2.67/2.89 154 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 2.67/2.89 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(154,b,133,b)].
% 2.67/2.89 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(154,b,135,b)].
% 2.67/2.89 155 -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].
% 2.67/2.89 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(155,b,133,b)].
% 2.67/2.89 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(155,b,135,b)].
% 2.67/2.89 156 -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].
% 2.67/2.89 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(156,b,133,b)].
% 2.67/2.89 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(156,b,135,b)].
% 2.67/2.90 157 -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].
% 2.67/2.90 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(157,b,133,b)].
% 2.67/2.90 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(157,b,135,b)].
% 2.67/2.90 158 -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].
% 2.67/2.91 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(158,b,133,b)].
% 2.67/2.91 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(158,b,135,b)].
% 2.67/2.91 159 -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].
% 2.67/2.91 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(159,b,133,b)].
% 2.67/2.91 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(159,b,135,b)].
% 2.67/2.91 160 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 2.67/2.91 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(160,b,133,b)].
% 2.67/2.91 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(160,b,135,b)].
% 2.67/2.91 161 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 2.67/2.91 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(161,b,133,b)].
% 2.67/2.91 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(161,b,135,b)].
% 2.67/2.91 162 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.67/2.91 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(162,b,133,b)].
% 2.67/2.91 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(162,b,135,b)].
% 2.67/2.91 163 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 2.67/2.91 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(163,b,133,b)].
% 2.67/2.91 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(163,b,135,b)].
% 2.67/2.91 164 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,134,a)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(164,a,139,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(164,a,140,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(164,a,141,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,142,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,143,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(164,a,144,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,145,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(164,a,147,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(164,a,148,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(164,a,149,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(164,a,150,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(164,a,151,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(164,a,152,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(164,a,154,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(164,a,155,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(164,a,157,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(164,a,158,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,159,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,161,b)].
% 2.67/2.91 165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(165,a,134,a)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,142,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,143,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,145,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,159,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,161,b)].
% 2.67/2.91 166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.67/2.91 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(166,a,134,a)].
% 2.67/2.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,142,b)].
% 2.67/2.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,143,b)].
% 2.67/2.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,145,b)].
% 2.67/2.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,159,b)].
% 2.67/2.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,161,b)].
% 2.67/2.91 167 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(167,a,134,a)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(167,a,140,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(167,a,142,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(167,a,143,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(167,a,144,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(167,a,145,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(167,a,147,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(167,a,148,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(167,a,149,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(167,a,150,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(167,a,151,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(167,a,152,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(167,a,153,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(167,a,155,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(167,a,156,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(167,a,157,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(167,a,159,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(167,a,160,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(167,a,161,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(167,a,162,b)].
% 2.67/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(167,a,163,b)].
% 2.67/2.91 168 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.67/2.91 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(168,a,134,a)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(168,a,140,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(168,a,142,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(168,a,143,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(168,a,144,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(168,a,145,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(168,a,147,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(168,a,148,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(168,a,149,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(168,a,150,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(168,a,151,b)].
% 2.67/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(168,a,152,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(168,a,153,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(168,a,155,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(168,a,156,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(168,a,157,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(168,a,159,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(168,a,160,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(168,a,161,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(168,a,162,b)].
% 2.85/3.09 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(168,a,163,b)].
% 2.85/3.09 169 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.85/3.09 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(169,b,133,b)].
% 2.85/3.09 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(169,b,135,b)].
% 2.85/3.09 170 -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].
% 2.85/3.09 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(170,b,133,b)].
% 2.85/3.09 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(170,b,135,b)].
% 2.85/3.09 171 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.85/3.09 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(171,b,133,b)].
% 2.85/3.09 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(171,b,135,b)].
% 2.85/3.09 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(171,b,166,a)].
% 2.85/3.09 172 -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].
% 2.85/3.09 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(172,b,133,b)].
% 2.85/3.09 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(172,b,135,b)].
% 2.85/3.09 173 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.85/3.09 174 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].
% 2.85/3.09 175 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.85/3.15 176 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.85/3.15 177 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.85/3.15 178 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.85/3.15 179 -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].
% 2.85/3.15 180 -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].
% 2.85/3.15 181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.85/3.15 182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.85/3.15 183 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.85/3.15 184 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.85/3.15 185 -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].
% 2.85/3.15 186 -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].
% 2.85/3.15 187 -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].
% 2.85/3.15 188 -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].
% 2.85/3.15 189 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.85/3.15 190 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.85/3.15 191 -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].
% 2.85/3.15 192 -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].
% 2.85/3.15 193 -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].
% 2.85/3.15 194 -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].
% 2.85/3.15 195 -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].
% 2.85/3.15 196 -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].
% 2.85/3.15 197 -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].
% 2.85/3.15 198 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(108,a,94,b)].
% 2.85/3.15 Derived: c_times(A,B,tc_fun(C,D)) = c_times(B,A,tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(198,b,174,a)].
% 2.85/3.15 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(198,b,175,a)].
% 2.94/3.16 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(198,b,176,a)].
% 2.94/3.16 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(198,b,177,b)].
% 2.94/3.16 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Power_Orecpower(C). [resolve(198,b,178,b)].
% 2.94/3.16 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(198,b,179,b)].
% 2.94/3.16 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(198,b,180,b)].
% 2.94/3.16 199 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(109,a,94,b)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_times(B,c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(199,b,174,a)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(199,b,175,a)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(199,b,176,a)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(199,b,177,b)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(199,b,178,b)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(199,b,179,b)].
% 2.94/3.16 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(199,b,180,b)].
% 2.94/3.16 200 -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(142,b,133,b)].
% 2.94/3.16 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(200,a,174,a)].
% 2.94/3.16 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(200,a,175,a)].
% 2.94/3.16 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(200,a,176,a)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(200,a,177,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(200,a,178,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,a,179,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(200,a,180,b)].
% 2.94/3.16 201 -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(142,b,135,b)].
% 2.94/3.16 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(201,a,174,a)].
% 2.94/3.16 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(201,a,175,a)].
% 2.94/3.16 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(201,a,176,a)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(201,a,177,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A). [resolve(201,a,178,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,a,179,b)].
% 2.94/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(201,a,180,b)].
% 2.94/3.16 202 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,142,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(202,b,176,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 2.94/3.16 203 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,142,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(203,b,174,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(203,b,175,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(203,b,176,a)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(203,b,178,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(203,b,180,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(203,b,186,b)].
% 2.94/3.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(203,b,189,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(203,b,190,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(203,b,191,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(203,b,192,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(203,b,193,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(203,b,195,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(203,b,196,b)].
% 2.94/3.17 204 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,142,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(204,b,174,a)].
% 2.94/3.17 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(204,b,175,a)].
% 2.94/3.17 Derived: class_HOL_Oplus(tc_nat). [resolve(204,b,176,a)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(204,b,178,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(204,b,180,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(204,b,186,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(204,b,189,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(204,b,190,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(204,b,191,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(204,b,192,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(204,b,193,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(204,b,195,b)].
% 2.94/3.17 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(204,b,196,b)].
% 2.94/3.17 205 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(167,a,142,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(205,b,174,a)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(205,b,175,a)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(205,b,176,a)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(205,b,177,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(205,b,178,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(205,b,179,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(205,b,180,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(205,b,188,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(205,b,194,b)].
% 2.94/3.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(205,b,196,b)].
% 2.94/3.17 206 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(168,a,142,b)].
% 2.94/3.17 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(206,b,174,a)].
% 3.10/3.36 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(206,b,175,a)].
% 3.10/3.36 Derived: class_HOL_Otimes(tc_nat). [resolve(206,b,176,a)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(206,b,177,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(206,b,178,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(206,b,179,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(206,b,180,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(206,b,188,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(206,b,194,b)].
% 3.10/3.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(206,b,196,b)].
% 3.10/3.36 207 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 3.10/3.36 208 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].
% 3.10/3.36 209 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 3.10/3.36 210 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 3.10/3.36 211 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 3.10/3.36 212 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 3.10/3.36 213 -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].
% 3.10/3.36 214 -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].
% 3.10/3.36 215 -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].
% 3.10/3.36 216 -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].
% 3.10/3.36 217 -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].
% 3.10/3.36 218 -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].
% 3.10/3.36 219 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 3.10/3.36 220 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 3.10/3.36 221 -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].
% 3.10/3.36 222 -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].
% 3.10/3.36 223 -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].
% 3.10/3.36 224 -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].
% 3.10/3.36 225 -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].
% 3.10/3.36 226 -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].
% 3.10/3.36 227 -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].
% 3.10/3.36 228 -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].
% 3.10/3.36 229 -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].
% 3.10/3.36 230 -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].
% 3.10/3.36 231 -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].
% 3.10/3.36 232 -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].
% 3.10/3.36 233 -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].
% 3.10/3.36 234 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 3.10/3.36 235 -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].
% 3.10/3.36 236 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 3.10/3.36 237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 3.10/3.36 238 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 3.10/3.36 239 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 3.10/3.36 240 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(240,a,208,a)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(240,a,209,a)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(240,a,210,a)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(240,a,212,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(240,a,214,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(240,a,219,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 3.10/3.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(240,a,223,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(240,a,224,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(240,a,230,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 3.10/3.37 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 3.10/3.37 241 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 3.10/3.37 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(241,a,208,a)].
% 3.10/3.37 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(241,a,209,a)].
% 3.10/3.37 Derived: class_HOL_Ozero(tc_nat). [resolve(241,a,210,a)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(241,a,212,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(241,a,214,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(241,a,219,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(241,a,223,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(241,a,224,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 3.10/3.37 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(241,a,230,b)].
% 3.16/3.42 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 3.16/3.42 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 3.16/3.42 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 3.16/3.42 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 3.16/3.42 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 3.16/3.42 242 -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].
% 3.16/3.42 243 -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].
% 3.16/3.42 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 3.16/3.42 244 -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].
% 3.16/3.42 245 -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(169,b,133,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(245,a,215,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(245,a,216,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(245,a,217,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(245,a,218,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(245,a,219,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(245,a,220,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(245,a,221,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(245,a,222,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(245,a,223,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(245,a,224,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(245,a,225,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(245,a,226,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(245,a,227,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(245,a,228,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(245,a,229,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(245,a,230,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(245,a,231,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(245,a,232,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(245,a,233,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(245,a,234,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(245,a,235,b)].
% 3.16/3.42 246 -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(169,b,135,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(246,a,215,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(246,a,216,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(246,a,217,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(246,a,218,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(246,a,219,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(246,a,220,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(246,a,221,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(246,a,222,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(246,a,223,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(246,a,224,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(246,a,225,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(246,a,226,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(246,a,227,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(246,a,228,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(246,a,229,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(246,a,230,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(246,a,231,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(246,a,232,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(246,a,233,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(246,a,234,b)].
% 3.16/3.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(246,a,235,b)].
% 3.33/3.59 247 -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].
% 3.33/3.59 248 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].
% 3.33/3.59 249 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.33/3.59 250 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.33/3.59 251 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.33/3.59 252 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.33/3.59 253 -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].
% 3.33/3.59 254 -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].
% 3.33/3.59 255 -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].
% 3.33/3.59 256 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.33/3.59 257 -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].
% 3.33/3.59 258 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.33/3.59 259 -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].
% 3.33/3.59 260 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.33/3.59 261 -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].
% 3.33/3.59 262 -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].
% 3.33/3.59 263 -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].
% 3.33/3.59 264 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.33/3.59 265 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.33/3.59 266 -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].
% 3.33/3.59 267 -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].
% 3.33/3.59 268 -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].
% 3.33/3.59 269 -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].
% 3.33/3.59 270 -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].
% 3.40/3.65 271 -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].
% 3.40/3.65 272 -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].
% 3.40/3.65 273 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(108,a,95,b)].
% 3.40/3.65 274 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(109,a,95,b)].
% 3.40/3.65 275 -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(143,b,133,b)].
% 3.40/3.65 276 -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(143,b,135,b)].
% 3.40/3.65 277 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,143,b)].
% 3.40/3.65 278 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,143,b)].
% 3.40/3.65 279 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,143,b)].
% 3.40/3.65 280 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(167,a,143,b)].
% 3.40/3.65 281 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(168,a,143,b)].
% 3.40/3.65 282 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(282,b,248,a)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(282,b,249,a)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(282,b,250,a)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(282,b,251,b)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(282,b,252,b)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(282,b,253,b)].
% 3.40/3.65 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(282,b,254,b)].
% 3.40/3.65 283 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 3.40/3.65 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(283,b,248,a)].
% 3.40/3.65 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(283,b,249,a)].
% 3.40/3.65 Derived: class_HOL_Ozero(tc_nat). [resolve(283,b,250,a)].
% 3.40/3.65 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(283,b,251,b)].
% 3.40/3.65 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(283,b,252,b)].
% 3.40/3.65 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(283,b,253,b)].
% 3.40/3.65 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(283,b,254,b)].
% 3.40/3.65 284 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(245,a,215,b)].
% 3.40/3.65 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(284,c,248,a)].
% 3.40/3.65 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(284,c,249,a)].
% 3.46/3.75 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(284,c,250,a)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(284,c,251,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(284,c,252,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,c,253,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(284,c,254,b)].
% 3.46/3.75 285 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(246,a,215,b)].
% 3.46/3.75 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(285,c,248,a)].
% 3.46/3.75 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(285,c,249,a)].
% 3.46/3.75 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(285,c,250,a)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(285,c,251,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A). [resolve(285,c,252,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,c,253,b)].
% 3.46/3.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(285,c,254,b)].
% 3.46/3.75 286 -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].
% 3.46/3.75 287 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].
% 3.46/3.75 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(286,a,287,a)].
% 3.46/3.75 288 -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].
% 3.46/3.75 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(288,a,287,a)].
% 3.57/3.81 289 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 3.57/3.81 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(289,a,286,a)].
% 3.57/3.81 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(289,a,288,a)].
% 3.57/3.81 290 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 3.57/3.81 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(290,a,286,a)].
% 3.57/3.81 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(290,a,288,a)].
% 3.57/3.81 291 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 3.57/3.81 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(291,b,286,a)].
% 3.57/3.81 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(291,b,288,a)].
% 3.57/3.81 292 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 3.57/3.81 Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0. [resolve(292,b,286,a)].
% 3.57/3.81 Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0. [resolve(292,b,288,a)].
% 3.57/3.81 293 -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].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,288,a)].
% 3.57/3.81 294 -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].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0. [resolve(294,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0. [resolve(294,b,288,a)].
% 3.57/3.81 295 -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].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,288,a)].
% 3.57/3.81 296 -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].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,288,a)].
% 3.57/3.81 297 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,288,a)].
% 3.57/3.81 298 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 3.57/3.81 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,288,a)].
% 3.57/3.81 299 -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].
% 3.57/3.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,286,a)].
% 3.57/3.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,288,a)].
% 3.57/3.81 300 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,288,a)].
% 3.62/3.84 301 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,288,a)].
% 3.62/3.84 302 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,288,a)].
% 3.62/3.84 303 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,288,a)].
% 3.62/3.84 304 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,288,a)].
% 3.62/3.84 305 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,288,a)].
% 3.62/3.84 306 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,288,a)].
% 3.62/3.84 307 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,288,a)].
% 3.62/3.84 308 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,288,a)].
% 3.62/3.84 309 -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].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,286,a)].
% 3.62/3.84 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,288,a)].
% 3.62/3.84 310 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 3.64/3.86 Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,286,a)].
% 3.64/3.86 Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,288,a)].
% 3.64/3.86 311 -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].
% 3.64/3.86 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,286,a)].
% 3.64/3.86 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,288,a)].
% 3.64/3.86 312 -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].
% 3.64/3.86 313 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 3.64/3.86 314 -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].
% 3.64/3.86 315 -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].
% 3.64/3.86 316 -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].
% 3.64/3.86 317 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 3.64/3.86 318 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 3.64/3.86 319 -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].
% 3.64/3.86 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(319,b,286,a)].
% 3.64/3.86 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(319,b,288,a)].
% 3.64/3.86 320 -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)].
% 3.64/3.86 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(320,a,287,a)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(320,a,292,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(320,a,293,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(320,a,294,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(320,a,295,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(320,a,296,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(320,a,297,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(320,a,298,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(320,a,299,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(320,a,300,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(320,a,301,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(320,a,302,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(320,a,303,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(320,a,304,b)].
% 3.64/3.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(320,a,305,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(320,a,306,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(320,a,307,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(320,a,308,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(320,a,309,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(320,a,310,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(320,a,311,b)].
% 3.64/3.87 321 -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)].
% 3.64/3.87 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(321,a,287,a)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(321,a,292,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(321,a,293,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(321,a,294,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(321,a,295,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(321,a,296,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(321,a,297,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(321,a,298,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(321,a,299,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(321,a,300,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(321,a,301,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(321,a,302,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(321,a,303,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(321,a,304,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(321,a,305,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(321,a,306,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(321,a,307,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(321,a,308,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(321,a,309,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(321,a,310,b)].
% 3.64/3.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(321,a,311,b)].
% 3.64/3.87 322 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 3.64/3.87 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(322,a,303,b)].
% 3.64/3.87 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(322,a,309,b)].
% 3.64/3.87 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(322,a,310,b)].
% 3.64/3.87 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(322,a,311,b)].
% 3.64/3.87 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(322,a,319,b)].
% 3.76/4.04 323 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 3.76/4.04 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(323,a,303,b)].
% 3.76/4.04 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(323,a,309,b)].
% 3.76/4.04 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(323,a,311,b)].
% 3.76/4.04 324 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 3.76/4.04 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,303,b)].
% 3.76/4.04 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(324,a,307,b)].
% 3.76/4.04 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,309,b)].
% 3.76/4.04 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,311,b)].
% 3.76/4.04 325 -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(170,b,133,b)].
% 3.76/4.04 326 -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(170,b,135,b)].
% 3.76/4.04 327 -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].
% 3.76/4.04 328 class_Ring__and__Field_Oring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_22) # label(axiom). [assumption].
% 3.76/4.04 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(327,b,328,a)].
% 3.76/4.04 329 -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].
% 3.76/4.04 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(329,b,328,a)].
% 3.76/4.04 330 -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].
% 3.76/4.04 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(330,a,328,a)].
% 3.76/4.04 331 -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].
% 3.76/4.04 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(331,a,328,a)].
% 3.76/4.04 332 -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].
% 3.76/4.04 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(332,a,328,a)].
% 3.76/4.04 333 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 3.84/4.06 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(333,a,327,b)].
% 3.84/4.06 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(333,a,329,b)].
% 3.84/4.06 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(333,a,330,a)].
% 3.84/4.06 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(333,a,331,a)].
% 3.84/4.06 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(333,a,332,a)].
% 3.84/4.06 334 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 3.84/4.06 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(334,b,327,b)].
% 3.84/4.06 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(334,b,329,b)].
% 3.84/4.06 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(334,b,330,a)].
% 3.84/4.06 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(334,b,331,a)].
% 3.84/4.06 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(334,b,332,a)].
% 3.84/4.06 335 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 3.84/4.06 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(335,b,327,b)].
% 3.84/4.06 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(335,b,329,b)].
% 3.84/4.06 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(335,b,330,a)].
% 3.84/4.06 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(335,b,331,a)].
% 3.84/4.06 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(335,b,332,a)].
% 3.84/4.06 336 -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].
% 3.84/4.06 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(336,b,327,b)].
% 3.84/4.06 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(336,b,329,b)].
% 3.84/4.06 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(336,b,330,a)].
% 3.84/4.06 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(336,b,331,a)].
% 3.86/4.08 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(336,b,332,a)].
% 3.86/4.08 337 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 3.86/4.08 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(337,b,327,b)].
% 3.86/4.08 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(337,b,329,b)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(337,b,330,a)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(337,b,331,a)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(337,b,332,a)].
% 3.86/4.08 338 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 3.86/4.08 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(338,b,327,b)].
% 3.86/4.08 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(338,b,329,b)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,330,a)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,331,a)].
% 3.86/4.08 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,332,a)].
% 3.86/4.08 339 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 3.86/4.08 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(339,b,327,b)].
% 3.86/4.08 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(339,b,329,b)].
% 3.86/4.08 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(339,b,330,a)].
% 3.86/4.08 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(339,b,331,a)].
% 3.86/4.08 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(339,b,332,a)].
% 3.86/4.08 340 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 3.86/4.08 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(340,b,327,b)].
% 3.86/4.08 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(340,b,329,b)].
% 3.86/4.08 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(340,b,330,a)].
% 3.86/4.08 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(340,b,331,a)].
% 3.86/4.09 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(340,b,332,a)].
% 3.86/4.09 341 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 3.86/4.09 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(341,b,327,b)].
% 3.86/4.09 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(341,b,329,b)].
% 3.86/4.09 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(341,b,330,a)].
% 3.86/4.09 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(341,b,331,a)].
% 3.86/4.09 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(341,b,332,a)].
% 3.86/4.09 342 -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].
% 3.86/4.09 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(342,b,327,b)].
% 3.86/4.09 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(342,b,329,b)].
% 3.86/4.09 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(342,b,330,a)].
% 3.86/4.09 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(342,b,331,a)].
% 3.86/4.09 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(342,b,332,a)].
% 3.86/4.09 343 -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].
% 3.86/4.09 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(343,b,327,b)].
% 3.86/4.09 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(343,b,329,b)].
% 3.86/4.09 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(343,b,330,a)].
% 3.86/4.09 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(343,b,331,a)].
% 3.86/4.09 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(343,b,332,a)].
% 3.86/4.09 344 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 3.86/4.09 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(344,b,327,b)].
% 3.86/4.09 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(344,b,329,b)].
% 3.86/4.10 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(344,b,330,a)].
% 3.86/4.10 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(344,b,331,a)].
% 3.86/4.10 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(344,b,332,a)].
% 3.86/4.10 345 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 3.86/4.10 346 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 3.86/4.10 347 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 3.86/4.10 348 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 3.86/4.10 349 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 3.86/4.10 350 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(350,a,328,a)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(350,a,333,a)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(350,a,334,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(350,a,335,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(350,a,336,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(350,a,337,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(350,a,338,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(350,a,339,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(350,a,340,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(350,a,341,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(350,a,342,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(350,a,343,b)].
% 3.86/4.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(350,a,344,b)].
% 3.86/4.10 351 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom). [assumption].
% 3.86/4.10 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(351,a,328,a)].
% 3.86/4.10 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(351,a,333,a)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(351,a,334,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(351,a,335,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(351,a,336,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(351,a,337,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(351,a,338,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(351,a,339,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(351,a,340,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(351,a,341,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(351,a,342,b)].
% 3.86/4.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(351,a,343,b)].
% 3.92/4.15 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(351,a,344,b)].
% 3.92/4.15 352 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 3.92/4.15 353 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 3.92/4.15 354 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 3.92/4.15 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(354,b,327,b)].
% 3.92/4.15 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(354,b,329,b)].
% 3.92/4.15 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(354,b,330,a)].
% 3.92/4.15 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(354,b,331,a)].
% 3.92/4.15 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(354,b,332,a)].
% 3.92/4.15 355 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 3.92/4.15 356 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 3.92/4.15 357 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 3.92/4.15 358 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(358,b,339,b)].
% 3.92/4.15 359 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 3.92/4.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(359,b,339,b)].
% 3.92/4.15 360 -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(162,b,133,b)].
% 3.92/4.15 361 -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(162,b,135,b)].
% 3.92/4.15 362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(167,a,162,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(362,b,337,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(362,b,338,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,339,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(362,b,340,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(362,b,341,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(362,b,342,b)].
% 3.92/4.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(362,b,344,b)].
% 3.92/4.15 363 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(168,a,162,b)].
% 3.92/4.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(363,b,337,b)].
% 3.92/4.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(363,b,338,b)].
% 3.92/4.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,339,b)].
% 3.92/4.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(363,b,340,b)].
% 3.92/4.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(363,b,341,b)].
% 3.95/4.16 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(363,b,342,b)].
% 3.95/4.16 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(363,b,344,b)].
% 3.95/4.16 364 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(364,b,337,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(364,b,338,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(364,b,339,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(364,b,340,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(364,b,341,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(364,b,342,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(364,b,343,b)].
% 3.95/4.16 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(364,b,344,b)].
% 3.95/4.16 365 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(365,b,337,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(365,b,338,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(365,b,339,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(365,b,340,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(365,b,341,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(365,b,342,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(365,b,343,b)].
% 3.95/4.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(365,b,344,b)].
% 3.95/4.16 366 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(245,a,234,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(366,c,337,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(366,c,338,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,c,339,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(366,c,340,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(366,c,341,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,c,342,b)].
% 3.95/4.16 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(366,c,343,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,c,344,b)].
% 3.95/4.17 367 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(246,a,234,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(367,c,337,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(367,c,338,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,c,339,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(367,c,340,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(367,c,341,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,c,342,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(367,c,343,b)].
% 3.95/4.17 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,c,344,b)].
% 3.95/4.17 368 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,286,a)].
% 3.95/4.17 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(368,a,328,a)].
% 3.95/4.17 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(368,a,333,a)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(368,a,334,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(368,a,335,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(368,a,336,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(368,a,337,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(368,a,338,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(368,a,339,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(368,a,340,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(368,a,341,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(368,a,342,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(368,a,343,b)].
% 3.95/4.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(368,a,344,b)].
% 3.95/4.17 369 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,288,a)].
% 3.95/4.17 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(369,a,328,a)].
% 3.95/4.18 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(369,a,333,a)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(369,a,334,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(369,a,335,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(369,a,336,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(369,a,337,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(369,a,338,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(369,a,339,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(369,a,340,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(369,a,341,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(369,a,342,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(369,a,343,b)].
% 3.95/4.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(369,a,344,b)].
% 3.95/4.18 370 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(320,a,310,b)].
% 3.95/4.18 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(370,c,328,a)].
% 3.95/4.18 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(370,c,333,a)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(370,c,334,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(370,c,335,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(370,c,336,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(370,c,337,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(370,c,338,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(370,c,339,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(370,c,340,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(370,c,341,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(370,c,342,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(370,c,343,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(370,c,344,b)].
% 3.95/4.18 371 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(321,a,310,b)].
% 3.95/4.18 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(371,c,328,a)].
% 3.95/4.18 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(371,c,333,a)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(371,c,334,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(371,c,335,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(371,c,336,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(371,c,337,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(371,c,338,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(371,c,339,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(371,c,340,b)].
% 3.95/4.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(371,c,341,b)].
% 4.07/4.34 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(371,c,342,b)].
% 4.07/4.34 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(371,c,343,b)].
% 4.07/4.34 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(371,c,344,b)].
% 4.07/4.34 372 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(322,a,310,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(372,b,328,a)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(372,b,333,a)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(372,b,334,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(372,b,335,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(372,b,336,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(372,b,337,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(372,b,338,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(372,b,339,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,b,340,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,b,341,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(372,b,342,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(372,b,343,b)].
% 4.07/4.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(372,b,344,b)].
% 4.07/4.34 373 -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].
% 4.07/4.34 374 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].
% 4.07/4.34 375 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 4.07/4.34 376 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 4.07/4.34 377 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 4.07/4.34 378 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 4.07/4.34 379 -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].
% 4.07/4.34 380 -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].
% 4.07/4.34 381 -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].
% 4.07/4.34 382 -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].
% 4.07/4.34 383 -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].
% 4.07/4.34 384 -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].
% 4.07/4.34 385 -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].
% 4.18/4.42 386 -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].
% 4.18/4.42 387 -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].
% 4.18/4.42 388 -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].
% 4.18/4.42 389 -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].
% 4.18/4.42 390 -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].
% 4.18/4.42 391 -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].
% 4.18/4.42 392 -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].
% 4.18/4.42 393 -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].
% 4.18/4.42 394 -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)].
% 4.18/4.42 395 -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)].
% 4.18/4.42 396 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 4.18/4.42 397 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 4.18/4.42 398 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(108,a,96,b)].
% 4.18/4.42 399 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(109,a,96,b)].
% 4.18/4.42 400 -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(144,b,133,b)].
% 4.18/4.42 401 -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(144,b,135,b)].
% 4.18/4.42 402 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(164,a,144,b)].
% 4.18/4.42 403 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(167,a,144,b)].
% 4.18/4.42 404 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(168,a,144,b)].
% 4.18/4.42 405 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(203,b,186,b)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(405,b,374,a)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(405,b,375,a)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(405,b,376,a)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(405,b,377,b)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(405,b,378,b)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(405,b,379,b)].
% 4.18/4.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(405,b,380,b)].
% 4.35/4.60 406 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(204,b,186,b)].
% 4.35/4.60 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(406,b,374,a)].
% 4.35/4.60 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(406,b,375,a)].
% 4.35/4.60 Derived: class_HOL_Oplus(tc_nat). [resolve(406,b,376,a)].
% 4.35/4.60 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(406,b,377,b)].
% 4.35/4.60 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(406,b,378,b)].
% 4.35/4.60 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(406,b,379,b)].
% 4.35/4.60 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(406,b,380,b)].
% 4.35/4.60 407 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 4.35/4.60 408 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 4.35/4.60 409 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(245,a,216,b)].
% 4.35/4.60 410 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(246,a,216,b)].
% 4.35/4.60 411 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,286,a)].
% 4.35/4.60 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(411,a,376,a)].
% 4.35/4.60 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(411,a,378,b)].
% 4.35/4.60 412 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,288,a)].
% 4.35/4.60 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(412,a,376,a)].
% 4.35/4.60 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(412,a,378,b)].
% 4.35/4.60 413 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(320,a,295,b)].
% 4.35/4.60 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(413,c,376,a)].
% 4.35/4.60 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(413,c,378,b)].
% 4.35/4.60 414 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(321,a,295,b)].
% 4.35/4.60 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(414,c,376,a)].
% 4.35/4.60 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(414,c,378,b)].
% 4.35/4.60 415 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom). [assumption].
% 4.35/4.60 416 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].
% 4.35/4.60 417 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 4.35/4.60 418 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 4.35/4.60 419 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 4.35/4.60 420 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 4.35/4.60 421 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom). [assumption].
% 4.35/4.60 422 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 4.35/4.60 423 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 4.35/4.60 424 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 4.35/4.60 425 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 4.42/4.66 426 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 4.42/4.66 427 -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].
% 4.42/4.66 428 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 4.42/4.66 429 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 4.42/4.66 430 -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].
% 4.42/4.66 431 -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].
% 4.42/4.66 432 -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].
% 4.42/4.66 433 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(20,b,1,a)].
% 4.42/4.66 434 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(20,b,3,a)].
% 4.42/4.66 435 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 4.42/4.66 436 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 4.42/4.66 437 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(108,a,92,b)].
% 4.42/4.66 438 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(109,a,92,b)].
% 4.42/4.66 439 -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(140,b,133,b)].
% 4.42/4.66 440 -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(140,b,135,b)].
% 4.42/4.66 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(164,a,140,b)].
% 4.42/4.66 442 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(167,a,140,b)].
% 4.42/4.66 443 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(168,a,140,b)].
% 4.42/4.66 444 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(198,b,179,b)].
% 4.42/4.66 Derived: c_times(A,B,tc_fun(C,D)) = c_times(B,A,tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(444,b,416,a)].
% 4.42/4.66 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(444,b,417,a)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(444,b,418,b)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(444,b,428,b)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(444,b,429,b)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(444,b,430,b)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(444,b,431,b)].
% 4.42/4.66 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(444,b,432,b)].
% 4.42/4.66 445 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(199,b,179,b)].
% 4.42/4.66 Derived: c_times(A,c_times(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_times(B,c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(445,b,416,a)].
% 4.42/4.66 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(445,b,417,a)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(445,b,418,b)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(445,b,428,b)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(445,b,429,b)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(445,b,430,b)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(445,b,431,b)].
% 4.46/4.68 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(445,b,432,b)].
% 4.46/4.68 446 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,a,179,b)].
% 4.46/4.68 447 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,a,179,b)].
% 4.46/4.68 448 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 4.46/4.68 449 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 4.46/4.68 450 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 4.46/4.68 451 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(205,b,179,b)].
% 4.46/4.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(451,b,416,a)].
% 4.46/4.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(451,b,417,a)].
% 4.46/4.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(451,b,418,b)].
% 4.46/4.68 452 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(206,b,179,b)].
% 4.46/4.68 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(452,b,416,a)].
% 4.46/4.68 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(452,b,417,a)].
% 4.46/4.68 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(452,b,418,b)].
% 4.46/4.68 453 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 4.46/4.68 454 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 4.46/4.68 455 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(282,b,253,b)].
% 4.46/4.68 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(455,b,416,a)].
% 4.46/4.68 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(455,b,417,a)].
% 4.46/4.68 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(455,b,418,b)].
% 4.46/4.68 456 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(283,b,253,b)].
% 4.46/4.68 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(456,b,416,a)].
% 4.46/4.68 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(456,b,417,a)].
% 4.46/4.68 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(456,b,418,b)].
% 4.46/4.68 457 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,c,253,b)].
% 4.46/4.68 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(457,c,416,a)].
% 4.46/4.68 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(457,c,417,a)].
% 4.46/4.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(457,c,418,b)].
% 4.46/4.70 458 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,c,253,b)].
% 4.46/4.70 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(458,c,416,a)].
% 4.46/4.70 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(458,c,417,a)].
% 4.46/4.70 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(458,c,418,b)].
% 4.46/4.70 459 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,286,a)].
% 4.46/4.70 460 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,288,a)].
% 4.46/4.70 461 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(320,a,293,b)].
% 4.46/4.70 462 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(321,a,293,b)].
% 4.46/4.70 463 -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(335,b,327,b)].
% 4.46/4.70 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(463,a,416,a)].
% 4.46/4.70 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(463,a,417,a)].
% 4.46/4.70 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(463,a,418,b)].
% 4.46/4.70 464 -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(335,b,329,b)].
% 4.46/4.70 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(464,a,416,a)].
% 4.46/4.70 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(464,a,417,a)].
% 4.46/4.72 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_Numeral_Onumber__ring(A). [resolve(464,a,418,b)].
% 4.46/4.72 465 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(335,b,330,a)].
% 4.46/4.72 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(465,a,416,a)].
% 4.46/4.72 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(465,a,417,a)].
% 4.46/4.72 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(465,a,418,b)].
% 4.46/4.72 466 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(335,b,331,a)].
% 4.46/4.72 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(466,a,416,a)].
% 4.46/4.72 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(466,a,417,a)].
% 4.46/4.72 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(466,a,418,b)].
% 4.46/4.72 467 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(335,b,332,a)].
% 4.46/4.72 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(467,a,416,a)].
% 4.46/4.72 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(467,a,417,a)].
% 4.46/4.72 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(467,a,418,b)].
% 4.46/4.72 468 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(350,a,335,b)].
% 4.46/4.72 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(468,b,416,a)].
% 4.46/4.72 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(468,b,417,a)].
% 4.46/4.72 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(468,b,418,b)].
% 4.46/4.72 469 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(351,a,335,b)].
% 4.46/4.72 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(469,b,416,a)].
% 4.46/4.72 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(469,b,417,a)].
% 4.46/4.72 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(469,b,418,b)].
% 4.46/4.72 470 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(368,a,335,b)].
% 4.46/4.72 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(470,b,416,a)].
% 4.46/4.72 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(470,b,417,a)].
% 4.46/4.72 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(470,b,418,b)].
% 4.46/4.72 471 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(369,a,335,b)].
% 4.46/4.72 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(471,b,416,a)].
% 4.46/4.72 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(471,b,417,a)].
% 4.46/4.72 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(471,b,418,b)].
% 4.46/4.72 472 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(370,c,335,b)].
% 4.46/4.72 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(472,c,416,a)].
% 4.46/4.72 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(472,c,417,a)].
% 4.46/4.72 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(472,c,418,b)].
% 4.46/4.72 473 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(371,c,335,b)].
% 4.46/4.72 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(473,c,416,a)].
% 4.65/4.86 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(473,c,417,a)].
% 4.65/4.86 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(473,c,418,b)].
% 4.65/4.86 474 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(372,b,335,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(474,b,416,a)].
% 4.65/4.86 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(474,b,417,a)].
% 4.65/4.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(474,b,418,b)].
% 4.65/4.86 475 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(405,b,379,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(475,b,416,a)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(475,b,417,a)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(475,b,418,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(475,b,428,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(475,b,429,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(475,b,430,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(475,b,431,b)].
% 4.65/4.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(475,b,432,b)].
% 4.65/4.86 476 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(406,b,379,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(476,b,416,a)].
% 4.65/4.86 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(476,b,417,a)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(476,b,418,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(476,b,428,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(476,b,429,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(476,b,430,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(476,b,431,b)].
% 4.65/4.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(476,b,432,b)].
% 4.65/4.86 477 -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].
% 4.65/4.86 478 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].
% 4.65/4.86 Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(477,a,478,a)].
% 4.65/4.86 479 -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].
% 4.65/4.86 Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(479,a,478,a)].
% 4.65/4.86 480 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 4.65/4.86 Derived: c_0 != c_1. [resolve(480,a,477,a)].
% 4.65/4.86 Derived: c_1 != c_0. [resolve(480,a,479,a)].
% 4.65/4.86 481 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 4.65/4.86 482 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 4.65/4.86 483 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 4.65/4.86 484 -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].
% 4.65/4.86 485 -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].
% 4.91/5.12 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(485,a,478,a)].
% 4.91/5.12 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(485,a,483,b)].
% 4.91/5.12 486 -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].
% 4.91/5.12 487 -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].
% 4.91/5.12 488 -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].
% 4.91/5.12 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(488,b,485,a)].
% 4.91/5.12 489 -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].
% 4.91/5.12 490 -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].
% 4.91/5.12 491 -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].
% 4.91/5.12 492 -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].
% 4.91/5.12 493 -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].
% 4.91/5.12 494 -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].
% 4.91/5.12 495 -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].
% 4.91/5.12 496 -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].
% 4.91/5.12 497 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 4.91/5.12 498 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].
% 4.91/5.12 499 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 4.91/5.12 500 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 4.91/5.12 501 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 4.91/5.12 502 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 4.91/5.12 503 -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].
% 4.91/5.12 504 -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].
% 4.91/5.12 505 -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].
% 4.91/5.12 506 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 4.91/5.12 507 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 4.91/5.12 508 -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].
% 4.94/5.15 509 -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].
% 4.94/5.15 510 -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].
% 4.94/5.15 511 -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].
% 4.94/5.15 512 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom). [assumption].
% 4.94/5.15 513 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(513,a,503,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(513,a,504,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(513,a,506,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(513,a,507,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(513,a,508,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(513,a,509,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(513,a,510,b)].
% 4.94/5.15 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(513,a,511,b)].
% 4.94/5.15 514 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 4.94/5.15 515 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 4.94/5.15 516 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 4.94/5.15 517 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 4.94/5.15 518 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 4.94/5.15 519 -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].
% 4.94/5.15 520 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(131,b,110,a)].
% 4.94/5.15 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(520,a,498,a)].
% 4.94/5.15 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(520,a,499,a)].
% 4.94/5.15 Derived: c_times(c_1,A,tc_nat) = A. [resolve(520,a,500,a)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(520,a,501,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(520,a,502,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(520,a,503,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(520,a,504,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(520,a,505,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(520,a,506,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(520,a,507,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(520,a,508,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(520,a,509,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(520,a,510,b)].
% 4.94/5.15 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(520,a,511,b)].
% 4.94/5.15 521 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(131,b,113,a)].
% 5.08/5.33 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(521,a,498,a)].
% 5.08/5.33 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(521,a,499,a)].
% 5.08/5.33 Derived: c_times(A,c_1,tc_nat) = A. [resolve(521,a,500,a)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(521,a,501,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(521,a,502,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(521,a,503,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(521,a,504,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(521,a,505,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(521,a,506,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(521,a,507,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(521,a,508,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(521,a,509,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(521,a,510,b)].
% 5.08/5.33 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(521,a,511,b)].
% 5.08/5.33 522 -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(171,b,133,b)].
% 5.08/5.33 523 -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(171,b,135,b)].
% 5.08/5.33 524 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(171,b,166,a)].
% 5.08/5.33 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(524,a,504,b)].
% 5.08/5.33 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(524,a,519,b)].
% 5.08/5.33 525 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 5.08/5.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(525,a,504,b)].
% 5.08/5.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(525,a,505,b)].
% 5.08/5.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(525,a,510,b)].
% 5.08/5.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(525,a,511,b)].
% 5.08/5.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(525,a,519,b)].
% 5.08/5.33 526 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 5.08/5.33 527 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].
% 5.08/5.33 528 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 5.08/5.33 529 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 5.08/5.33 530 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 5.08/5.33 531 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 5.08/5.33 532 -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].
% 5.08/5.33 533 -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].
% 5.08/5.33 534 -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].
% 5.08/5.33 535 -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].
% 5.17/5.40 536 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_13) # label(axiom). [assumption].
% 5.17/5.40 537 -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].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(537,a,527,a)].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(537,a,528,a)].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(537,a,529,a)].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(537,a,530,b)].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(537,a,531,b)].
% 5.17/5.40 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(537,a,532,b)].
% 5.17/5.40 538 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 5.17/5.40 539 -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].
% 5.17/5.40 540 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 5.17/5.40 541 -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].
% 5.17/5.40 542 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 5.17/5.40 543 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 5.17/5.40 544 -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].
% 5.17/5.40 545 -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].
% 5.17/5.40 546 -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].
% 5.17/5.40 547 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(108,a,97,b)].
% 5.17/5.40 548 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(109,a,97,b)].
% 5.17/5.40 549 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(123,b,110,a)].
% 5.17/5.40 550 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(123,b,113,a)].
% 5.17/5.40 551 -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(145,b,133,b)].
% 5.17/5.40 552 -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(145,b,135,b)].
% 5.17/5.40 553 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,145,b)].
% 5.17/5.40 554 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,145,b)].
% 5.17/5.40 555 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,145,b)].
% 5.17/5.40 556 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(167,a,145,b)].
% 5.17/5.40 557 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(168,a,145,b)].
% 5.26/5.46 558 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 5.26/5.46 559 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 5.26/5.46 560 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(245,a,217,b)].
% 5.26/5.46 561 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(246,a,217,b)].
% 5.26/5.46 562 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(513,a,504,b)].
% 5.26/5.46 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(562,b,527,a)].
% 5.26/5.46 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(562,b,528,a)].
% 5.26/5.46 Derived: class_HOL_Oone(tc_nat). [resolve(562,b,529,a)].
% 5.26/5.46 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(562,b,530,b)].
% 5.26/5.46 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(562,b,531,b)].
% 5.26/5.46 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(562,b,532,b)].
% 5.26/5.46 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(562,b,541,b)].
% 5.26/5.46 563 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(520,a,504,b)].
% 5.26/5.46 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(563,b,527,a)].
% 5.26/5.46 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(563,b,528,a)].
% 5.26/5.46 Derived: c_times(c_1,A,tc_nat) = A. [resolve(563,b,529,a)].
% 5.26/5.46 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(563,b,530,b)].
% 5.26/5.46 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(563,b,531,b)].
% 5.26/5.46 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(563,b,532,b)].
% 5.26/5.46 564 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(521,a,504,b)].
% 5.26/5.46 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(564,b,527,a)].
% 5.26/5.46 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(564,b,528,a)].
% 5.26/5.46 Derived: c_times(A,c_1,tc_nat) = A. [resolve(564,b,529,a)].
% 5.26/5.46 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(564,b,530,b)].
% 5.26/5.46 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(564,b,531,b)].
% 5.26/5.46 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(564,b,532,b)].
% 5.26/5.46 565 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(524,a,504,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(565,b,527,a)].
% 5.26/5.46 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(565,b,528,a)].
% 5.26/5.46 Derived: class_HOL_Oplus(tc_nat). [resolve(565,b,529,a)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(565,b,530,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(565,b,531,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(565,b,532,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(565,b,541,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(565,b,542,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(565,b,543,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(565,b,544,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(565,b,545,b)].
% 5.26/5.46 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(565,b,546,b)].
% 5.26/5.46 566 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(525,a,504,b)].
% 5.26/5.46 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(566,b,527,a)].
% 5.35/5.59 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(566,b,528,a)].
% 5.35/5.59 Derived: class_HOL_Ozero(tc_nat). [resolve(566,b,529,a)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(566,b,530,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(566,b,531,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(566,b,532,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(566,b,542,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(566,b,543,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(566,b,544,b)].
% 5.35/5.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(566,b,545,b)].
% 5.35/5.59 567 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 5.35/5.59 568 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].
% 5.35/5.59 569 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 5.35/5.59 570 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 5.35/5.59 571 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 5.35/5.59 572 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 5.35/5.59 573 -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].
% 5.35/5.59 574 -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].
% 5.35/5.59 575 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 5.35/5.59 576 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 5.35/5.59 577 -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].
% 5.35/5.59 578 -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].
% 5.35/5.59 579 -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].
% 5.35/5.59 580 -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].
% 5.35/5.59 581 -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].
% 5.35/5.59 582 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 5.35/5.59 583 -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].
% 5.35/5.59 584 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 5.35/5.59 585 -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].
% 5.35/5.59 586 -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].
% 5.35/5.59 587 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_8) # label(axiom). [assumption].
% 5.60/5.82 588 -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)].
% 5.60/5.82 589 -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)].
% 5.60/5.82 590 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 5.60/5.82 591 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 5.60/5.82 592 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(132,b,110,a)].
% 5.60/5.82 593 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(132,b,113,a)].
% 5.60/5.82 594 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(132,b,118,a)].
% 5.60/5.82 595 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(132,b,119,a)].
% 5.60/5.82 596 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(132,b,120,a)].
% 5.60/5.82 597 -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(172,b,133,b)].
% 5.60/5.82 598 -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(172,b,135,b)].
% 5.60/5.82 599 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(319,b,286,a)].
% 5.60/5.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,574,b)].
% 5.60/5.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,579,b)].
% 5.60/5.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,580,b)].
% 5.60/5.82 600 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(319,b,288,a)].
% 5.60/5.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(600,a,574,b)].
% 5.60/5.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(600,a,579,b)].
% 5.60/5.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(600,a,580,b)].
% 5.60/5.82 601 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(322,a,319,b)].
% 5.60/5.82 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(601,b,570,a)].
% 5.60/5.82 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(601,b,572,b)].
% 5.60/5.82 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(601,b,574,b)].
% 5.60/5.82 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(601,b,579,b)].
% 5.60/5.82 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(601,b,580,b)].
% 5.60/5.82 602 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(524,a,519,b)].
% 5.60/5.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(602,b,580,b)].
% 5.60/5.82 603 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(525,a,519,b)].
% 5.60/5.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(603,b,574,b)].
% 5.60/5.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(603,b,579,b)].
% 5.60/5.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(603,b,580,b)].
% 5.60/5.82 604 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 5.60/5.82 605 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].
% 5.60/5.82 606 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 5.65/5.88 607 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 5.65/5.88 608 -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].
% 5.65/5.88 609 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 5.65/5.88 610 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 5.65/5.88 611 -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].
% 5.65/5.88 612 -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].
% 5.65/5.88 613 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 5.65/5.88 614 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 5.65/5.88 615 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 5.65/5.88 616 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom). [assumption].
% 5.65/5.88 617 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 5.65/5.88 618 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 5.65/5.88 619 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom). [assumption].
% 5.65/5.88 620 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 5.65/5.88 621 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 5.65/5.88 622 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(38,b,1,a)].
% 5.65/5.88 623 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(38,b,3,a)].
% 5.65/5.88 624 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 5.65/5.88 625 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 5.65/5.88 626 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 5.65/5.88 627 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(130,b,110,a)].
% 5.65/5.88 628 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(130,b,113,a)].
% 5.65/5.88 629 -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(163,b,133,b)].
% 5.65/5.88 630 -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(163,b,135,b)].
% 5.65/5.88 631 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(167,a,163,b)].
% 5.65/5.88 632 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(168,a,163,b)].
% 5.65/5.88 633 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 5.65/5.88 634 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 5.65/5.88 635 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(245,a,235,b)].
% 5.65/5.88 636 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(246,a,235,b)].
% 5.65/5.90 637 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,286,a)].
% 5.65/5.90 638 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,288,a)].
% 5.65/5.90 639 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(320,a,311,b)].
% 5.65/5.90 640 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(321,a,311,b)].
% 5.65/5.90 641 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(322,a,311,b)].
% 5.65/5.90 642 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(323,a,311,b)].
% 5.65/5.90 643 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,311,b)].
% 5.65/5.90 644 -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(354,b,327,b)].
% 5.65/5.90 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(644,a,608,b)].
% 5.65/5.90 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(644,a,609,b)].
% 5.65/5.90 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(644,a,610,b)].
% 5.65/5.90 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(644,a,611,b)].
% 5.65/5.90 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(644,a,612,b)].
% 5.65/5.90 645 -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(354,b,329,b)].
% 5.65/5.90 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(645,a,608,b)].
% 5.65/5.90 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(645,a,609,b)].
% 5.65/5.90 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(645,a,610,b)].
% 5.65/5.90 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(645,a,611,b)].
% 5.65/5.90 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(645,a,612,b)].
% 5.65/5.90 646 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(354,b,330,a)].
% 5.65/5.90 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(646,a,608,b)].
% 5.65/5.93 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(646,a,609,b)].
% 5.65/5.93 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(646,a,610,b)].
% 5.65/5.93 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(646,a,611,b)].
% 5.65/5.93 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(646,a,612,b)].
% 5.65/5.93 647 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(354,b,331,a)].
% 5.65/5.93 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(647,a,608,b)].
% 5.65/5.93 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(647,a,609,b)].
% 5.65/5.93 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(647,a,610,b)].
% 5.65/5.93 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(647,a,611,b)].
% 5.65/5.93 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(647,a,612,b)].
% 5.65/5.93 648 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(354,b,332,a)].
% 5.65/5.93 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(648,a,608,b)].
% 5.65/5.93 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(648,a,609,b)].
% 5.65/5.93 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(648,a,610,b)].
% 5.65/5.93 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(648,a,611,b)].
% 5.65/5.93 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(648,a,612,b)].
% 5.65/5.93 649 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(513,a,511,b)].
% 5.65/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(649,b,609,b)].
% 5.65/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(649,b,610,b)].
% 5.65/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(649,b,611,b)].
% 5.65/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(649,b,612,b)].
% 5.65/5.93 650 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(520,a,511,b)].
% 5.65/5.93 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(650,b,609,b)].
% 5.65/5.93 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(650,b,610,b)].
% 5.65/5.93 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(650,b,611,b)].
% 5.65/5.93 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(650,b,612,b)].
% 5.65/5.93 651 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(521,a,511,b)].
% 5.65/5.93 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(651,b,609,b)].
% 5.65/5.93 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(651,b,610,b)].
% 5.65/5.93 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(651,b,611,b)].
% 5.65/5.93 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(651,b,612,b)].
% 5.65/5.93 652 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(525,a,511,b)].
% 5.65/5.93 653 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,580,b)].
% 5.65/5.93 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(653,b,605,a)].
% 5.65/5.93 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(653,b,606,a)].
% 5.65/5.93 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(653,b,607,b)].
% 5.65/5.93 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(653,b,608,b)].
% 5.75/5.99 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(653,b,609,b)].
% 5.75/5.99 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(653,b,610,b)].
% 5.75/5.99 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(653,b,611,b)].
% 5.75/5.99 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(653,b,612,b)].
% 5.75/5.99 654 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(600,a,580,b)].
% 5.75/5.99 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(654,b,605,a)].
% 5.75/5.99 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(654,b,606,a)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(654,b,607,b)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(654,b,608,b)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(654,b,609,b)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(654,b,610,b)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(654,b,611,b)].
% 5.75/5.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(654,b,612,b)].
% 5.75/5.99 655 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(601,b,580,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(655,b,605,a)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(655,b,606,a)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(655,b,607,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(655,b,608,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(655,b,609,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(655,b,610,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(655,b,611,b)].
% 5.75/5.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(655,b,612,b)].
% 5.75/5.99 656 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(602,b,580,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(656,b,605,a)].
% 5.75/5.99 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(656,b,606,a)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(656,b,607,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(656,b,608,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(656,b,609,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(656,b,610,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(656,b,611,b)].
% 5.75/5.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(656,b,612,b)].
% 5.75/5.99 657 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(603,b,580,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(657,b,605,a)].
% 5.75/5.99 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(657,b,606,a)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(657,b,607,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(657,b,608,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(657,b,609,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(657,b,610,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(657,b,611,b)].
% 5.75/5.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(657,b,612,b)].
% 5.75/5.99 658 -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].
% 5.80/6.04 659 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].
% 5.80/6.04 Derived: c_in(c_0,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(658,a,659,a)].
% 5.80/6.04 660 -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].
% 5.80/6.04 Derived: c_in(c_1,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(660,a,659,a)].
% 5.80/6.04 661 -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].
% 5.80/6.04 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(661,a,659,a)].
% 5.80/6.04 662 -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].
% 5.80/6.04 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(662,a,659,a)].
% 5.80/6.04 663 -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].
% 5.80/6.04 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(663,a,659,a)].
% 5.80/6.04 664 -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].
% 5.80/6.04 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(664,a,659,a)].
% 5.80/6.04 665 -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].
% 5.80/6.04 Derived: c_NatArith_Oof__nat(c_1,tc_fun(A,B)) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(665,a,659,a)].
% 5.80/6.04 666 -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].
% 5.80/6.04 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(666,a,659,a)].
% 5.80/6.04 667 -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].
% 5.80/6.04 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(667,a,659,a)].
% 5.80/6.04 668 -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].
% 5.80/6.04 Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(668,a,659,a)].
% 5.80/6.04 669 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 5.80/6.04 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,658,a)].
% 5.80/6.04 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,660,a)].
% 5.80/6.04 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(669,a,661,a)].
% 5.80/6.04 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(669,a,662,a)].
% 5.86/6.06 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,663,a)].
% 5.86/6.06 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(669,a,664,a)].
% 5.86/6.06 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(669,a,665,a)].
% 5.86/6.06 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(669,a,666,a)].
% 5.86/6.06 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(669,a,667,a)].
% 5.86/6.06 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(669,a,668,a)].
% 5.86/6.06 670 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 5.86/6.06 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(670,a,658,a)].
% 5.86/6.06 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(670,a,660,a)].
% 5.86/6.06 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(670,a,661,a)].
% 5.86/6.06 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(670,a,662,a)].
% 5.86/6.06 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(670,a,663,a)].
% 5.86/6.06 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(670,a,664,a)].
% 5.86/6.06 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(670,a,665,a)].
% 5.86/6.06 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(670,a,666,a)].
% 5.86/6.06 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(670,a,667,a)].
% 5.86/6.06 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(670,a,668,a)].
% 5.86/6.06 671 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 5.86/6.06 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(671,b,658,a)].
% 5.86/6.06 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(671,b,660,a)].
% 5.86/6.06 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(671,b,661,a)].
% 5.86/6.06 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(671,b,662,a)].
% 5.86/6.06 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(671,b,663,a)].
% 5.86/6.06 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(671,b,664,a)].
% 5.86/6.06 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(671,b,665,a)].
% 5.86/6.06 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(671,b,666,a)].
% 5.86/6.06 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(671,b,667,a)].
% 5.86/6.06 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(671,b,668,a)].
% 5.86/6.06 672 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 5.86/6.06 Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(672,b,658,a)].
% 5.86/6.06 Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(672,b,660,a)].
% 5.86/6.06 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(672,b,661,a)].
% 5.86/6.07 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(672,b,662,a)].
% 5.86/6.07 Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(672,b,663,a)].
% 5.86/6.07 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(672,b,664,a)].
% 5.86/6.07 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(672,b,665,a)].
% 5.86/6.07 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(672,b,666,a)].
% 5.86/6.07 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(672,b,667,a)].
% 5.86/6.07 Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A). [resolve(672,b,668,a)].
% 5.86/6.07 673 -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].
% 5.86/6.07 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(673,b,658,a)].
% 5.86/6.07 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(673,b,660,a)].
% 5.86/6.07 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(673,b,661,a)].
% 5.86/6.07 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(673,b,662,a)].
% 5.86/6.07 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(673,b,663,a)].
% 5.86/6.07 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(673,b,664,a)].
% 5.86/6.07 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(673,b,665,a)].
% 5.86/6.07 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(673,b,666,a)].
% 5.86/6.07 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(673,b,667,a)].
% 5.86/6.07 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A). [resolve(673,b,668,a)].
% 5.86/6.07 674 -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].
% 5.86/6.07 675 -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].
% 5.86/6.07 676 -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].
% 5.86/6.07 677 -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].
% 5.86/6.07 678 -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].
% 5.86/6.07 679 -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].
% 5.86/6.07 680 -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].
% 5.86/6.07 681 -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].
% 5.86/6.07 682 -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].
% 5.86/6.08 683 -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].
% 5.86/6.08 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(683,b,658,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(683,b,660,a)].
% 5.86/6.08 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(683,b,661,a)].
% 5.86/6.08 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(683,b,662,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(683,b,663,a)].
% 5.86/6.08 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(683,b,664,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(683,b,665,a)].
% 5.86/6.08 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(683,b,666,a)].
% 5.86/6.08 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(683,b,667,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A). [resolve(683,b,668,a)].
% 5.86/6.08 684 -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].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(684,b,658,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(684,b,660,a)].
% 5.86/6.08 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(684,b,661,a)].
% 5.86/6.08 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(684,b,662,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(684,b,663,a)].
% 5.86/6.08 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(684,b,664,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(684,b,665,a)].
% 5.86/6.08 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(684,b,666,a)].
% 5.86/6.08 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(684,b,667,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(684,b,668,a)].
% 5.86/6.08 685 -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].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(685,b,658,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(685,b,660,a)].
% 5.86/6.08 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(685,b,661,a)].
% 5.86/6.08 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(685,b,662,a)].
% 5.86/6.08 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(685,b,663,a)].
% 5.86/6.08 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(685,b,664,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(685,b,665,a)].
% 5.86/6.10 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(685,b,666,a)].
% 5.86/6.10 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(685,b,667,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A). [resolve(685,b,668,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(685,b,681,a)].
% 5.86/6.10 686 -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].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(686,b,658,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(686,b,660,a)].
% 5.86/6.10 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(686,b,661,a)].
% 5.86/6.10 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(686,b,662,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(686,b,663,a)].
% 5.86/6.10 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(686,b,664,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(686,b,665,a)].
% 5.86/6.10 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(686,b,666,a)].
% 5.86/6.10 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(686,b,667,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(686,b,668,a)].
% 5.86/6.10 687 -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].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(687,b,658,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(687,b,660,a)].
% 5.86/6.10 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(687,b,661,a)].
% 5.86/6.10 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(687,b,662,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(687,b,663,a)].
% 5.86/6.10 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(687,b,664,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(687,b,665,a)].
% 5.86/6.10 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(687,b,666,a)].
% 5.86/6.10 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(687,b,667,a)].
% 5.86/6.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(687,b,668,a)].
% 5.86/6.10 688 -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)].
% 5.97/6.18 689 -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)].
% 5.97/6.18 690 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 5.97/6.18 691 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 5.97/6.18 692 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 5.97/6.18 693 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 5.97/6.18 694 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 5.97/6.18 695 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(108,a,98,b)].
% 5.97/6.18 696 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(109,a,98,b)].
% 5.97/6.18 697 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(124,b,110,a)].
% 5.97/6.18 698 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(124,b,113,a)].
% 5.97/6.18 699 -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(146,b,133,b)].
% 5.97/6.18 700 -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(146,b,135,b)].
% 5.97/6.18 701 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 5.97/6.18 702 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 5.97/6.18 703 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 5.97/6.18 704 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(205,b,188,b)].
% 5.97/6.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(704,b,670,a)].
% 5.97/6.18 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(704,b,672,b)].
% 5.97/6.18 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(704,b,673,b)].
% 5.97/6.18 705 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(206,b,188,b)].
% 5.97/6.18 Derived: class_HOL_Otimes(tc_nat). [resolve(705,b,670,a)].
% 5.97/6.18 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(705,b,672,b)].
% 5.97/6.18 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(705,b,673,b)].
% 5.97/6.18 706 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 5.97/6.18 707 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 5.97/6.18 708 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(245,a,218,b)].
% 5.97/6.18 709 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(246,a,218,b)].
% 5.97/6.18 710 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,286,a)].
% 5.97/6.18 711 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,288,a)].
% 5.97/6.18 712 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(320,a,296,b)].
% 5.97/6.18 713 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(321,a,296,b)].
% 5.97/6.18 714 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(488,b,485,a)].
% 6.07/6.31 715 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(520,a,505,b)].
% 6.07/6.31 716 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(521,a,505,b)].
% 6.07/6.31 717 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(525,a,505,b)].
% 6.07/6.31 718 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(562,b,541,b)].
% 6.07/6.31 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(718,b,659,a)].
% 6.07/6.31 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(718,b,669,a)].
% 6.07/6.31 Derived: class_HOL_Oone(tc_nat). [resolve(718,b,670,a)].
% 6.07/6.31 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(718,b,671,b)].
% 6.07/6.31 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(718,b,672,b)].
% 6.07/6.31 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(718,b,673,b)].
% 6.07/6.31 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(718,b,687,b)].
% 6.07/6.31 719 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(565,b,541,b)].
% 6.07/6.31 Derived: class_HOL_Oplus(tc_nat). [resolve(719,b,670,a)].
% 6.07/6.31 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(719,b,672,b)].
% 6.07/6.31 720 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,574,b)].
% 6.07/6.31 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(720,b,670,a)].
% 6.07/6.31 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(720,b,672,b)].
% 6.07/6.31 721 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(600,a,574,b)].
% 6.07/6.31 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(721,b,670,a)].
% 6.07/6.31 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(721,b,672,b)].
% 6.07/6.31 722 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(601,b,574,b)].
% 6.07/6.31 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(722,b,670,a)].
% 6.07/6.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(722,b,672,b)].
% 6.07/6.31 723 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(603,b,574,b)].
% 6.07/6.31 Derived: class_HOL_Ozero(tc_nat). [resolve(723,b,670,a)].
% 6.07/6.31 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(723,b,672,b)].
% 6.07/6.31 724 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom). [assumption].
% 6.07/6.31 725 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom). [assumption].
% 6.07/6.31 726 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom). [assumption].
% 6.07/6.31 727 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom). [assumption].
% 6.07/6.31 728 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom). [assumption].
% 6.07/6.31 729 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 6.07/6.31 730 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom). [assumption].
% 6.07/6.31 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(724,a,725,a)].
% 6.07/6.31 Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(724,a,726,a)].
% 6.07/6.31 731 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom). [assumption].
% 6.07/6.31 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(731,a,725,a)].
% 6.07/6.31 Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(731,a,726,a)].
% 6.07/6.31 732 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 6.07/6.34 733 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 6.07/6.34 734 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 6.07/6.34 735 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 6.07/6.34 736 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 6.07/6.34 737 -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].
% 6.07/6.34 738 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom). [assumption].
% 6.07/6.34 739 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 6.07/6.34 740 -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].
% 6.07/6.34 741 -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].
% 6.07/6.34 742 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom). [assumption].
% 6.07/6.34 743 -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].
% 6.07/6.34 744 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom). [assumption].
% 6.07/6.34 745 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 6.07/6.34 746 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 6.07/6.34 747 -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].
% 6.07/6.34 748 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_27) # label(axiom). [assumption].
% 6.07/6.34 749 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 6.07/6.34 750 -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].
% 6.07/6.34 751 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 6.07/6.34 752 -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].
% 6.07/6.34 753 -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].
% 6.07/6.34 754 -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].
% 6.17/6.37 755 -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].
% 6.17/6.37 756 -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].
% 6.17/6.37 757 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 6.17/6.37 758 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 6.17/6.37 759 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 6.17/6.37 760 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 6.17/6.37 761 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 6.17/6.37 762 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 6.17/6.37 763 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 6.17/6.37 764 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 6.17/6.37 765 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 6.17/6.37 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(765,b,724,a)].
% 6.17/6.37 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(765,b,731,a)].
% 6.17/6.37 766 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 6.17/6.37 767 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 6.17/6.37 768 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 6.17/6.37 769 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,134,a)].
% 6.17/6.37 770 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(164,a,139,b)].
% 6.17/6.37 771 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(164,a,141,b)].
% 6.17/6.37 772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(164,a,147,b)].
% 6.17/6.37 773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(164,a,148,b)].
% 6.17/6.37 774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(164,a,149,b)].
% 6.17/6.37 775 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(164,a,150,b)].
% 6.17/6.37 776 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(164,a,151,b)].
% 6.17/6.37 777 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(164,a,152,b)].
% 6.17/6.37 778 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(164,a,154,b)].
% 6.17/6.37 779 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(164,a,155,b)].
% 6.17/6.37 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(779,a,724,a)].
% 6.17/6.37 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(779,a,731,a)].
% 6.17/6.37 780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(164,a,157,b)].
% 6.17/6.37 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(780,a,724,a)].
% 6.17/6.37 781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(164,a,158,b)].
% 6.21/6.43 782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,159,b)].
% 6.21/6.43 783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,161,b)].
% 6.21/6.43 784 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 6.21/6.43 785 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 6.21/6.43 786 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(202,b,176,a)].
% 6.21/6.43 787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 6.21/6.43 788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 6.21/6.43 789 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 6.21/6.43 790 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 6.21/6.43 791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(322,a,303,b)].
% 6.21/6.43 792 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(322,a,309,b)].
% 6.21/6.43 793 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(372,b,328,a)].
% 6.21/6.43 794 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(372,b,333,a)].
% 6.21/6.43 795 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(372,b,334,b)].
% 6.21/6.43 796 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(372,b,336,b)].
% 6.21/6.43 797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(372,b,337,b)].
% 6.21/6.43 798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(372,b,338,b)].
% 6.21/6.43 799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(372,b,339,b)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(799,a,724,a)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(799,a,731,a)].
% 6.21/6.43 800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,b,340,b)].
% 6.21/6.43 801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,b,341,b)].
% 6.21/6.43 802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(372,b,342,b)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(802,a,724,a)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(802,a,731,a)].
% 6.21/6.43 803 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(372,b,343,b)].
% 6.21/6.43 804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(372,b,344,b)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(804,a,724,a)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(804,a,731,a)].
% 6.21/6.43 805 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(474,b,416,a)].
% 6.21/6.43 806 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(474,b,417,a)].
% 6.21/6.43 807 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(474,b,418,b)].
% 6.21/6.43 808 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(601,b,570,a)].
% 6.21/6.43 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(808,a,724,a)].
% 6.21/6.43 809 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(601,b,572,b)].
% 6.21/6.43 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,724,a)].
% 6.21/6.43 810 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(601,b,579,b)].
% 6.21/6.43 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(810,a,724,a)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(810,a,731,a)].
% 6.35/6.55 811 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(655,b,605,a)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)). [resolve(811,a,724,a)].
% 6.35/6.55 812 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(655,b,606,a)].
% 6.35/6.55 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(812,a,724,a)].
% 6.35/6.55 813 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(655,b,607,b)].
% 6.35/6.55 Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(813,a,724,a)].
% 6.35/6.55 814 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(655,b,608,b)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,724,a)].
% 6.35/6.55 815 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(655,b,609,b)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(815,a,724,a)].
% 6.35/6.55 816 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(655,b,610,b)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(816,a,724,a)].
% 6.35/6.55 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(655,b,611,b)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(817,a,724,a)].
% 6.35/6.55 818 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(655,b,612,b)].
% 6.35/6.55 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(818,a,724,a)].
% 6.35/6.55 819 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(722,b,670,a)].
% 6.35/6.55 Derived: class_HOL_Oplus(tc_nat). [resolve(819,a,731,a)].
% 6.35/6.55 820 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(722,b,672,b)].
% 6.35/6.55 Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A). [resolve(820,a,731,a)].
% 6.35/6.55 821 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 6.35/6.55 822 -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].
% 6.35/6.55 823 -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].
% 6.35/6.55 824 -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].
% 6.35/6.55 825 -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].
% 6.35/6.55 826 -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].
% 6.35/6.55 827 -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].
% 6.35/6.55 828 -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].
% 6.35/6.55 829 -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].
% 6.35/6.55 830 -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].
% 6.35/6.55 831 -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].
% 6.35/6.55 832 -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].
% 6.35/6.55 833 -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].
% 6.35/6.55 834 -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].
% 6.35/6.55 835 -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].
% 6.35/6.55 836 -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].
% 6.35/6.55 837 -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].
% 6.35/6.55 838 -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].
% 6.35/6.55 839 -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].
% 6.35/6.55 840 -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].
% 6.35/6.55 841 -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].
% 6.35/6.55 842 -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].
% 6.35/6.55 843 -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].
% 6.35/6.55 844 -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].
% 6.35/6.55 845 -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].
% 6.35/6.55 846 -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].
% 6.35/6.55 847 -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].
% 6.35/6.55 848 -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].
% 6.35/6.55 849 -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].
% 6.35/6.55 850 -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].
% 6.35/6.55 851 -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].
% 6.35/6.55 852 -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].
% 6.35/6.55 853 -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].
% 6.35/6.55 854 -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].
% 6.35/6.55 855 -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].
% 6.35/6.55 856 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 6.35/6.55 857 -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].
% 6.35/6.55 858 -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].
% 6.35/6.55 859 -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].
% 6.35/6.55 860 -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].
% 6.35/6.55 861 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 6.35/6.55 862 -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].
% 6.35/6.55 863 -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].
% 6.35/6.55 864 -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].
% 6.35/6.55 865 -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].
% 6.35/6.55 866 -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].
% 6.35/6.55 867 -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].
% 6.35/6.55 868 -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].
% 6.35/6.55 869 -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].
% 6.35/6.55 870 -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].
% 6.35/6.55 871 -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].
% 6.35/6.55 872 -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].
% 6.35/6.55 873 -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].
% 6.35/6.55 874 -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].
% 6.35/6.55 875 -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].
% 6.35/6.55 876 -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].
% 6.35/6.55 877 -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].
% 6.35/6.55 878 -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].
% 6.35/6.55 879 -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].
% 6.35/6.55 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(821,a,822,a)].
% 6.35/6.55 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(821,a,823,a)].
% 6.35/6.55 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(821,a,824,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(821,a,825,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,826,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,827,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(821,a,828,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,829,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,830,a)].
% 6.35/6.55 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,831,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(821,a,832,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,833,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,834,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(821,a,835,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,836,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,837,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,838,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(821,a,839,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(821,a,840,a)].
% 6.35/6.55 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,841,a)].
% 6.35/6.55 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(821,a,842,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,843,a)].
% 6.35/6.55 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,844,a)].
% 6.35/6.55 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(821,a,845,b)].
% 6.35/6.55 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(821,a,846,b)].
% 6.35/6.55 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(821,a,847,a)].
% 6.35/6.56 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(821,a,848,a)].
% 6.35/6.56 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(821,a,849,a)].
% 6.35/6.56 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(821,a,850,a)].
% 6.35/6.56 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(821,a,851,a)].
% 6.35/6.56 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(821,a,852,a)].
% 6.35/6.56 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(821,a,853,a)].
% 6.35/6.56 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(821,a,854,a)].
% 6.35/6.56 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(821,a,855,a)].
% 6.35/6.56 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(821,a,856,a)].
% 6.35/6.56 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(821,a,857,a)].
% 6.35/6.56 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(821,a,858,a)].
% 6.35/6.56 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(821,a,859,a)].
% 6.35/6.56 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(821,a,860,a)].
% 6.35/6.56 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(821,a,861,a)].
% 6.35/6.56 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(821,a,862,a)].
% 6.35/6.56 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(821,a,863,a)].
% 6.35/6.56 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(821,a,864,a)].
% 6.35/6.56 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(821,a,865,a)].
% 6.35/6.56 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(821,a,866,a)].
% 6.35/6.56 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(821,a,867,a)].
% 6.35/6.56 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(821,a,868,a)].
% 6.35/6.56 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(821,a,869,a)].
% 6.35/6.56 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(821,a,870,a)].
% 6.35/6.56 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(821,a,871,a)].
% 6.35/6.56 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(821,a,872,a)].
% 6.35/6.56 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(821,a,873,a)].
% 6.35/6.56 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(821,a,874,a)].
% 6.35/6.57 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(821,a,875,a)].
% 6.35/6.57 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(821,a,876,a)].
% 6.35/6.57 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(821,a,877,a)].
% 6.35/6.57 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(821,a,878,a)].
% 6.35/6.57 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(821,a,879,a)].
% 6.35/6.57 880 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 6.35/6.57 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(880,a,822,a)].
% 6.35/6.57 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(880,a,823,a)].
% 6.35/6.57 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(880,a,824,a)].
% 6.35/6.57 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(880,a,825,a)].
% 6.35/6.57 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(880,a,826,a)].
% 6.35/6.57 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(880,a,827,a)].
% 6.35/6.57 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(880,a,828,a)].
% 6.35/6.57 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(880,a,829,a)].
% 6.35/6.57 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(880,a,830,a)].
% 6.35/6.57 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(880,a,831,a)].
% 6.35/6.57 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(880,a,832,a)].
% 6.35/6.57 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(880,a,833,a)].
% 6.35/6.57 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(880,a,834,a)].
% 6.35/6.57 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(880,a,835,a)].
% 6.35/6.57 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(880,a,836,a)].
% 6.35/6.57 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(880,a,837,a)].
% 6.35/6.58 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(880,a,838,a)].
% 6.35/6.58 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(880,a,839,a)].
% 6.35/6.58 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(880,a,840,a)].
% 6.35/6.58 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(880,a,841,a)].
% 6.35/6.58 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(880,a,842,a)].
% 6.35/6.58 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(880,a,843,a)].
% 6.35/6.58 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(880,a,844,a)].
% 6.35/6.58 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(880,a,845,b)].
% 6.35/6.58 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(880,a,846,b)].
% 6.35/6.58 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(880,a,847,a)].
% 6.35/6.58 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(880,a,848,a)].
% 6.35/6.58 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(880,a,849,a)].
% 6.35/6.58 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(880,a,850,a)].
% 6.35/6.58 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(880,a,851,a)].
% 6.35/6.58 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(880,a,852,a)].
% 6.35/6.58 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(880,a,853,a)].
% 6.35/6.58 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(880,a,854,a)].
% 6.35/6.58 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(880,a,855,a)].
% 6.35/6.58 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(880,a,856,a)].
% 6.35/6.58 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(880,a,857,a)].
% 6.35/6.58 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(880,a,858,a)].
% 6.35/6.58 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(880,a,859,a)].
% 6.35/6.58 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(880,a,860,a)].
% 6.35/6.58 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(880,a,861,a)].
% 6.35/6.58 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(880,a,862,a)].
% 6.35/6.58 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(880,a,863,a)].
% 6.35/6.58 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(880,a,864,a)].
% 6.35/6.58 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(880,a,865,a)].
% 6.35/6.58 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(880,a,866,a)].
% 6.35/6.58 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(880,a,867,a)].
% 6.35/6.58 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(880,a,868,a)].
% 6.35/6.59 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(880,a,869,a)].
% 6.35/6.59 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(880,a,870,a)].
% 6.35/6.59 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(880,a,871,a)].
% 6.35/6.59 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(880,a,872,a)].
% 6.35/6.59 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(880,a,873,a)].
% 6.35/6.59 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(880,a,874,a)].
% 6.35/6.59 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(880,a,875,a)].
% 6.35/6.59 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(880,a,876,a)].
% 6.35/6.59 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(880,a,877,a)].
% 6.35/6.59 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(880,a,878,a)].
% 6.35/6.59 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(880,a,879,a)].
% 6.35/6.59 881 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 6.35/6.59 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(881,b,822,a)].
% 6.35/6.59 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(881,b,823,a)].
% 6.35/6.59 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(881,b,824,a)].
% 6.35/6.59 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(881,b,825,a)].
% 6.35/6.59 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(881,b,826,a)].
% 6.35/6.59 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(881,b,827,a)].
% 6.35/6.59 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(881,b,828,a)].
% 6.35/6.59 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(881,b,829,a)].
% 6.35/6.59 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(881,b,830,a)].
% 6.35/6.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(881,b,831,a)].
% 6.35/6.59 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(881,b,832,a)].
% 6.35/6.59 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(881,b,833,a)].
% 6.35/6.59 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(881,b,834,a)].
% 6.35/6.59 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(881,b,835,a)].
% 6.35/6.59 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(881,b,836,a)].
% 6.35/6.59 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(881,b,837,a)].
% 6.35/6.59 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(881,b,838,a)].
% 6.35/6.59 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(881,b,839,a)].
% 6.35/6.59 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(881,b,840,a)].
% 6.35/6.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(881,b,841,a)].
% 6.35/6.59 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(881,b,842,a)].
% 6.35/6.59 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(881,b,843,a)].
% 6.35/6.59 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(881,b,844,a)].
% 6.35/6.59 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(881,b,845,b)].
% 6.35/6.59 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(881,b,846,b)].
% 6.35/6.59 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(881,b,847,a)].
% 6.35/6.59 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(881,b,848,a)].
% 6.35/6.59 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(881,b,849,a)].
% 6.35/6.59 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(881,b,850,a)].
% 6.41/6.60 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(881,b,851,a)].
% 6.41/6.60 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(881,b,852,a)].
% 6.41/6.60 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(881,b,853,a)].
% 6.41/6.60 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(881,b,854,a)].
% 6.41/6.60 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(881,b,855,a)].
% 6.41/6.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(881,b,856,a)].
% 6.41/6.60 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(881,b,857,a)].
% 6.41/6.60 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(881,b,858,a)].
% 6.41/6.60 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(881,b,859,a)].
% 6.41/6.60 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(881,b,860,a)].
% 6.41/6.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(881,b,861,a)].
% 6.41/6.60 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(881,b,862,a)].
% 6.41/6.60 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(881,b,863,a)].
% 6.41/6.60 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(881,b,864,a)].
% 6.41/6.60 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(881,b,865,a)].
% 6.41/6.60 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(881,b,866,a)].
% 6.41/6.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(881,b,867,a)].
% 6.41/6.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(881,b,868,a)].
% 6.41/6.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(881,b,869,a)].
% 6.41/6.60 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(881,b,870,a)].
% 6.41/6.60 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(881,b,871,a)].
% 6.41/6.60 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(881,b,872,a)].
% 6.41/6.60 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(881,b,873,a)].
% 6.41/6.61 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(881,b,874,a)].
% 6.41/6.61 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(881,b,875,a)].
% 6.41/6.61 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(881,b,876,a)].
% 6.41/6.61 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(881,b,877,a)].
% 6.41/6.61 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(881,b,878,a)].
% 6.41/6.61 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(881,b,879,a)].
% 6.41/6.61 882 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 6.41/6.61 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(882,a,821,a)].
% 6.41/6.61 Derived: class_LOrder_Olorder(tc_nat). [resolve(882,a,880,a)].
% 6.41/6.61 Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(882,a,881,b)].
% 6.41/6.61 883 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 6.41/6.61 Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(883,a,821,a)].
% 6.41/6.61 Derived: class_LOrder_Ojoin__semilorder(tc_nat). [resolve(883,a,880,a)].
% 6.41/6.61 Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(883,a,881,b)].
% 6.41/6.61 884 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 6.41/6.61 Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(884,a,821,a)].
% 6.41/6.61 Derived: class_LOrder_Omeet__semilorder(tc_nat). [resolve(884,a,880,a)].
% 6.41/6.61 Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(884,a,881,b)].
% 6.41/6.61 885 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 6.41/6.61 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(885,a,821,a)].
% 6.41/6.61 Derived: class_Orderings_Oord(tc_nat). [resolve(885,a,880,a)].
% 6.41/6.61 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(885,a,881,b)].
% 6.41/6.61 886 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 6.41/6.61 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(886,a,821,a)].
% 6.41/6.61 Derived: class_Orderings_Oorder(tc_nat). [resolve(886,a,880,a)].
% 6.41/6.61 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(886,a,881,b)].
% 6.41/6.61 887 -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].
% 6.41/6.61 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(887,b,822,a)].
% 6.41/6.61 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(887,b,823,a)].
% 6.41/6.61 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(887,b,824,a)].
% 6.41/6.62 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(887,b,825,a)].
% 6.41/6.62 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(887,b,826,a)].
% 6.41/6.62 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(887,b,827,a)].
% 6.41/6.62 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(887,b,828,a)].
% 6.41/6.62 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(887,b,829,a)].
% 6.41/6.62 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(887,b,830,a)].
% 6.41/6.62 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(887,b,831,a)].
% 6.41/6.62 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(887,b,832,a)].
% 6.41/6.62 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(887,b,833,a)].
% 6.41/6.62 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(887,b,834,a)].
% 6.41/6.62 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(887,b,835,a)].
% 6.41/6.62 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(887,b,836,a)].
% 6.41/6.62 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(887,b,837,a)].
% 6.41/6.62 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(887,b,838,a)].
% 6.41/6.62 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(887,b,839,a)].
% 6.41/6.62 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(887,b,840,a)].
% 6.41/6.62 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(887,b,841,a)].
% 6.41/6.62 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(887,b,842,a)].
% 6.41/6.62 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(887,b,843,a)].
% 6.41/6.62 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(887,b,844,a)].
% 6.41/6.62 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(887,b,845,b)].
% 6.41/6.62 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(887,b,846,b)].
% 6.41/6.62 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(887,b,847,a)].
% 6.41/6.62 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(887,b,848,a)].
% 6.41/6.62 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(887,b,849,a)].
% 6.41/6.62 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(887,b,850,a)].
% 6.41/6.62 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(887,b,851,a)].
% 6.41/6.62 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(887,b,852,a)].
% 6.41/6.62 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(887,b,853,a)].
% 6.41/6.62 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(887,b,854,a)].
% 6.41/6.62 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(887,b,855,a)].
% 6.41/6.62 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(887,b,856,a)].
% 6.41/6.62 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(887,b,857,a)].
% 6.41/6.62 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(887,b,858,a)].
% 6.41/6.62 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(887,b,859,a)].
% 6.41/6.62 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(887,b,860,a)].
% 6.41/6.62 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(887,b,861,a)].
% 6.41/6.62 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(887,b,862,a)].
% 6.41/6.62 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(887,b,863,a)].
% 6.41/6.62 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(887,b,864,a)].
% 6.41/6.62 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(887,b,865,a)].
% 6.41/6.62 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(887,b,866,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(887,b,867,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(887,b,868,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(887,b,869,a)].
% 6.41/6.63 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(887,b,870,a)].
% 6.41/6.63 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(887,b,871,a)].
% 6.41/6.63 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(887,b,872,a)].
% 6.41/6.63 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(887,b,873,a)].
% 6.41/6.63 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(887,b,874,a)].
% 6.41/6.63 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(887,b,875,a)].
% 6.41/6.63 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(887,b,876,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(887,b,877,a)].
% 6.41/6.63 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(887,b,878,a)].
% 6.41/6.63 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(887,b,879,a)].
% 6.41/6.63 888 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 6.41/6.63 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(888,b,822,a)].
% 6.41/6.63 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(888,b,823,a)].
% 6.41/6.63 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(888,b,824,a)].
% 6.41/6.63 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(888,b,825,a)].
% 6.41/6.63 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(888,b,826,a)].
% 6.41/6.63 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(888,b,827,a)].
% 6.41/6.63 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(888,b,828,a)].
% 6.41/6.63 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(888,b,829,a)].
% 6.41/6.63 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(888,b,830,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(888,b,831,a)].
% 6.41/6.63 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(888,b,832,a)].
% 6.41/6.63 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(888,b,833,a)].
% 6.41/6.63 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(888,b,834,a)].
% 6.41/6.63 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(888,b,835,a)].
% 6.41/6.63 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(888,b,836,a)].
% 6.41/6.63 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(888,b,837,a)].
% 6.41/6.63 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(888,b,838,a)].
% 6.41/6.63 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(888,b,839,a)].
% 6.41/6.63 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(888,b,840,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(888,b,841,a)].
% 6.41/6.63 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(888,b,842,a)].
% 6.41/6.63 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(888,b,843,a)].
% 6.41/6.63 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(888,b,844,a)].
% 6.41/6.63 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(888,b,845,b)].
% 6.41/6.63 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(888,b,846,b)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(888,b,847,a)].
% 6.41/6.63 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(888,b,848,a)].
% 6.41/6.64 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(888,b,849,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(888,b,850,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(888,b,851,a)].
% 6.41/6.64 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(888,b,852,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(888,b,853,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(888,b,854,a)].
% 6.41/6.64 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(888,b,855,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B. [resolve(888,b,856,a)].
% 6.41/6.64 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(888,b,857,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(888,b,858,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(888,b,859,a)].
% 6.41/6.64 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(888,b,860,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B. [resolve(888,b,861,a)].
% 6.41/6.64 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(888,b,862,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(888,b,863,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(888,b,864,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(888,b,865,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(888,b,866,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(888,b,867,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(888,b,868,a)].
% 6.41/6.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(888,b,869,a)].
% 6.41/6.64 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(888,b,870,a)].
% 6.41/6.64 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(888,b,871,a)].
% 6.41/6.64 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(888,b,872,a)].
% 6.41/6.64 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(888,b,873,a)].
% 6.41/6.64 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(888,b,874,a)].
% 6.41/6.65 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(888,b,875,a)].
% 6.41/6.65 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(888,b,876,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(888,b,877,a)].
% 6.41/6.65 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(888,b,878,a)].
% 6.41/6.65 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(888,b,879,a)].
% 6.41/6.65 889 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 6.41/6.65 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(889,b,822,a)].
% 6.41/6.65 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(889,b,823,a)].
% 6.41/6.65 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(889,b,824,a)].
% 6.41/6.65 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(889,b,825,a)].
% 6.41/6.65 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(889,b,826,a)].
% 6.41/6.65 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(889,b,827,a)].
% 6.41/6.65 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(889,b,828,a)].
% 6.41/6.65 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(889,b,829,a)].
% 6.41/6.65 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(889,b,830,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(889,b,831,a)].
% 6.41/6.65 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(889,b,832,a)].
% 6.41/6.65 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(889,b,833,a)].
% 6.41/6.65 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(889,b,834,a)].
% 6.41/6.65 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(889,b,835,a)].
% 6.41/6.65 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(889,b,836,a)].
% 6.41/6.65 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(889,b,837,a)].
% 6.41/6.65 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(889,b,838,a)].
% 6.41/6.65 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(889,b,839,a)].
% 6.41/6.65 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(889,b,840,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(889,b,841,a)].
% 6.41/6.65 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(889,b,842,a)].
% 6.41/6.65 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(889,b,843,a)].
% 6.41/6.65 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(889,b,844,a)].
% 6.41/6.65 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(889,b,845,b)].
% 6.41/6.65 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(889,b,846,b)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(889,b,847,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(889,b,848,a)].
% 6.41/6.65 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(889,b,849,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(889,b,850,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(889,b,851,a)].
% 6.41/6.65 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(889,b,852,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(889,b,853,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(889,b,854,a)].
% 6.41/6.65 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(889,b,855,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(889,b,856,a)].
% 6.41/6.65 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(889,b,857,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(889,b,858,a)].
% 6.41/6.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(889,b,859,a)].
% 6.41/6.65 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(889,b,860,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(889,b,861,a)].
% 6.47/6.66 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(889,b,862,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(889,b,863,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(889,b,864,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(889,b,865,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(889,b,866,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(889,b,867,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(889,b,868,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(889,b,869,a)].
% 6.47/6.66 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(889,b,870,a)].
% 6.47/6.66 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(889,b,871,a)].
% 6.47/6.66 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(889,b,872,a)].
% 6.47/6.66 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(889,b,873,a)].
% 6.47/6.66 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(889,b,874,a)].
% 6.47/6.66 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(889,b,875,a)].
% 6.47/6.66 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(889,b,876,a)].
% 6.47/6.66 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(889,b,877,a)].
% 6.47/6.66 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(889,b,878,a)].
% 6.47/6.66 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(889,b,879,a)].
% 6.47/6.66 890 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 6.47/6.66 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(890,b,822,a)].
% 6.47/6.66 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(890,b,823,a)].
% 6.47/6.66 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(890,b,824,a)].
% 6.47/6.67 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(890,b,825,a)].
% 6.47/6.67 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(890,b,826,a)].
% 6.47/6.67 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(890,b,827,a)].
% 6.47/6.67 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(890,b,828,a)].
% 6.47/6.67 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(890,b,829,a)].
% 6.47/6.67 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(890,b,830,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(890,b,831,a)].
% 6.47/6.67 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(890,b,832,a)].
% 6.47/6.67 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(890,b,833,a)].
% 6.47/6.67 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(890,b,834,a)].
% 6.47/6.67 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(890,b,835,a)].
% 6.47/6.67 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(890,b,836,a)].
% 6.47/6.67 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(890,b,837,a)].
% 6.47/6.67 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(890,b,838,a)].
% 6.47/6.67 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(890,b,839,a)].
% 6.47/6.67 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(890,b,840,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(890,b,841,a)].
% 6.47/6.67 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(890,b,842,a)].
% 6.47/6.67 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(890,b,843,a)].
% 6.47/6.67 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(890,b,844,a)].
% 6.47/6.67 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(890,b,845,b)].
% 6.47/6.67 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(890,b,846,b)].
% 6.47/6.67 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(890,b,847,a)].
% 6.47/6.67 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(890,b,848,a)].
% 6.47/6.67 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(890,b,849,a)].
% 6.47/6.67 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(890,b,850,a)].
% 6.47/6.67 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(890,b,851,a)].
% 6.47/6.67 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(890,b,852,a)].
% 6.47/6.67 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(890,b,853,a)].
% 6.47/6.67 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(890,b,854,a)].
% 6.47/6.67 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(890,b,855,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(890,b,856,a)].
% 6.47/6.67 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(890,b,857,a)].
% 6.47/6.67 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(890,b,858,a)].
% 6.47/6.67 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(890,b,859,a)].
% 6.47/6.67 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(890,b,860,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(890,b,861,a)].
% 6.47/6.67 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(890,b,862,a)].
% 6.47/6.67 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(890,b,863,a)].
% 6.47/6.67 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(890,b,864,a)].
% 6.47/6.67 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(890,b,865,a)].
% 6.47/6.67 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(890,b,866,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(890,b,867,a)].
% 6.47/6.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(890,b,868,a)].
% 6.47/6.68 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(890,b,869,a)].
% 6.47/6.68 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(890,b,870,a)].
% 6.47/6.68 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(890,b,871,a)].
% 6.47/6.68 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(890,b,872,a)].
% 6.47/6.68 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(890,b,873,a)].
% 6.47/6.68 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(890,b,874,a)].
% 6.47/6.68 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(890,b,875,a)].
% 6.47/6.68 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(890,b,876,a)].
% 6.47/6.68 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(890,b,877,a)].
% 6.47/6.68 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(890,b,878,a)].
% 6.47/6.68 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(890,b,879,a)].
% 6.47/6.68 891 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 6.47/6.68 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(891,b,822,a)].
% 6.47/6.68 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(891,b,823,a)].
% 6.47/6.68 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(891,b,824,a)].
% 6.47/6.68 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(891,b,825,a)].
% 6.47/6.68 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(891,b,826,a)].
% 6.47/6.68 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(891,b,827,a)].
% 6.47/6.68 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(891,b,828,a)].
% 6.47/6.68 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(891,b,829,a)].
% 6.47/6.69 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(891,b,830,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,831,a)].
% 6.47/6.69 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(891,b,832,a)].
% 6.47/6.69 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(891,b,833,a)].
% 6.47/6.69 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(891,b,834,a)].
% 6.47/6.69 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(891,b,835,a)].
% 6.47/6.69 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(891,b,836,a)].
% 6.47/6.69 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(891,b,837,a)].
% 6.47/6.69 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(891,b,838,a)].
% 6.47/6.69 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(891,b,839,a)].
% 6.47/6.69 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(891,b,840,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 6.47/6.69 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(891,b,842,a)].
% 6.47/6.69 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(891,b,843,a)].
% 6.47/6.69 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(891,b,844,a)].
% 6.47/6.69 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(891,b,845,b)].
% 6.47/6.69 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(891,b,846,b)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(891,b,847,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(891,b,848,a)].
% 6.47/6.69 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(891,b,849,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(891,b,850,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(891,b,851,a)].
% 6.47/6.69 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(891,b,852,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(891,b,853,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(891,b,854,a)].
% 6.47/6.69 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(891,b,855,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,856,a)].
% 6.47/6.69 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(891,b,857,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(891,b,858,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(891,b,859,a)].
% 6.47/6.69 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(891,b,860,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,861,a)].
% 6.47/6.69 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(891,b,862,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(891,b,863,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(891,b,864,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(891,b,865,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(891,b,866,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,867,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,868,a)].
% 6.47/6.69 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,869,a)].
% 6.47/6.69 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(891,b,870,a)].
% 6.47/6.69 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(891,b,871,a)].
% 6.47/6.69 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(891,b,872,a)].
% 6.47/6.69 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(891,b,873,a)].
% 6.47/6.69 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(891,b,874,a)].
% 6.47/6.69 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(891,b,875,a)].
% 6.47/6.69 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(891,b,876,a)].
% 6.47/6.70 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,877,a)].
% 6.47/6.70 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(891,b,878,a)].
% 6.47/6.70 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(891,b,879,a)].
% 6.47/6.70 892 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 6.47/6.70 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(892,b,822,a)].
% 6.47/6.70 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(892,b,823,a)].
% 6.47/6.70 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(892,b,824,a)].
% 6.47/6.70 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(892,b,825,a)].
% 6.47/6.70 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(892,b,826,a)].
% 6.47/6.70 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(892,b,827,a)].
% 6.47/6.70 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(892,b,828,a)].
% 6.47/6.70 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(892,b,829,a)].
% 6.47/6.70 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(892,b,830,a)].
% 6.47/6.70 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(892,b,831,a)].
% 6.47/6.70 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(892,b,832,a)].
% 6.47/6.70 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(892,b,833,a)].
% 6.47/6.70 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(892,b,834,a)].
% 6.47/6.70 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(892,b,835,a)].
% 6.47/6.70 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(892,b,836,a)].
% 6.47/6.71 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(892,b,837,a)].
% 6.47/6.71 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(892,b,838,a)].
% 6.47/6.71 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(892,b,839,a)].
% 6.47/6.71 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(892,b,840,a)].
% 6.47/6.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(892,b,841,a)].
% 6.47/6.71 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(892,b,842,a)].
% 6.47/6.71 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(892,b,843,a)].
% 6.47/6.71 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(892,b,844,a)].
% 6.47/6.71 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(892,b,845,b)].
% 6.47/6.71 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(892,b,846,b)].
% 6.47/6.71 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(892,b,847,a)].
% 6.47/6.71 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(892,b,848,a)].
% 6.47/6.71 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(892,b,849,a)].
% 6.47/6.71 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(892,b,850,a)].
% 6.47/6.71 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(892,b,851,a)].
% 6.47/6.71 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(892,b,852,a)].
% 6.47/6.71 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(892,b,853,a)].
% 6.47/6.71 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(892,b,854,a)].
% 6.47/6.71 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(892,b,855,a)].
% 6.47/6.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(892,b,856,a)].
% 6.47/6.71 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(892,b,857,a)].
% 6.47/6.71 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(892,b,858,a)].
% 6.47/6.71 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(892,b,859,a)].
% 6.47/6.72 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(892,b,860,a)].
% 6.47/6.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(892,b,861,a)].
% 6.47/6.72 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(892,b,862,a)].
% 6.47/6.72 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(892,b,863,a)].
% 6.47/6.72 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(892,b,864,a)].
% 6.47/6.72 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(892,b,865,a)].
% 6.47/6.72 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(892,b,866,a)].
% 6.47/6.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(892,b,867,a)].
% 6.47/6.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(892,b,868,a)].
% 6.47/6.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(892,b,869,a)].
% 6.47/6.72 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(892,b,870,a)].
% 6.47/6.72 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(892,b,871,a)].
% 6.47/6.72 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(892,b,872,a)].
% 6.47/6.72 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(892,b,873,a)].
% 6.47/6.72 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(892,b,874,a)].
% 6.47/6.72 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(892,b,875,a)].
% 6.47/6.72 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(892,b,876,a)].
% 6.47/6.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(892,b,877,a)].
% 6.47/6.72 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(892,b,878,a)].
% 6.47/6.72 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(892,b,879,a)].
% 6.47/6.72 893 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 6.47/6.72 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(893,b,822,a)].
% 6.47/6.72 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(893,b,823,a)].
% 6.47/6.72 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(893,b,824,a)].
% 6.47/6.72 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(893,b,825,a)].
% 6.47/6.72 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(893,b,826,a)].
% 6.47/6.72 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(893,b,827,a)].
% 6.47/6.72 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(893,b,828,a)].
% 6.47/6.72 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(893,b,829,a)].
% 6.47/6.72 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(893,b,830,a)].
% 6.47/6.72 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,831,a)].
% 6.47/6.72 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(893,b,832,a)].
% 6.47/6.72 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(893,b,833,a)].
% 6.47/6.72 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(893,b,834,a)].
% 6.47/6.72 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(893,b,835,a)].
% 6.47/6.72 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(893,b,836,a)].
% 6.47/6.72 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(893,b,837,a)].
% 6.47/6.72 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(893,b,838,a)].
% 6.47/6.72 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(893,b,839,a)].
% 6.47/6.72 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(893,b,840,a)].
% 6.47/6.72 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,841,a)].
% 6.47/6.72 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(893,b,842,a)].
% 6.47/6.73 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(893,b,843,a)].
% 6.47/6.73 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(893,b,844,a)].
% 6.47/6.73 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(893,b,845,b)].
% 6.47/6.73 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(893,b,846,b)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(893,b,847,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(893,b,848,a)].
% 6.47/6.73 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(893,b,849,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(893,b,850,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(893,b,851,a)].
% 6.47/6.73 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(893,b,852,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(893,b,853,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(893,b,854,a)].
% 6.47/6.73 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(893,b,855,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(893,b,856,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(893,b,857,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(893,b,858,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(893,b,859,a)].
% 6.47/6.73 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(893,b,860,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(893,b,861,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(893,b,862,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(893,b,863,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(893,b,864,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(893,b,865,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(893,b,866,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(893,b,867,a)].
% 6.47/6.73 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(893,b,868,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(893,b,869,a)].
% 6.78/7.01 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(893,b,870,a)].
% 6.78/7.01 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(893,b,871,a)].
% 6.78/7.01 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(893,b,872,a)].
% 6.78/7.01 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(893,b,873,a)].
% 6.78/7.01 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(893,b,874,a)].
% 6.78/7.01 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(893,b,875,a)].
% 6.78/7.01 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(893,b,876,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(893,b,877,a)].
% 6.78/7.01 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(893,b,878,a)].
% 6.78/7.01 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(893,b,879,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(893,b,882,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(893,b,883,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(893,b,884,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(893,b,885,a)].
% 6.78/7.01 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(893,b,886,a)].
% 6.78/7.01 894 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 6.78/7.01 895 -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].
% 6.78/7.01 896 -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].
% 6.78/7.01 897 -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].
% 6.78/7.01 898 -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].
% 6.78/7.01 899 -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].
% 6.78/7.01 900 -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].
% 6.78/7.01 901 -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].
% 6.78/7.01 902 -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].
% 6.78/7.01 903 -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].
% 6.78/7.01 904 -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].
% 6.78/7.01 905 -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].
% 6.78/7.01 906 -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].
% 6.78/7.01 907 -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].
% 6.78/7.01 908 -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].
% 6.78/7.01 909 -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].
% 6.78/7.01 910 -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_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_1) # label(axiom). [assumption].
% 6.78/7.01 911 -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].
% 6.78/7.01 912 -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_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_1) # label(axiom). [assumption].
% 6.78/7.01 913 -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].
% 6.78/7.01 914 -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].
% 6.78/7.01 915 -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].
% 6.78/7.01 916 -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].
% 6.78/7.01 917 -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].
% 6.78/7.01 918 -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].
% 6.78/7.01 919 -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].
% 6.78/7.01 920 -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].
% 6.78/7.01 921 -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].
% 6.78/7.01 922 -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].
% 6.78/7.01 923 -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].
% 6.78/7.01 924 -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].
% 6.78/7.01 925 -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].
% 6.78/7.01 926 -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].
% 6.78/7.01 927 -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].
% 6.78/7.01 928 -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].
% 6.78/7.01 929 -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].
% 6.78/7.01 930 -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].
% 6.78/7.01 931 -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].
% 6.78/7.01 932 -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].
% 6.78/7.01 933 -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].
% 6.78/7.01 934 -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].
% 6.78/7.01 935 -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].
% 6.78/7.01 936 -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].
% 6.78/7.01 937 -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].
% 6.78/7.01 938 -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].
% 6.78/7.01 939 -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].
% 6.78/7.01 940 -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].
% 6.78/7.01 941 -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].
% 6.78/7.01 942 -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].
% 6.78/7.01 943 -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].
% 6.78/7.01 944 -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].
% 6.78/7.01 945 -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].
% 6.78/7.01 946 -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].
% 6.78/7.01 947 -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].
% 6.78/7.01 948 -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].
% 6.78/7.01 949 -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].
% 6.78/7.01 950 -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].
% 6.78/7.01 951 -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].
% 6.78/7.01 952 -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].
% 6.78/7.01 953 -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].
% 6.78/7.01 954 -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].
% 6.78/7.01 955 -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].
% 6.78/7.01 956 -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].
% 6.78/7.01 957 -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].
% 6.78/7.01 958 -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].
% 6.78/7.01 959 -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].
% 6.84/7.01 960 -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].
% 6.84/7.01 961 -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].
% 6.84/7.01 962 -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].
% 6.84/7.01 963 -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].
% 6.84/7.01 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(894,a,895,a)].
% 6.84/7.01 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(894,a,896,a)].
% 6.84/7.01 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(894,a,897,a)].
% 6.84/7.01 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(894,a,898,a)].
% 6.84/7.01 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(894,a,899,a)].
% 6.84/7.01 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(894,a,900,a)].
% 6.84/7.01 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(894,a,901,a)].
% 6.84/7.01 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(894,a,902,a)].
% 6.84/7.01 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(894,a,903,a)].
% 6.84/7.01 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(894,a,904,a)].
% 6.84/7.01 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(894,a,905,a)].
% 6.84/7.02 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(894,a,906,a)].
% 6.84/7.02 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(894,a,907,a)].
% 6.84/7.02 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(894,a,908,a)].
% 6.84/7.02 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(894,a,909,a)].
% 6.84/7.02 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(894,a,910,a)].
% 6.84/7.02 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(894,a,911,a)].
% 6.84/7.02 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(894,a,912,a)].
% 6.84/7.02 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(894,a,913,a)].
% 6.84/7.02 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(894,a,914,a)].
% 6.84/7.02 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(894,a,915,a)].
% 6.84/7.02 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(894,a,916,a)].
% 6.84/7.02 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(894,a,917,a)].
% 6.84/7.02 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(894,a,918,a)].
% 6.84/7.02 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(894,a,919,a)].
% 6.84/7.02 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(894,a,920,a)].
% 6.84/7.02 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(894,a,921,a)].
% 6.84/7.02 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(894,a,922,a)].
% 6.84/7.02 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(894,a,923,a)].
% 6.84/7.02 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(894,a,924,a)].
% 6.84/7.02 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(894,a,925,a)].
% 6.84/7.02 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(894,a,926,a)].
% 6.84/7.02 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(894,a,927,a)].
% 6.84/7.02 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(894,a,928,a)].
% 6.84/7.02 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(894,a,929,a)].
% 6.84/7.02 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(894,a,930,a)].
% 6.84/7.02 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(894,a,931,a)].
% 6.84/7.02 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(894,a,932,a)].
% 6.84/7.02 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(894,a,933,a)].
% 6.84/7.02 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(894,a,934,a)].
% 6.84/7.02 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(894,a,935,a)].
% 6.84/7.02 Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(894,a,936,a)].
% 6.84/7.02 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(894,a,937,a)].
% 6.84/7.02 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(894,a,938,a)].
% 6.84/7.03 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(894,a,939,a)].
% 6.84/7.03 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(894,a,940,a)].
% 6.84/7.03 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(894,a,941,a)].
% 6.84/7.03 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(894,a,942,a)].
% 6.84/7.03 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(894,a,943,a)].
% 6.84/7.03 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(894,a,944,a)].
% 6.84/7.03 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(894,a,945,a)].
% 6.84/7.03 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(894,a,946,a)].
% 6.84/7.03 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(894,a,947,a)].
% 6.84/7.03 Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(894,a,948,a)].
% 6.84/7.03 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(894,a,949,a)].
% 6.84/7.03 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(894,a,950,a)].
% 6.84/7.03 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(894,a,951,a)].
% 6.84/7.03 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(894,a,952,a)].
% 6.84/7.03 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(894,a,953,a)].
% 6.84/7.03 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(894,a,954,a)].
% 6.84/7.03 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(894,a,955,a)].
% 6.84/7.07 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(894,a,956,a)].
% 6.84/7.07 Derived: c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(894,a,957,a)].
% 6.84/7.07 Derived: c_times(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(894,a,958,a)].
% 6.84/7.07 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(894,a,959,a)].
% 6.84/7.07 Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0. [resolve(894,a,960,a)].
% 6.84/7.07 Derived: c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_IntDef_Oint) = c_1. [resolve(894,a,961,a)].
% 6.84/7.07 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(894,a,962,a)].
% 6.84/7.07 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(894,a,963,a)].
% 6.84/7.07 964 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom). [assumption].
% 6.84/7.07 965 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom). [assumption].
% 6.84/7.07 966 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom). [assumption].
% 6.84/7.07 967 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 6.84/7.07 968 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 6.84/7.07 969 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 6.84/7.07 970 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 6.84/7.07 Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(970,a,894,a)].
% 6.84/7.07 971 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom). [assumption].
% 6.84/7.07 972 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom). [assumption].
% 6.84/7.07 Derived: class_Numeral_Onumber(tc_IntDef_Oint). [resolve(972,a,894,a)].
% 6.84/7.07 973 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 6.84/7.07 974 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom). [assumption].
% 6.84/7.07 975 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 6.84/7.07 976 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 6.84/7.07 977 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 6.84/7.07 978 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 6.84/7.07 979 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 6.84/7.07 980 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 6.84/7.07 981 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 6.84/7.07 982 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 6.90/7.11 983 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 6.90/7.11 984 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 6.90/7.11 985 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 6.90/7.11 986 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(108,a,88,b)].
% 6.90/7.11 987 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(109,a,88,b)].
% 6.90/7.11 988 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(116,b,110,a)].
% 6.90/7.11 989 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(116,b,113,a)].
% 6.90/7.11 990 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(118,a,116,b)].
% 6.90/7.11 991 -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(138,b,133,b)].
% 6.90/7.11 992 -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(138,b,135,b)].
% 6.90/7.11 993 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(198,b,177,b)].
% 6.90/7.11 994 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(199,b,177,b)].
% 6.90/7.11 995 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(200,a,177,b)].
% 6.90/7.11 996 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(201,a,177,b)].
% 6.90/7.11 997 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 6.90/7.11 998 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 6.90/7.11 999 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(205,b,177,b)].
% 6.90/7.11 1000 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(206,b,177,b)].
% 6.90/7.11 1001 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 6.90/7.11 1002 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 6.90/7.11 1003 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(282,b,251,b)].
% 6.90/7.11 1004 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(283,b,251,b)].
% 6.90/7.11 1005 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(284,c,251,b)].
% 6.90/7.11 1006 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(285,c,251,b)].
% 6.90/7.11 1007 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(291,b,286,a)].
% 6.90/7.11 1008 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(291,b,288,a)].
% 6.90/7.11 1009 -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(334,b,327,b)].
% 6.90/7.11 1010 -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(334,b,329,b)].
% 6.90/7.11 1011 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(334,b,330,a)].
% 6.90/7.11 1012 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(334,b,331,a)].
% 6.90/7.11 1013 -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(334,b,332,a)].
% 6.90/7.13 1014 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(350,a,334,b)].
% 6.90/7.13 1015 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(351,a,334,b)].
% 6.90/7.13 1016 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(368,a,334,b)].
% 6.90/7.13 1017 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(369,a,334,b)].
% 6.90/7.13 1018 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(370,c,334,b)].
% 6.90/7.13 1019 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(371,c,334,b)].
% 6.90/7.13 1020 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(405,b,377,b)].
% 6.90/7.13 1021 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(406,b,377,b)].
% 6.90/7.13 1022 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(444,b,418,b)].
% 6.90/7.13 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(1022,b,894,a)].
% 6.90/7.13 1023 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(445,b,418,b)].
% 6.90/7.13 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1023,b,894,a)].
% 6.90/7.13 1024 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(451,b,418,b)].
% 6.90/7.13 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1024,b,894,a)].
% 6.90/7.13 1025 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(452,b,418,b)].
% 6.90/7.13 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1025,b,894,a)].
% 6.90/7.13 1026 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(455,b,418,b)].
% 6.90/7.13 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1026,b,894,a)].
% 6.90/7.13 1027 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(456,b,418,b)].
% 6.90/7.13 1028 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(457,c,418,b)].
% 6.90/7.13 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(1028,c,894,a)].
% 6.90/7.13 1029 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(458,c,418,b)].
% 6.90/7.13 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(1029,c,894,a)].
% 6.90/7.13 1030 -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(463,a,418,b)].
% 6.90/7.13 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(1030,c,894,a)].
% 6.90/7.13 1031 -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(464,a,418,b)].
% 6.90/7.13 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(1031,c,894,a)].
% 6.90/7.15 1032 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(465,a,418,b)].
% 6.90/7.15 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(1032,b,894,a)].
% 6.90/7.15 1033 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(466,a,418,b)].
% 6.90/7.15 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(1033,b,894,a)].
% 6.90/7.15 1034 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(467,a,418,b)].
% 6.90/7.15 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(1034,b,894,a)].
% 6.90/7.15 1035 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(468,b,418,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1035,b,894,a)].
% 6.90/7.15 1036 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(469,b,418,b)].
% 6.90/7.15 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1036,b,894,a)].
% 6.90/7.15 1037 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(470,b,418,b)].
% 6.90/7.15 1038 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(471,b,418,b)].
% 6.90/7.15 1039 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(472,c,418,b)].
% 6.90/7.15 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1039,c,894,a)].
% 6.90/7.15 1040 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(473,c,418,b)].
% 6.90/7.15 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1040,c,894,a)].
% 6.90/7.15 1041 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(475,b,418,b)].
% 6.90/7.15 1042 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(476,b,418,b)].
% 6.90/7.15 1043 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(520,a,501,b)].
% 6.90/7.15 1044 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(521,a,501,b)].
% 6.90/7.15 1045 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(537,a,530,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(1045,b,894,a)].
% 6.90/7.15 1046 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(562,b,530,b)].
% 6.90/7.15 1047 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(563,b,530,b)].
% 6.90/7.15 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1047,b,894,a)].
% 6.90/7.15 1048 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(564,b,530,b)].
% 6.90/7.15 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1048,b,894,a)].
% 6.90/7.15 1049 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(565,b,530,b)].
% 6.90/7.15 1050 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(566,b,530,b)].
% 6.90/7.15 1051 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(653,b,607,b)].
% 6.90/7.15 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1051,b,894,a)].
% 6.90/7.15 1052 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(654,b,607,b)].
% 6.90/7.15 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1052,b,894,a)].
% 6.90/7.15 1053 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(656,b,607,b)].
% 6.90/7.15 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1053,b,894,a)].
% 6.90/7.15 1054 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(657,b,607,b)].
% 6.90/7.15 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1054,b,894,a)].
% 6.90/7.15 1055 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(671,b,658,a)].
% 6.90/7.15 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1055,a,894,a)].
% 6.90/7.15 1056 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(671,b,660,a)].
% 6.90/7.15 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1056,a,894,a)].
% 6.90/7.15 1057 -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(671,b,661,a)].
% 6.90/7.15 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(1057,a,894,a)].
% 7.14/7.36 1058 -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(671,b,662,a)].
% 7.14/7.36 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(1058,a,894,a)].
% 7.14/7.36 1059 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(671,b,663,a)].
% 7.14/7.36 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1059,a,894,a)].
% 7.14/7.36 1060 -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(671,b,664,a)].
% 7.14/7.36 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(1060,a,894,a)].
% 7.14/7.36 1061 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(671,b,665,a)].
% 7.14/7.36 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1061,a,894,a)].
% 7.14/7.36 1062 -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(671,b,666,a)].
% 7.14/7.36 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(1062,a,894,a)].
% 7.14/7.36 1063 -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(671,b,667,a)].
% 7.14/7.36 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(1063,a,894,a)].
% 7.14/7.36 1064 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(671,b,668,a)].
% 7.14/7.36 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1064,a,894,a)].
% 7.14/7.36 1065 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(718,b,671,b)].
% 7.14/7.36 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(1065,b,894,a)].
% 7.14/7.36 1066 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(813,a,724,a)].
% 7.14/7.36 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1066,a,894,a)].
% 7.14/7.36 1067 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 7.14/7.36 1068 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 7.14/7.36 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1067,a,1068,a)].
% 7.14/7.36 1069 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 7.14/7.36 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1069,a,1068,a)].
% 7.14/7.36 1070 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 7.14/7.36 1071 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 7.14/7.36 1072 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 7.14/7.36 Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1072,b,1068,a)].
% 7.14/7.36 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1072,b,1070,a)].
% 7.14/7.36 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1072,b,1071,a)].
% 7.14/7.36 1073 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 7.14/7.36 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1073,b,1068,a)].
% 7.14/7.36 1074 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 7.14/7.36 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1074,b,1068,a)].
% 7.45/7.64 1075 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1075,b,1068,a)].
% 7.45/7.64 1076 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1076,b,1068,a)].
% 7.45/7.64 1077 -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].
% 7.45/7.64 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1077,b,1068,a)].
% 7.45/7.64 1078 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1078,b,1068,a)].
% 7.45/7.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1078,b,1070,a)].
% 7.45/7.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1078,b,1071,a)].
% 7.45/7.64 1079 -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].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1079,b,1068,a)].
% 7.45/7.64 1080 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1068,a)].
% 7.45/7.64 1081 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1068,a)].
% 7.45/7.64 1082 -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].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1068,a)].
% 7.45/7.64 1083 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1068,a)].
% 7.45/7.64 1084 -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].
% 7.45/7.64 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1068,a)].
% 7.45/7.64 1085 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 7.45/7.64 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1068,a)].
% 7.45/7.64 1086 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(883,a,821,a)].
% 7.45/7.64 1087 class_LOrder_Ojoin__semilorder(tc_nat). [resolve(883,a,880,a)].
% 7.45/7.64 1088 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(883,a,881,b)].
% 7.45/7.64 1089 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(893,b,883,a)].
% 7.45/7.64 1090 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 7.45/7.64 1091 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 7.45/7.67 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1090,a,1091,a)].
% 7.45/7.67 1092 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 7.45/7.67 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1092,a,1091,a)].
% 7.45/7.67 1093 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1093,b,1091,a)].
% 7.45/7.67 1094 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 7.45/7.67 1095 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 7.45/7.67 1096 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1096,b,1091,a)].
% 7.45/7.67 1097 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1097,b,1091,a)].
% 7.45/7.67 1098 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1098,b,1091,a)].
% 7.45/7.67 1099 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1099,b,1091,a)].
% 7.45/7.67 1100 -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].
% 7.45/7.67 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1100,b,1091,a)].
% 7.45/7.67 1101 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1091,a)].
% 7.45/7.67 1102 -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].
% 7.45/7.67 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1102,b,1091,a)].
% 7.45/7.67 1103 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1103,b,1091,a)].
% 7.45/7.67 1104 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1091,a)].
% 7.45/7.67 1105 -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].
% 7.45/7.67 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1091,a)].
% 7.45/7.67 1106 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 7.45/7.67 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1091,a)].
% 7.45/7.67 1107 -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].
% 7.75/7.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1091,a)].
% 7.75/7.93 1108 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 7.75/7.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1091,a)].
% 7.75/7.93 1109 class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(884,a,821,a)].
% 7.75/7.93 1110 class_LOrder_Omeet__semilorder(tc_nat). [resolve(884,a,880,a)].
% 7.75/7.93 1111 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(884,a,881,b)].
% 7.75/7.93 1112 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(893,b,884,a)].
% 7.75/7.93 1113 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 7.75/7.93 1114 -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].
% 7.75/7.93 1115 -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].
% 7.75/7.93 1116 -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].
% 7.75/7.93 1117 -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].
% 7.75/7.93 1118 -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].
% 7.75/7.93 1119 -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].
% 7.75/7.93 1120 -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].
% 7.75/7.93 1121 -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].
% 7.75/7.93 1122 -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].
% 7.75/7.93 1123 -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].
% 7.75/7.93 1124 -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].
% 7.75/7.93 1125 -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].
% 7.75/7.93 1126 -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].
% 7.75/7.93 1127 -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].
% 7.75/7.93 1128 -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].
% 7.75/7.93 1129 -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].
% 7.75/7.93 1130 -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].
% 7.75/7.94 1131 -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].
% 7.75/7.94 1132 -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].
% 7.75/7.94 1133 -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].
% 7.75/7.94 1134 -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].
% 7.75/7.94 1135 -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].
% 7.75/7.94 1136 -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].
% 7.75/7.94 1137 -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].
% 7.75/7.94 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(1113,a,1114,a)].
% 7.75/7.94 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(1113,a,1115,a)].
% 7.75/7.94 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1113,a,1116,a)].
% 7.75/7.94 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(1113,a,1117,a)].
% 7.75/7.94 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1113,a,1118,a)].
% 7.75/7.94 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1113,a,1119,a)].
% 7.75/7.94 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(1113,a,1120,a)].
% 7.75/7.94 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(1113,a,1121,a)].
% 7.75/7.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1113,a,1122,a)].
% 7.75/7.94 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1113,a,1123,a)].
% 7.75/7.94 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(1113,a,1124,a)].
% 7.75/7.94 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(1113,a,1125,a)].
% 7.75/7.94 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1113,a,1126,a)].
% 7.75/7.94 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(1113,a,1127,a)].
% 7.75/7.94 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(1113,a,1128,a)].
% 7.75/7.94 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(1113,a,1129,b)].
% 7.75/7.94 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(1113,a,1130,b)].
% 7.75/7.94 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(1113,a,1131,b)].
% 7.75/7.94 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(1113,a,1132,b)].
% 7.75/7.96 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(1113,a,1133,b)].
% 7.75/7.96 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(1113,a,1134,a)].
% 7.75/7.96 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(1113,a,1135,a)].
% 7.75/7.96 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(1113,a,1136,a)].
% 7.75/7.96 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(1113,a,1137,a)].
% 7.75/7.96 1138 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 7.75/7.96 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(1138,a,1114,a)].
% 7.75/7.96 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(1138,a,1115,a)].
% 7.75/7.96 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1138,a,1116,a)].
% 7.75/7.96 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat). [resolve(1138,a,1117,a)].
% 7.75/7.96 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1138,a,1118,a)].
% 7.75/7.96 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(1138,a,1119,a)].
% 7.75/7.96 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(1138,a,1120,a)].
% 7.75/7.96 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(1138,a,1121,a)].
% 7.75/7.96 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(1138,a,1122,a)].
% 7.75/7.96 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(1138,a,1123,a)].
% 7.75/7.96 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(1138,a,1124,a)].
% 7.75/7.96 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(1138,a,1125,a)].
% 7.75/7.96 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat). [resolve(1138,a,1126,a)].
% 7.75/7.96 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(1138,a,1127,a)].
% 7.75/7.96 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(1138,a,1128,a)].
% 7.75/7.96 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(1138,a,1129,b)].
% 7.75/7.96 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(1138,a,1130,b)].
% 7.75/7.96 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(1138,a,1131,b)].
% 7.75/7.96 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(1138,a,1132,b)].
% 7.75/7.96 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(1138,a,1133,b)].
% 7.75/7.96 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(1138,a,1134,a)].
% 7.75/7.96 Derived: -c_less(c_1,c_0,tc_nat). [resolve(1138,a,1135,a)].
% 7.75/7.96 Derived: c_less(c_0,c_1,tc_nat). [resolve(1138,a,1136,a)].
% 7.75/7.96 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(1138,a,1137,a)].
% 7.75/7.96 1139 -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].
% 7.75/7.96 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1139,b,1114,a)].
% 7.75/7.96 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1139,b,1115,a)].
% 7.75/7.96 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1139,b,1116,a)].
% 7.75/7.96 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(1139,b,1117,a)].
% 7.80/7.97 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(1139,b,1118,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1139,b,1119,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1139,b,1120,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1139,b,1121,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1139,b,1122,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1139,b,1123,a)].
% 7.80/7.97 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(1139,b,1124,a)].
% 7.80/7.97 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(1139,b,1125,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1139,b,1126,a)].
% 7.80/7.97 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(1139,b,1127,a)].
% 7.80/7.97 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(1139,b,1128,a)].
% 7.80/7.97 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(1139,b,1129,b)].
% 7.80/7.97 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(1139,b,1130,b)].
% 7.80/7.97 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(1139,b,1131,b)].
% 7.80/7.97 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(1139,b,1132,b)].
% 7.80/7.97 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(1139,b,1133,b)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A). [resolve(1139,b,1134,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A). [resolve(1139,b,1135,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A). [resolve(1139,b,1136,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A). [resolve(1139,b,1137,a)].
% 7.80/7.97 1140 -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].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1140,b,1114,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1140,b,1115,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1140,b,1116,a)].
% 7.80/7.97 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(1140,b,1117,a)].
% 7.80/7.97 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(1140,b,1118,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1140,b,1119,a)].
% 7.80/7.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1140,b,1120,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1140,b,1121,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1140,b,1122,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1140,b,1123,a)].
% 7.80/7.98 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(1140,b,1124,a)].
% 7.80/7.98 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(1140,b,1125,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1140,b,1126,a)].
% 7.80/7.98 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(1140,b,1127,a)].
% 7.80/7.98 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(1140,b,1128,a)].
% 7.80/7.98 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(1140,b,1129,b)].
% 7.80/7.98 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(1140,b,1130,b)].
% 7.80/7.98 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(1140,b,1131,b)].
% 7.80/7.98 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(1140,b,1132,b)].
% 7.80/7.98 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(1140,b,1133,b)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A). [resolve(1140,b,1134,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A). [resolve(1140,b,1135,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A). [resolve(1140,b,1136,a)].
% 7.80/7.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A). [resolve(1140,b,1137,a)].
% 7.80/7.98 1141 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 7.80/7.98 1142 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom). [assumption].
% 7.80/7.98 1143 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 7.80/7.98 1144 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom). [assumption].
% 7.80/7.98 1145 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 7.80/7.98 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1145,a,1140,b)].
% 7.80/7.98 1146 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 7.80/7.98 1147 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom). [assumption].
% 7.80/7.98 1148 -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].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1148,a,1113,a)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1148,a,1138,a)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1148,a,1139,b)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1148,a,1140,b)].
% 7.80/7.99 1149 -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].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1149,a,1113,a)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1149,a,1138,a)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1149,a,1139,b)].
% 7.80/7.99 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1149,a,1140,b)].
% 7.80/7.99 1150 -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].
% 7.80/7.99 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1150,a,1113,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1150,a,1138,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1150,a,1139,b)].
% 7.80/7.99 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1150,a,1140,b)].
% 7.80/7.99 1151 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 7.80/7.99 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1151,a,1139,b)].
% 7.80/7.99 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1151,a,1140,b)].
% 7.80/7.99 1152 -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].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1152,a,1113,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1152,a,1138,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1152,a,1139,b)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1152,a,1140,b)].
% 7.80/7.99 1153 -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].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1153,a,1113,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1153,a,1138,a)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1153,a,1139,b)].
% 7.80/7.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1140,b)].
% 7.80/7.99 1154 -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].
% 7.80/7.99 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1154,a,1113,a)].
% 7.80/7.99 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1154,a,1138,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1154,a,1139,b)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1154,a,1140,b)].
% 7.80/8.01 1155 -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].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1155,a,1113,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1155,a,1138,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1155,a,1139,b)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1155,a,1140,b)].
% 7.80/8.01 1156 -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].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1156,a,1113,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1156,a,1138,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1139,b)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1140,b)].
% 7.80/8.01 1157 -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].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1157,a,1113,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1157,a,1138,a)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1139,b)].
% 7.80/8.01 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1140,b)].
% 7.80/8.01 1158 -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].
% 7.80/8.01 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1113,a)].
% 7.80/8.01 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1158,a,1138,a)].
% 7.80/8.01 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1139,b)].
% 7.80/8.01 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1140,b)].
% 7.80/8.01 1159 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 7.80/8.01 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1139,b)].
% 7.80/8.01 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1140,b)].
% 7.80/8.01 1160 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 7.80/8.01 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1139,b)].
% 7.80/8.01 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1140,b)].
% 7.80/8.01 1161 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 7.80/8.01 1162 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(31,b,1,a)].
% 7.80/8.01 1163 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(31,b,3,a)].
% 7.80/8.01 1164 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 7.87/8.08 1165 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 7.87/8.08 1166 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(108,a,104,b)].
% 7.87/8.08 1167 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(109,a,104,b)].
% 7.87/8.08 1168 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(129,b,110,a)].
% 7.87/8.08 1169 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(129,b,113,a)].
% 7.87/8.08 1170 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(129,b,119,a)].
% 7.87/8.08 1171 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(129,b,120,a)].
% 7.87/8.08 1172 -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(154,b,133,b)].
% 7.87/8.08 1173 -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(154,b,135,b)].
% 7.87/8.08 1174 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 7.87/8.08 1175 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 7.87/8.08 1176 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(205,b,194,b)].
% 7.87/8.08 1177 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(206,b,194,b)].
% 7.87/8.08 1178 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 7.87/8.08 1179 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 7.87/8.08 1180 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(245,a,226,b)].
% 7.87/8.08 1181 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(246,a,226,b)].
% 7.87/8.08 1182 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,286,a)].
% 7.87/8.08 1183 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,288,a)].
% 7.87/8.08 1184 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(320,a,304,b)].
% 7.87/8.08 1185 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(321,a,304,b)].
% 7.87/8.08 1186 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(513,a,510,b)].
% 7.87/8.08 1187 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(520,a,510,b)].
% 7.87/8.08 1188 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(521,a,510,b)].
% 7.87/8.08 1189 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(525,a,510,b)].
% 7.87/8.08 1190 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(565,b,546,b)].
% 7.87/8.08 1191 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,579,b)].
% 7.87/8.08 1192 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(600,a,579,b)].
% 7.87/8.08 1193 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(603,b,579,b)].
% 7.87/8.08 1194 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(687,b,658,a)].
% 7.87/8.08 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(1194,a,1138,a)].
% 7.87/8.08 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1194,a,1139,b)].
% 7.87/8.08 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1194,a,1140,b)].
% 7.87/8.08 1195 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(687,b,660,a)].
% 7.91/8.08 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(1195,a,1138,a)].
% 7.91/8.08 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1195,a,1139,b)].
% 7.91/8.08 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1195,a,1140,b)].
% 7.91/8.08 1196 -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(687,b,661,a)].
% 7.91/8.08 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(1196,a,1138,a)].
% 7.91/8.08 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(1196,a,1139,b)].
% 7.91/8.08 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(1196,a,1140,b)].
% 7.91/8.08 1197 -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(687,b,662,a)].
% 7.91/8.08 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(1197,a,1138,a)].
% 7.91/8.08 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(1197,a,1139,b)].
% 7.91/8.08 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(1197,a,1140,b)].
% 7.91/8.08 1198 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(687,b,663,a)].
% 7.91/8.08 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1198,a,1138,a)].
% 7.91/8.08 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1198,a,1139,b)].
% 7.91/8.08 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1198,a,1140,b)].
% 7.91/8.08 1199 -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(687,b,664,a)].
% 7.91/8.08 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(1199,a,1138,a)].
% 7.91/8.08 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(1199,a,1139,b)].
% 7.91/8.08 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(1199,a,1140,b)].
% 7.91/8.08 1200 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(687,b,665,a)].
% 7.91/8.08 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(1200,a,1138,a)].
% 7.91/8.08 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1200,a,1139,b)].
% 7.91/8.08 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1200,a,1140,b)].
% 7.91/8.08 1201 -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(687,b,666,a)].
% 7.91/8.08 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(1201,a,1138,a)].
% 7.91/8.08 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(1201,a,1139,b)].
% 7.91/8.08 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(1201,a,1140,b)].
% 7.91/8.08 1202 -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(687,b,667,a)].
% 7.91/8.08 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(1202,a,1138,a)].
% 7.97/8.14 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(1202,a,1139,b)].
% 7.97/8.14 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(1202,a,1140,b)].
% 7.97/8.14 1203 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(687,b,668,a)].
% 7.97/8.14 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(1203,a,1138,a)].
% 7.97/8.14 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1203,a,1139,b)].
% 7.97/8.14 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1203,a,1140,b)].
% 7.97/8.14 1204 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(718,b,687,b)].
% 7.97/8.14 Derived: class_HOL_Oone(tc_nat). [resolve(1204,b,1138,a)].
% 7.97/8.14 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1204,b,1139,b)].
% 7.97/8.14 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1204,b,1140,b)].
% 7.97/8.14 1205 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(810,a,724,a)].
% 7.97/8.14 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1205,a,1138,a)].
% 7.97/8.14 1206 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(810,a,731,a)].
% 7.97/8.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1206,a,1139,b)].
% 7.97/8.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1206,a,1140,b)].
% 7.97/8.14 1207 -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(891,b,822,a)].
% 7.97/8.14 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(1207,a,1113,a)].
% 7.97/8.14 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(1207,a,1138,a)].
% 7.97/8.14 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__field(C). [resolve(1207,a,1139,b)].
% 7.97/8.14 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__idom(C). [resolve(1207,a,1140,b)].
% 7.97/8.14 1208 -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(891,b,823,a)].
% 7.97/8.14 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(1208,a,1113,a)].
% 7.97/8.14 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(1208,a,1138,a)].
% 7.97/8.14 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__field(B). [resolve(1208,a,1139,b)].
% 7.97/8.14 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__idom(B). [resolve(1208,a,1140,b)].
% 7.97/8.14 1209 -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(891,b,824,a)].
% 7.97/8.14 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(1209,a,1113,a)].
% 7.97/8.14 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(1209,a,1138,a)].
% 7.97/8.14 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__field(B). [resolve(1209,a,1139,b)].
% 7.97/8.14 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__idom(B). [resolve(1209,a,1140,b)].
% 7.97/8.14 1210 -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(891,b,825,a)].
% 7.97/8.14 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(1210,a,1113,a)].
% 7.97/8.14 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(1210,a,1138,a)].
% 7.97/8.14 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__field(C). [resolve(1210,a,1139,b)].
% 7.97/8.14 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__idom(C). [resolve(1210,a,1140,b)].
% 7.97/8.14 1211 -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(891,b,826,a)].
% 7.97/8.14 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(1211,a,1113,a)].
% 7.97/8.14 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(1211,a,1138,a)].
% 7.97/8.14 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__field(B). [resolve(1211,a,1139,b)].
% 7.97/8.14 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__idom(B). [resolve(1211,a,1140,b)].
% 7.97/8.14 1212 -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(891,b,827,a)].
% 7.97/8.14 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(1212,a,1113,a)].
% 7.97/8.14 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(1212,a,1138,a)].
% 7.97/8.14 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__field(B). [resolve(1212,a,1139,b)].
% 7.97/8.14 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__idom(B). [resolve(1212,a,1140,b)].
% 7.97/8.14 1213 -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(891,b,828,a)].
% 7.97/8.15 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(1213,a,1113,a)].
% 7.97/8.15 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(1213,a,1138,a)].
% 7.97/8.15 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(1213,a,1139,b)].
% 7.97/8.15 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(1213,a,1140,b)].
% 7.97/8.15 1214 -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(891,b,829,a)].
% 7.97/8.15 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(1214,a,1113,a)].
% 7.97/8.15 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(1214,a,1138,a)].
% 7.97/8.15 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(1214,a,1139,b)].
% 7.97/8.15 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(1214,a,1140,b)].
% 7.97/8.15 1215 -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(891,b,830,a)].
% 7.97/8.15 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(1215,a,1113,a)].
% 7.97/8.15 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(1215,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1215,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1215,a,1140,b)].
% 7.97/8.15 1216 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,831,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1216,a,1113,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1216,a,1138,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1216,a,1139,b)].
% 7.97/8.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1216,a,1140,b)].
% 7.97/8.15 1217 -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(891,b,832,a)].
% 7.97/8.15 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(1217,a,1113,a)].
% 7.97/8.15 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(1217,a,1138,a)].
% 7.97/8.15 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__field(C). [resolve(1217,a,1139,b)].
% 7.97/8.15 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__idom(C). [resolve(1217,a,1140,b)].
% 7.97/8.15 1218 -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(891,b,833,a)].
% 7.97/8.15 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(1218,a,1113,a)].
% 7.97/8.15 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(1218,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1218,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1218,a,1140,b)].
% 7.97/8.15 1219 -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(891,b,834,a)].
% 7.97/8.15 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(1219,a,1113,a)].
% 7.97/8.15 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(1219,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1219,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1219,a,1140,b)].
% 7.97/8.15 1220 -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(891,b,835,a)].
% 7.97/8.15 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(1220,a,1113,a)].
% 7.97/8.15 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(1220,a,1138,a)].
% 7.97/8.15 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__field(C). [resolve(1220,a,1139,b)].
% 7.97/8.15 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__idom(C). [resolve(1220,a,1140,b)].
% 7.97/8.15 1221 -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(891,b,836,a)].
% 7.97/8.15 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(1221,a,1113,a)].
% 7.97/8.15 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(1221,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1221,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1221,a,1140,b)].
% 7.97/8.15 1222 -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(891,b,837,a)].
% 7.97/8.15 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(1222,a,1113,a)].
% 7.97/8.15 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(1222,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1222,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1222,a,1140,b)].
% 7.97/8.15 1223 -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(891,b,838,a)].
% 7.97/8.15 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(1223,a,1113,a)].
% 7.97/8.15 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(1223,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1223,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1223,a,1140,b)].
% 7.97/8.15 1224 -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(891,b,839,a)].
% 7.97/8.15 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(1224,a,1113,a)].
% 7.97/8.15 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(1224,a,1138,a)].
% 7.97/8.15 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__field(B). [resolve(1224,a,1139,b)].
% 7.97/8.15 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__idom(B). [resolve(1224,a,1140,b)].
% 7.97/8.15 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(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(891,b,840,a)].
% 7.97/8.15 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(1225,a,1113,a)].
% 7.97/8.15 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(1225,a,1138,a)].
% 7.97/8.15 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(1225,a,1139,b)].
% 7.97/8.15 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(1225,a,1140,b)].
% 7.97/8.15 1226 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1226,a,1113,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1226,a,1138,a)].
% 7.97/8.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1226,a,1139,b)].
% 7.97/8.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1140,b)].
% 7.97/8.15 1227 -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(891,b,842,a)].
% 7.97/8.15 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(1227,a,1113,a)].
% 7.97/8.15 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(1227,a,1138,a)].
% 7.97/8.15 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(1227,a,1139,b)].
% 7.97/8.15 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(1227,a,1140,b)].
% 7.97/8.15 1228 -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(891,b,843,a)].
% 7.97/8.15 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(1228,a,1113,a)].
% 7.97/8.15 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(1228,a,1138,a)].
% 7.97/8.15 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(1228,a,1139,b)].
% 7.97/8.15 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(1228,a,1140,b)].
% 7.97/8.15 1229 -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(891,b,844,a)].
% 7.97/8.15 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(1229,a,1113,a)].
% 7.97/8.16 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(1229,a,1138,a)].
% 7.97/8.16 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__field(C). [resolve(1229,a,1139,b)].
% 7.97/8.16 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__idom(C). [resolve(1229,a,1140,b)].
% 7.97/8.16 1230 -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(891,b,845,b)].
% 7.97/8.16 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(1230,a,1113,a)].
% 7.97/8.16 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(1230,a,1138,a)].
% 7.97/8.16 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__field(A). [resolve(1230,a,1139,b)].
% 7.97/8.16 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__idom(A). [resolve(1230,a,1140,b)].
% 7.97/8.16 1231 -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(891,b,846,b)].
% 7.97/8.16 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(1231,a,1113,a)].
% 7.97/8.16 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(1231,a,1138,a)].
% 7.97/8.16 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__field(A). [resolve(1231,a,1139,b)].
% 7.97/8.16 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__idom(A). [resolve(1231,a,1140,b)].
% 7.97/8.16 1232 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(891,b,847,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1232,a,1113,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1232,a,1138,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1232,a,1139,b)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1232,a,1140,b)].
% 7.97/8.16 1233 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(891,b,848,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1233,a,1113,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1233,a,1138,a)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1233,a,1139,b)].
% 7.97/8.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1233,a,1140,b)].
% 7.97/8.16 1234 -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(891,b,849,a)].
% 7.97/8.16 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(1234,a,1113,a)].
% 7.97/8.16 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(1234,a,1138,a)].
% 7.97/8.16 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__field(C). [resolve(1234,a,1139,b)].
% 7.97/8.16 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__idom(C). [resolve(1234,a,1140,b)].
% 7.97/8.16 1235 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(891,b,850,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1235,a,1113,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1235,a,1138,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1235,a,1139,b)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1235,a,1140,b)].
% 7.97/8.16 1236 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(891,b,851,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1236,a,1113,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1236,a,1138,a)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1236,a,1139,b)].
% 7.97/8.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1236,a,1140,b)].
% 7.97/8.16 1237 -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(891,b,852,a)].
% 7.97/8.16 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(1237,a,1113,a)].
% 7.97/8.16 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(1237,a,1138,a)].
% 7.97/8.16 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(1237,a,1139,b)].
% 7.97/8.16 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(1237,a,1140,b)].
% 7.97/8.16 1238 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(891,b,853,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1238,a,1113,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1238,a,1138,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1238,a,1139,b)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1238,a,1140,b)].
% 7.97/8.16 1239 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(891,b,854,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1239,a,1113,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1239,a,1138,a)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1239,a,1139,b)].
% 7.97/8.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1239,a,1140,b)].
% 7.97/8.16 1240 -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(891,b,855,a)].
% 7.97/8.16 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(1240,a,1113,a)].
% 7.97/8.16 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(1240,a,1138,a)].
% 7.97/8.16 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(1240,a,1139,b)].
% 7.97/8.16 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(1240,a,1140,b)].
% 7.97/8.16 1241 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,856,a)].
% 7.97/8.16 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1241,a,1113,a)].
% 7.97/8.16 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1241,a,1138,a)].
% 7.97/8.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1241,a,1139,b)].
% 7.97/8.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1241,a,1140,b)].
% 7.97/8.16 1242 -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(891,b,857,a)].
% 7.97/8.16 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(1242,a,1113,a)].
% 7.97/8.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(1242,a,1138,a)].
% 7.97/8.16 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(1242,a,1139,b)].
% 7.97/8.16 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(1242,a,1140,b)].
% 7.97/8.16 1243 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(891,b,858,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1243,a,1113,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1243,a,1138,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1243,a,1139,b)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1243,a,1140,b)].
% 7.97/8.16 1244 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(891,b,859,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1244,a,1113,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1244,a,1138,a)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1244,a,1139,b)].
% 7.97/8.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1244,a,1140,b)].
% 7.97/8.16 1245 -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(891,b,860,a)].
% 7.97/8.16 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(1245,a,1113,a)].
% 7.97/8.16 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(1245,a,1138,a)].
% 7.97/8.16 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(1245,a,1139,b)].
% 7.97/8.16 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(1245,a,1140,b)].
% 7.97/8.16 1246 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,861,a)].
% 7.97/8.16 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1246,a,1113,a)].
% 7.97/8.16 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1246,a,1138,a)].
% 7.97/8.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1246,a,1139,b)].
% 7.97/8.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1246,a,1140,b)].
% 7.97/8.16 1247 -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(891,b,862,a)].
% 7.97/8.16 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(1247,a,1113,a)].
% 7.97/8.16 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(1247,a,1138,a)].
% 7.97/8.16 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(1247,a,1139,b)].
% 7.97/8.16 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(1247,a,1140,b)].
% 7.97/8.16 1248 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(891,b,863,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1248,a,1113,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1248,a,1138,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1248,a,1139,b)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1248,a,1140,b)].
% 7.97/8.16 1249 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(891,b,864,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1249,a,1113,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1249,a,1138,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1249,a,1139,b)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1249,a,1140,b)].
% 7.97/8.16 1250 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(891,b,865,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1250,a,1113,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1250,a,1138,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1250,a,1139,b)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1250,a,1140,b)].
% 7.97/8.16 1251 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(891,b,866,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1251,a,1113,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1251,a,1138,a)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1251,a,1139,b)].
% 7.97/8.16 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1251,a,1140,b)].
% 8.00/8.17 1252 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,867,a)].
% 8.00/8.17 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1252,a,1113,a)].
% 8.00/8.17 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1252,a,1138,a)].
% 8.00/8.17 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1252,a,1139,b)].
% 8.00/8.17 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1252,a,1140,b)].
% 8.00/8.17 1253 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,868,a)].
% 8.00/8.17 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1253,a,1113,a)].
% 8.00/8.17 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1253,a,1138,a)].
% 8.00/8.17 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1253,a,1139,b)].
% 8.00/8.17 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1253,a,1140,b)].
% 8.00/8.17 1254 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,869,a)].
% 8.00/8.17 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1254,a,1113,a)].
% 8.00/8.17 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1254,a,1138,a)].
% 8.00/8.17 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1254,a,1139,b)].
% 8.00/8.17 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1254,a,1140,b)].
% 8.00/8.17 1255 -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(891,b,870,a)].
% 8.00/8.17 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(1255,a,1113,a)].
% 8.00/8.17 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(1255,a,1138,a)].
% 8.00/8.17 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(1255,a,1139,b)].
% 8.00/8.17 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(1255,a,1140,b)].
% 8.00/8.17 1256 -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(891,b,871,a)].
% 8.00/8.17 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(1256,a,1113,a)].
% 8.00/8.17 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(1256,a,1138,a)].
% 8.00/8.17 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(1256,a,1139,b)].
% 8.00/8.17 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(1256,a,1140,b)].
% 8.00/8.17 1257 -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(891,b,872,a)].
% 8.00/8.17 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(1257,a,1113,a)].
% 8.00/8.17 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(1257,a,1138,a)].
% 8.00/8.17 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(1257,a,1139,b)].
% 8.00/8.17 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(1257,a,1140,b)].
% 8.00/8.17 1258 -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(891,b,873,a)].
% 8.00/8.17 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(1258,a,1113,a)].
% 8.00/8.17 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(1258,a,1138,a)].
% 8.00/8.17 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(1258,a,1139,b)].
% 8.00/8.17 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(1258,a,1140,b)].
% 8.00/8.17 1259 -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(891,b,874,a)].
% 8.00/8.17 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(1259,a,1113,a)].
% 8.00/8.17 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(1259,a,1138,a)].
% 8.00/8.17 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(1259,a,1139,b)].
% 8.00/8.17 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(1259,a,1140,b)].
% 8.00/8.17 1260 -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(891,b,875,a)].
% 8.00/8.17 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(1260,a,1113,a)].
% 8.00/8.17 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(1260,a,1138,a)].
% 8.00/8.17 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(1260,a,1139,b)].
% 8.00/8.20 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(1260,a,1140,b)].
% 8.00/8.20 1261 -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(891,b,876,a)].
% 8.00/8.20 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(1261,a,1113,a)].
% 8.00/8.20 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(1261,a,1138,a)].
% 8.00/8.20 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(1261,a,1139,b)].
% 8.00/8.20 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(1261,a,1140,b)].
% 8.00/8.20 1262 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,877,a)].
% 8.00/8.20 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1262,a,1113,a)].
% 8.00/8.20 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1262,a,1138,a)].
% 8.00/8.20 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1262,a,1139,b)].
% 8.00/8.20 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1262,a,1140,b)].
% 8.00/8.20 1263 -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(891,b,878,a)].
% 8.00/8.20 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(1263,a,1113,a)].
% 8.00/8.20 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(1263,a,1138,a)].
% 8.00/8.20 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(1263,a,1139,b)].
% 8.00/8.20 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(1263,a,1140,b)].
% 8.00/8.20 1264 -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(891,b,879,a)].
% 8.00/8.20 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(1264,a,1113,a)].
% 8.00/8.20 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(1264,a,1138,a)].
% 8.00/8.20 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(1264,a,1139,b)].
% 8.00/8.20 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(1264,a,1140,b)].
% 8.00/8.20 1265 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1068,a)].
% 8.00/8.20 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1265,a,1113,a)].
% 8.16/8.36 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1265,a,1138,a)].
% 8.16/8.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1265,a,1139,b)].
% 8.16/8.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1265,a,1140,b)].
% 8.16/8.36 1266 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1091,a)].
% 8.16/8.36 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1266,a,1113,a)].
% 8.16/8.36 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1266,a,1138,a)].
% 8.16/8.36 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1266,a,1139,b)].
% 8.16/8.36 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1266,a,1140,b)].
% 8.16/8.36 1267 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 8.16/8.36 1268 -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].
% 8.16/8.36 1269 -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].
% 8.16/8.36 1270 -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].
% 8.16/8.36 1271 -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].
% 8.16/8.36 1272 -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].
% 8.16/8.36 1273 -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].
% 8.16/8.36 1274 -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].
% 8.16/8.36 1275 -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].
% 8.16/8.36 1276 -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].
% 8.16/8.36 1277 -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].
% 8.16/8.36 1278 -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].
% 8.16/8.36 1279 -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].
% 8.16/8.36 1280 -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].
% 8.16/8.36 1281 -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].
% 8.16/8.36 1282 -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].
% 8.16/8.36 1283 -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].
% 8.16/8.36 1284 -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].
% 8.16/8.36 1285 -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].
% 8.16/8.36 1286 -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].
% 8.16/8.36 1287 -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].
% 8.16/8.36 1288 -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].
% 8.16/8.36 1289 -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].
% 8.16/8.36 1290 -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].
% 8.16/8.36 1291 -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].
% 8.16/8.36 1292 -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].
% 8.16/8.36 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(1267,a,1268,b)].
% 8.16/8.36 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(1267,a,1269,b)].
% 8.16/8.36 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(1267,a,1270,b)].
% 8.16/8.36 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(1267,a,1271,b)].
% 8.16/8.36 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(1267,a,1272,b)].
% 8.16/8.36 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(1267,a,1273,b)].
% 8.16/8.36 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(1267,a,1274,b)].
% 8.16/8.36 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(1267,a,1275,b)].
% 8.16/8.36 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(1267,a,1276,b)].
% 8.20/8.37 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(1267,a,1277,b)].
% 8.20/8.37 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(1267,a,1278,b)].
% 8.20/8.37 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(1267,a,1279,b)].
% 8.20/8.37 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(1267,a,1280,b)].
% 8.20/8.37 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(1267,a,1281,b)].
% 8.20/8.37 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(1267,a,1282,b)].
% 8.20/8.37 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(1267,a,1283,b)].
% 8.20/8.37 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(1267,a,1284,b)].
% 8.20/8.37 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(1267,a,1285,b)].
% 8.20/8.37 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(1267,a,1286,b)].
% 8.20/8.37 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(1267,a,1287,b)].
% 8.20/8.37 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(1267,a,1288,b)].
% 8.20/8.39 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(1267,a,1289,b)].
% 8.20/8.39 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(1267,a,1290,b)].
% 8.20/8.39 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(1267,a,1291,b)].
% 8.20/8.39 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(1267,a,1292,a)].
% 8.20/8.39 1293 -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].
% 8.20/8.39 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(1293,b,1268,b)].
% 8.20/8.39 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(1293,b,1269,b)].
% 8.20/8.39 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(1293,b,1270,b)].
% 8.20/8.39 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(1293,b,1271,b)].
% 8.20/8.39 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(1293,b,1272,b)].
% 8.20/8.39 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(1293,b,1273,b)].
% 8.20/8.39 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(1293,b,1274,b)].
% 8.20/8.39 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(1293,b,1275,b)].
% 8.20/8.39 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(1293,b,1276,b)].
% 8.20/8.39 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(1293,b,1277,b)].
% 8.20/8.39 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(1293,b,1278,b)].
% 8.20/8.40 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(1293,b,1279,b)].
% 8.20/8.40 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(1293,b,1280,b)].
% 8.20/8.40 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(1293,b,1281,b)].
% 8.20/8.40 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(1293,b,1282,b)].
% 8.20/8.40 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(1293,b,1283,b)].
% 8.20/8.40 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(1293,b,1284,b)].
% 8.20/8.40 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(1293,b,1285,b)].
% 8.20/8.40 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(1293,b,1286,b)].
% 8.20/8.40 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(1293,b,1287,b)].
% 8.20/8.40 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(1293,b,1288,b)].
% 8.20/8.40 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(1293,b,1289,b)].
% 8.20/8.40 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(1293,b,1290,b)].
% 8.20/8.40 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(1293,b,1291,b)].
% 8.20/8.40 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1293,b,1292,a)].
% 8.20/8.40 1294 -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].
% 8.20/8.40 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(1294,b,1268,b)].
% 8.20/8.40 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(1294,b,1269,b)].
% 8.20/8.40 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(1294,b,1270,b)].
% 8.20/8.40 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(1294,b,1271,b)].
% 8.20/8.40 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(1294,b,1272,b)].
% 8.20/8.40 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(1294,b,1273,b)].
% 8.20/8.40 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(1294,b,1274,b)].
% 8.20/8.40 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(1294,b,1275,b)].
% 8.20/8.40 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(1294,b,1276,b)].
% 8.20/8.40 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(1294,b,1277,b)].
% 8.20/8.40 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(1294,b,1278,b)].
% 8.20/8.40 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(1294,b,1279,b)].
% 8.20/8.40 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(1294,b,1280,b)].
% 8.20/8.40 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(1294,b,1281,b)].
% 8.20/8.40 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(1294,b,1282,b)].
% 8.20/8.40 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(1294,b,1283,b)].
% 8.20/8.41 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(1294,b,1284,b)].
% 8.20/8.41 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(1294,b,1285,b)].
% 8.20/8.41 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(1294,b,1286,b)].
% 8.20/8.41 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(1294,b,1287,b)].
% 8.20/8.41 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(1294,b,1288,b)].
% 8.20/8.41 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(1294,b,1289,b)].
% 8.20/8.41 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(1294,b,1290,b)].
% 8.20/8.41 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(1294,b,1291,b)].
% 8.20/8.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1294,b,1292,a)].
% 8.20/8.41 1295 -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].
% 8.20/8.41 1296 -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].
% 8.20/8.41 1297 -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].
% 8.20/8.41 1298 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_13) # label(axiom). [assumption].
% 8.20/8.41 1299 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_14) # label(axiom). [assumption].
% 8.20/8.41 1300 -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].
% 8.20/8.41 1301 -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].
% 8.20/8.41 1302 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 8.20/8.41 1303 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_2) # label(axiom). [assumption].
% 8.20/8.41 1304 -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].
% 8.20/8.42 1305 -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].
% 8.20/8.42 1306 -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].
% 8.20/8.42 1307 -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].
% 8.20/8.42 1308 -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].
% 8.20/8.42 1309 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom). [assumption].
% 8.20/8.42 1310 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 8.20/8.42 1311 -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].
% 8.20/8.42 Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1311,a,1267,a)].
% 8.20/8.42 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1311,a,1293,b)].
% 8.20/8.42 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1311,a,1294,b)].
% 8.20/8.42 1312 -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].
% 8.20/8.42 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1312,a,1267,a)].
% 8.20/8.42 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1312,a,1293,b)].
% 8.20/8.42 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1312,a,1294,b)].
% 8.20/8.42 1313 -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].
% 8.20/8.42 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1313,a,1267,a)].
% 8.20/8.42 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1313,a,1293,b)].
% 8.20/8.42 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1313,a,1294,b)].
% 8.20/8.42 1314 -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].
% 8.20/8.42 Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1314,a,1267,a)].
% 8.20/8.42 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1314,a,1293,b)].
% 8.20/8.42 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1314,a,1294,b)].
% 8.20/8.42 1315 -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].
% 8.20/8.42 Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1315,a,1267,a)].
% 8.20/8.42 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1315,a,1293,b)].
% 8.20/8.42 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1315,a,1294,b)].
% 8.20/8.42 1316 -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].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1316,a,1267,a)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1316,a,1293,b)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1316,a,1294,b)].
% 8.28/8.45 1317 -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].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1317,a,1267,a)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1317,a,1293,b)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1317,a,1294,b)].
% 8.28/8.45 1318 -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].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1318,a,1267,a)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1318,a,1293,b)].
% 8.28/8.45 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1318,a,1294,b)].
% 8.28/8.45 1319 -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].
% 8.28/8.45 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1319,a,1267,a)].
% 8.28/8.45 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1319,a,1293,b)].
% 8.28/8.45 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1319,a,1294,b)].
% 8.28/8.45 1320 -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].
% 8.28/8.45 1321 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_9) # label(axiom). [assumption].
% 8.28/8.45 1322 -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)].
% 8.28/8.45 1323 -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)].
% 8.28/8.45 1324 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 8.28/8.45 1325 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 8.28/8.45 1326 -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(153,b,133,b)].
% 8.28/8.45 1327 -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(153,b,135,b)].
% 8.28/8.45 1328 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(167,a,153,b)].
% 8.28/8.45 1329 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(168,a,153,b)].
% 8.28/8.45 1330 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 8.28/8.45 1331 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 8.28/8.45 1332 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(245,a,225,b)].
% 8.31/8.48 1333 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(246,a,225,b)].
% 8.31/8.48 1334 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,286,a)].
% 8.31/8.48 1335 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,288,a)].
% 8.31/8.48 1336 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(320,a,303,b)].
% 8.31/8.48 1337 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(321,a,303,b)].
% 8.31/8.48 1338 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(323,a,303,b)].
% 8.31/8.48 1339 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,303,b)].
% 8.31/8.48 1340 -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(342,b,327,b)].
% 8.31/8.48 1341 -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(342,b,329,b)].
% 8.31/8.48 1342 -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(342,b,330,a)].
% 8.31/8.48 1343 -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(342,b,331,a)].
% 8.31/8.48 1344 -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(342,b,332,a)].
% 8.31/8.48 1345 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(350,a,342,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1345,b,1293,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1345,b,1294,b)].
% 8.31/8.48 1346 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(351,a,342,b)].
% 8.31/8.48 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1346,b,1293,b)].
% 8.31/8.48 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1346,b,1294,b)].
% 8.31/8.48 1347 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(362,b,342,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1347,b,1293,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1347,b,1294,b)].
% 8.31/8.48 1348 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(363,b,342,b)].
% 8.31/8.48 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1348,b,1293,b)].
% 8.31/8.48 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1348,b,1294,b)].
% 8.31/8.48 1349 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(364,b,342,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1349,b,1293,b)].
% 8.31/8.48 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1349,b,1294,b)].
% 8.31/8.48 1350 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(365,b,342,b)].
% 8.31/8.48 1351 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,c,342,b)].
% 8.31/8.48 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1351,c,1293,b)].
% 8.37/8.55 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1351,c,1294,b)].
% 8.37/8.55 1352 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,c,342,b)].
% 8.37/8.55 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1352,c,1293,b)].
% 8.37/8.55 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1352,c,1294,b)].
% 8.37/8.55 1353 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(368,a,342,b)].
% 8.37/8.55 1354 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(369,a,342,b)].
% 8.37/8.55 1355 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(370,c,342,b)].
% 8.37/8.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1355,c,1293,b)].
% 8.37/8.55 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1355,c,1294,b)].
% 8.37/8.55 1356 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(371,c,342,b)].
% 8.37/8.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1356,c,1293,b)].
% 8.37/8.55 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1356,c,1294,b)].
% 8.37/8.55 1357 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(802,a,724,a)].
% 8.37/8.55 1358 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(802,a,731,a)].
% 8.37/8.55 1359 -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(890,b,822,a)].
% 8.37/8.55 1360 -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(890,b,823,a)].
% 8.37/8.55 1361 -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(890,b,824,a)].
% 8.37/8.55 1362 -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(890,b,825,a)].
% 8.37/8.55 1363 -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(890,b,826,a)].
% 8.37/8.55 1364 -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(890,b,827,a)].
% 8.37/8.55 1365 -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(890,b,828,a)].
% 8.37/8.55 1366 -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(890,b,829,a)].
% 8.37/8.55 1367 -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(890,b,830,a)].
% 8.40/8.56 1368 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(890,b,831,a)].
% 8.40/8.56 1369 -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(890,b,832,a)].
% 8.40/8.56 1370 -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(890,b,833,a)].
% 8.40/8.56 1371 -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(890,b,834,a)].
% 8.40/8.56 1372 -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(890,b,835,a)].
% 8.40/8.56 1373 -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(890,b,836,a)].
% 8.40/8.56 1374 -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(890,b,837,a)].
% 8.40/8.56 1375 -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(890,b,838,a)].
% 8.40/8.56 1376 -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(890,b,839,a)].
% 8.40/8.56 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_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(890,b,840,a)].
% 8.40/8.56 1378 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(890,b,841,a)].
% 8.40/8.56 1379 -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(890,b,842,a)].
% 8.40/8.56 1380 -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(890,b,843,a)].
% 8.40/8.56 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 = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(890,b,844,a)].
% 8.40/8.56 1382 -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(890,b,845,b)].
% 8.40/8.56 1383 -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(890,b,846,b)].
% 8.40/8.56 1384 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(890,b,847,a)].
% 8.40/8.56 1385 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(890,b,848,a)].
% 8.40/8.56 1386 -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(890,b,849,a)].
% 8.40/8.56 1387 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(890,b,850,a)].
% 8.40/8.56 1388 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(890,b,851,a)].
% 8.40/8.56 1389 -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(890,b,852,a)].
% 8.40/8.57 1390 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(890,b,853,a)].
% 8.40/8.57 1391 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(890,b,854,a)].
% 8.40/8.57 1392 -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(890,b,855,a)].
% 8.40/8.57 1393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(890,b,856,a)].
% 8.40/8.57 1394 -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(890,b,857,a)].
% 8.40/8.57 1395 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(890,b,858,a)].
% 8.40/8.57 1396 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(890,b,859,a)].
% 8.40/8.57 1397 -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(890,b,860,a)].
% 8.40/8.57 1398 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(890,b,861,a)].
% 8.40/8.57 1399 -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(890,b,862,a)].
% 8.40/8.57 1400 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(890,b,863,a)].
% 8.40/8.57 1401 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(890,b,864,a)].
% 8.40/8.57 1402 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(890,b,865,a)].
% 8.40/8.57 1403 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(890,b,866,a)].
% 8.40/8.57 1404 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(890,b,867,a)].
% 8.40/8.57 1405 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(890,b,868,a)].
% 8.40/8.57 1406 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(890,b,869,a)].
% 8.40/8.57 1407 -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(890,b,870,a)].
% 8.40/8.57 1408 -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(890,b,871,a)].
% 8.40/8.57 1409 -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(890,b,872,a)].
% 8.40/8.57 1410 -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(890,b,873,a)].
% 8.40/8.57 1411 -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(890,b,874,a)].
% 8.40/8.57 1412 -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(890,b,875,a)].
% 8.40/8.57 1413 -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(890,b,876,a)].
% 8.61/8.78 1414 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(890,b,877,a)].
% 8.61/8.78 1415 -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(890,b,878,a)].
% 8.61/8.78 1416 -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(890,b,879,a)].
% 8.61/8.78 1417 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1068,a)].
% 8.61/8.78 1418 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1091,a)].
% 8.61/8.78 1419 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 8.61/8.78 1420 -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].
% 8.61/8.78 1421 -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].
% 8.61/8.78 1422 -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].
% 8.61/8.78 1423 -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].
% 8.61/8.78 1424 -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].
% 8.61/8.78 1425 -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].
% 8.61/8.78 1426 -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].
% 8.61/8.78 1427 -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].
% 8.61/8.78 1428 -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].
% 8.61/8.78 1429 -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].
% 8.61/8.78 1430 -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].
% 8.61/8.78 1431 -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].
% 8.61/8.78 1432 -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].
% 8.61/8.78 1433 -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].
% 8.61/8.78 1434 -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].
% 8.61/8.78 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1420,a)].
% 8.61/8.78 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(1419,a,1421,a)].
% 8.61/8.78 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(1419,a,1422,a)].
% 8.61/8.78 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1419,a,1423,a)].
% 8.61/8.78 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(1419,a,1424,a)].
% 8.61/8.80 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1419,a,1425,a)].
% 8.61/8.80 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1419,a,1426,a)].
% 8.61/8.80 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1427,a)].
% 8.61/8.80 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1419,a,1428,a)].
% 8.61/8.80 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1419,a,1429,a)].
% 8.61/8.80 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1419,a,1430,a)].
% 8.61/8.80 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(1419,a,1431,a)].
% 8.61/8.80 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(1419,a,1432,a)].
% 8.61/8.80 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1419,a,1433,a)].
% 8.61/8.80 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1434,a)].
% 8.61/8.80 1435 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 8.61/8.80 1436 -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].
% 8.61/8.80 1437 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 8.61/8.80 1438 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom). [assumption].
% 8.61/8.80 1439 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 8.61/8.80 1440 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 8.61/8.80 1441 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 8.61/8.80 1442 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 8.61/8.80 1443 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom). [assumption].
% 8.61/8.80 1444 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 8.61/8.80 1445 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom). [assumption].
% 8.61/8.80 1446 -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].
% 8.61/8.80 1447 -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].
% 8.61/8.80 1448 -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].
% 8.61/8.80 1449 -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].
% 8.61/8.80 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1449,b,1420,a)].
% 8.61/8.80 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1449,b,1421,a)].
% 8.61/8.80 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(1449,b,1422,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1449,b,1423,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1449,b,1424,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1449,b,1425,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1449,b,1426,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1449,b,1427,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1449,b,1428,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1449,b,1429,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1449,b,1430,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1449,b,1431,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1449,b,1432,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1449,b,1433,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1449,b,1434,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1449,b,1436,a)].
% 8.65/8.81 1450 -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].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1450,b,1420,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1450,b,1421,a)].
% 8.65/8.81 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(1450,b,1422,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1450,b,1423,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1450,b,1424,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1450,b,1425,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1450,b,1426,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1450,b,1427,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1450,b,1428,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1450,b,1429,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1450,b,1430,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1450,b,1431,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1450,b,1432,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1450,b,1433,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1450,b,1434,a)].
% 8.65/8.81 1451 -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].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1451,b,1420,a)].
% 8.65/8.81 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1451,b,1421,a)].
% 8.82/9.02 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(1451,b,1422,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1451,b,1423,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1451,b,1424,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1451,b,1425,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1451,b,1426,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1451,b,1427,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1451,b,1428,a)].
% 8.82/9.02 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1451,b,1429,a)].
% 8.82/9.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1451,b,1430,a)].
% 8.82/9.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1451,b,1431,a)].
% 8.82/9.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1451,b,1432,a)].
% 8.82/9.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1451,b,1433,a)].
% 8.82/9.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1451,b,1434,a)].
% 8.82/9.03 1452 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(12,b,1,a)].
% 8.82/9.03 1453 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(12,b,3,a)].
% 8.82/9.03 1454 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 8.82/9.03 1455 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 8.82/9.03 1456 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1074,b,1068,a)].
% 8.82/9.03 1457 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1097,b,1091,a)].
% 8.82/9.03 1458 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1316,a,1267,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1458,a,1435,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1458,a,1436,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1458,a,1437,a)].
% 8.82/9.03 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1458,a,1438,a)].
% 8.82/9.03 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1458,a,1439,a)].
% 8.82/9.03 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1458,a,1440,a)].
% 8.82/9.03 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1458,a,1441,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1458,a,1442,a)].
% 8.82/9.03 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1458,a,1443,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1458,a,1444,a)].
% 8.82/9.03 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1458,a,1445,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1458,a,1446,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1447,a)].
% 8.82/9.03 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1448,a)].
% 8.82/9.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1458,a,1452,a)].
% 8.82/9.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1458,a,1453,a)].
% 8.82/9.03 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1458,a,1456,a)].
% 8.82/9.03 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1458,a,1457,a)].
% 8.82/9.03 1459 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1316,a,1293,b)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1459,a,1435,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1459,a,1436,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1459,a,1437,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1459,a,1438,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1459,a,1439,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1459,a,1440,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1459,a,1441,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A). [resolve(1459,a,1445,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1459,a,1446,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1459,a,1447,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1459,a,1448,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1459,a,1456,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1459,a,1457,a)].
% 8.95/9.14 1460 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1316,a,1294,b)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1460,a,1435,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1460,a,1436,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1460,a,1437,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1460,a,1438,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1460,a,1439,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1460,a,1440,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1460,a,1441,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(1460,a,1445,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1460,a,1446,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1460,a,1447,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1460,a,1448,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1460,a,1456,a)].
% 8.95/9.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1460,a,1457,a)].
% 8.95/9.14 1461 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 8.95/9.14 1462 -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].
% 8.95/9.14 1463 -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].
% 8.95/9.14 1464 -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].
% 8.95/9.14 1465 -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].
% 8.95/9.15 1466 -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].
% 8.95/9.15 1467 -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].
% 8.95/9.15 1468 -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].
% 8.95/9.15 1469 -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].
% 8.95/9.15 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(1461,a,1462,a)].
% 8.95/9.15 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(1461,a,1463,a)].
% 8.95/9.15 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(1461,a,1464,a)].
% 8.95/9.15 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(1461,a,1465,a)].
% 8.95/9.15 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(1461,a,1466,a)].
% 8.95/9.15 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(1461,a,1467,a)].
% 8.95/9.15 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(1461,a,1468,a)].
% 8.95/9.15 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(1461,a,1469,a)].
% 8.95/9.15 1470 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 8.95/9.15 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1470,a,1462,a)].
% 8.95/9.15 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1470,a,1463,a)].
% 8.95/9.15 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1470,a,1464,a)].
% 8.95/9.15 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1470,a,1465,a)].
% 8.95/9.15 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1470,a,1466,a)].
% 8.95/9.15 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1470,a,1467,a)].
% 8.95/9.15 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1470,a,1468,a)].
% 8.95/9.15 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1470,a,1469,a)].
% 8.95/9.15 1471 -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].
% 8.95/9.15 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(1471,b,1462,a)].
% 8.95/9.15 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(1471,b,1463,a)].
% 8.95/9.15 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(1471,b,1464,a)].
% 8.95/9.15 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(1471,b,1465,a)].
% 8.95/9.15 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(1471,b,1466,a)].
% 9.00/9.16 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(1471,b,1467,a)].
% 9.00/9.16 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(1471,b,1468,a)].
% 9.00/9.16 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(1471,b,1469,a)].
% 9.00/9.16 1472 -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].
% 9.00/9.16 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(1472,b,1462,a)].
% 9.00/9.16 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(1472,b,1463,a)].
% 9.00/9.16 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(1472,b,1464,a)].
% 9.00/9.16 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(1472,b,1465,a)].
% 9.00/9.16 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(1472,b,1466,a)].
% 9.00/9.16 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(1472,b,1467,a)].
% 9.00/9.16 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(1472,b,1468,a)].
% 9.00/9.16 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(1472,b,1469,a)].
% 9.00/9.16 1473 -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].
% 9.00/9.16 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(1473,b,1462,a)].
% 9.00/9.16 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(1473,b,1463,a)].
% 9.00/9.16 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(1473,b,1464,a)].
% 9.00/9.16 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(1473,b,1465,a)].
% 9.00/9.16 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(1473,b,1466,a)].
% 9.00/9.16 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(1473,b,1467,a)].
% 9.00/9.16 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(1473,b,1468,a)].
% 9.00/9.16 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(1473,b,1469,a)].
% 9.00/9.16 1474 -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].
% 9.00/9.16 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(1474,b,1462,a)].
% 9.00/9.16 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(1474,b,1463,a)].
% 9.00/9.16 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(1474,b,1464,a)].
% 9.00/9.16 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(1474,b,1465,a)].
% 9.00/9.17 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(1474,b,1466,a)].
% 9.00/9.17 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(1474,b,1467,a)].
% 9.00/9.17 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(1474,b,1468,a)].
% 9.00/9.17 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(1474,b,1469,a)].
% 9.00/9.17 1475 -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].
% 9.00/9.17 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(1475,b,1462,a)].
% 9.00/9.17 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(1475,b,1463,a)].
% 9.00/9.17 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(1475,b,1464,a)].
% 9.00/9.17 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(1475,b,1465,a)].
% 9.00/9.17 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(1475,b,1466,a)].
% 9.00/9.17 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(1475,b,1467,a)].
% 9.00/9.17 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(1475,b,1468,a)].
% 9.00/9.17 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(1475,b,1469,a)].
% 9.00/9.17 1476 -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].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1476,a,1471,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1476,a,1472,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1476,a,1473,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1476,a,1474,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1476,a,1475,b)].
% 9.00/9.17 1477 -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].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1477,a,1471,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1477,a,1472,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1477,a,1473,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1477,a,1474,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1477,a,1475,b)].
% 9.00/9.17 1478 -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].
% 9.00/9.19 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1478,a,1471,b)].
% 9.00/9.19 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1478,a,1472,b)].
% 9.00/9.19 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1478,a,1473,b)].
% 9.00/9.19 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1478,a,1475,b)].
% 9.00/9.19 1479 -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].
% 9.00/9.19 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1479,a,1471,b)].
% 9.00/9.19 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1479,a,1472,b)].
% 9.00/9.19 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1479,a,1473,b)].
% 9.00/9.19 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1479,a,1475,b)].
% 9.00/9.19 1480 -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].
% 9.00/9.19 1481 -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].
% 9.00/9.19 1482 -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].
% 9.00/9.19 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(1482,b,1462,a)].
% 9.00/9.19 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(1482,b,1463,a)].
% 9.00/9.19 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(1482,b,1464,a)].
% 9.00/9.19 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(1482,b,1465,a)].
% 9.00/9.19 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(1482,b,1466,a)].
% 9.00/9.19 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(1482,b,1467,a)].
% 9.00/9.19 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(1482,b,1468,a)].
% 9.00/9.19 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(1482,b,1469,a)].
% 9.00/9.19 1483 -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].
% 9.00/9.19 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(1483,b,1462,a)].
% 9.00/9.19 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(1483,b,1463,a)].
% 9.00/9.19 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(1483,b,1464,a)].
% 9.00/9.19 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(1483,b,1465,a)].
% 9.00/9.19 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(1483,b,1466,a)].
% 9.00/9.19 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(1483,b,1467,a)].
% 9.00/9.20 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(1483,b,1468,a)].
% 9.00/9.20 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(1483,b,1469,a)].
% 9.00/9.20 1484 -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].
% 9.00/9.20 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(1484,b,1462,a)].
% 9.00/9.20 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(1484,b,1463,a)].
% 9.00/9.20 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(1484,b,1464,a)].
% 9.00/9.20 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(1484,b,1465,a)].
% 9.00/9.20 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(1484,b,1466,a)].
% 9.00/9.20 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(1484,b,1467,a)].
% 9.00/9.20 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(1484,b,1468,a)].
% 9.00/9.20 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(1484,b,1469,a)].
% 9.00/9.20 1485 -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].
% 9.00/9.20 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(1485,b,1462,a)].
% 9.00/9.20 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(1485,b,1463,a)].
% 9.00/9.20 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(1485,b,1464,a)].
% 9.00/9.20 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(1485,b,1465,a)].
% 9.00/9.20 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(1485,b,1466,a)].
% 9.00/9.20 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(1485,b,1467,a)].
% 9.00/9.20 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(1485,b,1468,a)].
% 9.00/9.20 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(1485,b,1469,a)].
% 9.00/9.20 1486 -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].
% 9.00/9.20 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(1486,b,1462,a)].
% 9.00/9.20 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(1486,b,1463,a)].
% 9.00/9.20 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(1486,b,1464,a)].
% 9.00/9.20 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(1486,b,1465,a)].
% 9.00/9.20 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(1486,b,1466,a)].
% 9.00/9.20 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(1486,b,1467,a)].
% 9.00/9.22 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(1486,b,1468,a)].
% 9.00/9.22 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(1486,b,1469,a)].
% 9.00/9.22 1487 -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].
% 9.00/9.22 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(1487,b,1462,a)].
% 9.00/9.22 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(1487,b,1463,a)].
% 9.00/9.22 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(1487,b,1464,a)].
% 9.00/9.22 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(1487,b,1465,a)].
% 9.00/9.22 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(1487,b,1466,a)].
% 9.00/9.22 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(1487,b,1467,a)].
% 9.00/9.22 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(1487,b,1468,a)].
% 9.00/9.22 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(1487,b,1469,a)].
% 9.00/9.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1487,b,1477,a)].
% 9.00/9.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1487,b,1478,a)].
% 9.00/9.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1487,b,1479,a)].
% 9.00/9.22 1488 -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)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1488,a,1471,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1488,a,1472,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1488,a,1473,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1488,a,1474,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1488,a,1475,b)].
% 9.00/9.22 1489 -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)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1489,a,1471,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1489,a,1472,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1489,a,1473,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1489,a,1474,b)].
% 9.00/9.22 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1489,a,1475,b)].
% 9.00/9.22 1490 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 9.00/9.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1490,b,1471,b)].
% 9.00/9.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1490,b,1472,b)].
% 9.00/9.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1490,b,1473,b)].
% 9.39/9.56 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1490,b,1474,b)].
% 9.39/9.56 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1490,b,1475,b)].
% 9.39/9.56 1491 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 9.39/9.56 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,b,1471,b)].
% 9.39/9.56 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,b,1472,b)].
% 9.39/9.56 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,b,1473,b)].
% 9.39/9.56 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,b,1474,b)].
% 9.39/9.56 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,b,1475,b)].
% 9.39/9.56 1492 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1152,a,1113,a)].
% 9.39/9.56 1493 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1152,a,1138,a)].
% 9.39/9.56 Derived: class_Orderings_Oorder(tc_nat). [resolve(1493,a,1478,a)].
% 9.39/9.56 Derived: class_Orderings_Oord(tc_nat). [resolve(1493,a,1479,a)].
% 9.39/9.56 Derived: class_HOL_Oplus(tc_nat). [resolve(1493,a,1481,a)].
% 9.39/9.56 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1493,a,1488,a)].
% 9.39/9.56 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1493,a,1489,a)].
% 9.39/9.56 1494 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1152,a,1139,b)].
% 9.39/9.56 1495 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1152,a,1140,b)].
% 9.39/9.56 1496 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1458,a,1446,a)].
% 9.39/9.56 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1496,a,1478,a)].
% 9.39/9.56 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1496,a,1479,a)].
% 9.39/9.56 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1496,a,1480,a)].
% 9.39/9.56 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1496,a,1481,a)].
% 9.39/9.56 1497 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1459,a,1446,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1497,b,1478,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1497,b,1479,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1497,b,1480,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1497,b,1481,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1497,b,1488,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1497,b,1489,a)].
% 9.39/9.56 1498 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1460,a,1446,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1498,b,1478,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1498,b,1479,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1498,b,1480,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1498,b,1481,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1498,b,1488,a)].
% 9.39/9.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1498,b,1489,a)].
% 9.39/9.56 1499 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 9.39/9.56 1500 -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].
% 9.39/9.56 1501 -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].
% 9.39/9.56 1502 -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].
% 9.39/9.56 1503 -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].
% 9.39/9.56 1504 -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].
% 9.39/9.56 1505 -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].
% 9.39/9.56 1506 -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].
% 9.39/9.56 1507 -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].
% 9.39/9.56 1508 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 9.39/9.56 1509 -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].
% 9.39/9.56 1510 -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].
% 9.39/9.56 1511 -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].
% 9.39/9.56 1512 -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].
% 9.39/9.56 1513 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 9.39/9.56 1514 -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].
% 9.39/9.56 1515 -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].
% 9.39/9.56 1516 -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].
% 9.39/9.56 1517 -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].
% 9.39/9.56 1518 -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].
% 9.39/9.56 1519 -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].
% 9.39/9.56 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(1499,a,1500,a)].
% 9.39/9.56 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1499,a,1501,a)].
% 9.39/9.56 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1499,a,1502,a)].
% 9.39/9.56 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1499,a,1503,a)].
% 9.39/9.57 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1499,a,1504,a)].
% 9.39/9.57 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1499,a,1505,a)].
% 9.39/9.57 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(1499,a,1506,a)].
% 9.39/9.57 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(1499,a,1507,a)].
% 9.39/9.57 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1499,a,1508,a)].
% 9.39/9.57 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(1499,a,1509,a)].
% 9.39/9.57 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(1499,a,1510,a)].
% 9.39/9.57 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1499,a,1511,a)].
% 9.39/9.57 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(1499,a,1512,a)].
% 9.39/9.57 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1499,a,1513,a)].
% 9.39/9.57 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(1499,a,1514,a)].
% 9.39/9.57 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(1499,a,1515,a)].
% 9.39/9.57 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(1499,a,1516,a)].
% 9.39/9.57 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(1499,a,1517,a)].
% 9.39/9.57 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1499,a,1518,a)].
% 9.39/9.57 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1499,a,1519,a)].
% 9.39/9.57 1520 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 9.39/9.57 1521 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 9.39/9.57 1522 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 9.39/9.57 1523 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom). [assumption].
% 9.39/9.57 1524 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 9.39/9.57 1525 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom). [assumption].
% 9.39/9.57 1526 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 9.39/9.57 1527 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom). [assumption].
% 9.39/9.57 1528 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 9.39/9.57 1529 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 9.39/9.57 1530 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 9.39/9.57 1531 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 9.39/9.58 1532 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 9.39/9.58 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(1532,b,1500,a)].
% 9.39/9.58 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(1532,b,1501,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1532,b,1502,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1532,b,1503,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1532,b,1504,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1532,b,1505,a)].
% 9.39/9.58 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(1532,b,1506,a)].
% 9.39/9.58 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(1532,b,1507,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1532,b,1508,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1532,b,1509,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1532,b,1510,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1532,b,1511,a)].
% 9.39/9.58 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(1532,b,1512,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1532,b,1513,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1532,b,1514,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1532,b,1515,a)].
% 9.39/9.58 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(1532,b,1516,a)].
% 9.39/9.58 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(1532,b,1517,a)].
% 9.39/9.58 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(1532,b,1518,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1532,b,1519,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1532,b,1520,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1532,b,1521,a)].
% 9.39/9.58 1533 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 9.39/9.58 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(1533,b,1500,a)].
% 9.39/9.58 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(1533,b,1501,a)].
% 9.39/9.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1533,b,1502,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1533,b,1503,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1533,b,1504,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1533,b,1505,a)].
% 9.45/9.60 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(1533,b,1506,a)].
% 9.45/9.60 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(1533,b,1507,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1533,b,1508,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1533,b,1509,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1533,b,1510,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1533,b,1511,a)].
% 9.45/9.60 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(1533,b,1512,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1533,b,1513,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1533,b,1514,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1533,b,1515,a)].
% 9.45/9.60 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(1533,b,1516,a)].
% 9.45/9.60 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(1533,b,1517,a)].
% 9.45/9.60 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(1533,b,1518,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1533,b,1519,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1533,b,1520,a)].
% 9.45/9.60 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1533,b,1521,a)].
% 9.45/9.60 1534 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 9.45/9.60 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(1534,b,1500,a)].
% 9.45/9.60 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(1534,b,1501,a)].
% 9.45/9.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1534,b,1502,a)].
% 9.45/9.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1534,b,1503,a)].
% 9.45/9.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1534,b,1504,a)].
% 9.45/9.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1534,b,1505,a)].
% 9.45/9.60 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(1534,b,1506,a)].
% 9.45/9.60 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(1534,b,1507,a)].
% 9.45/9.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1534,b,1508,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1534,b,1509,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1534,b,1510,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1534,b,1511,a)].
% 9.45/9.61 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(1534,b,1512,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1534,b,1513,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1534,b,1514,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1534,b,1515,a)].
% 9.45/9.61 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(1534,b,1516,a)].
% 9.45/9.61 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(1534,b,1517,a)].
% 9.45/9.61 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(1534,b,1518,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1534,b,1519,a)].
% 9.45/9.61 1535 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 9.45/9.61 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(1535,b,1500,a)].
% 9.45/9.61 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(1535,b,1501,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1535,b,1502,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1535,b,1503,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1535,b,1504,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1535,b,1505,a)].
% 9.45/9.61 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(1535,b,1506,a)].
% 9.45/9.61 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(1535,b,1507,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1535,b,1508,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1535,b,1509,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1535,b,1510,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1535,b,1511,a)].
% 9.45/9.61 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(1535,b,1512,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1535,b,1513,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1535,b,1514,a)].
% 9.45/9.61 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1535,b,1515,a)].
% 9.45/9.61 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(1535,b,1516,a)].
% 9.60/9.76 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(1535,b,1517,a)].
% 9.60/9.76 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(1535,b,1518,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1535,b,1519,a)].
% 9.60/9.76 1536 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 9.60/9.76 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(1536,b,1500,a)].
% 9.60/9.76 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(1536,b,1501,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1536,b,1502,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1536,b,1503,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1536,b,1504,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1536,b,1505,a)].
% 9.60/9.76 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(1536,b,1506,a)].
% 9.60/9.76 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(1536,b,1507,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1536,b,1508,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1536,b,1509,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1536,b,1510,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1536,b,1511,a)].
% 9.60/9.76 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(1536,b,1512,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1536,b,1513,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1536,b,1514,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1536,b,1515,a)].
% 9.60/9.76 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(1536,b,1516,a)].
% 9.60/9.76 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(1536,b,1517,a)].
% 9.60/9.76 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(1536,b,1518,a)].
% 9.60/9.76 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1536,b,1519,a)].
% 9.60/9.76 1537 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 9.60/9.76 1538 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 9.60/9.76 1539 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 9.60/9.76 1540 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 9.60/9.76 1541 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1073,b,1068,a)].
% 9.60/9.76 1542 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1096,b,1091,a)].
% 9.71/9.86 1543 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1312,a,1267,a)].
% 9.71/9.86 1544 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1312,a,1293,b)].
% 9.71/9.86 1545 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1312,a,1294,b)].
% 9.71/9.86 1546 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1458,a,1435,a)].
% 9.71/9.86 1547 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1459,a,1435,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1521,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A). [resolve(1547,b,1525,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1547,b,1526,a)].
% 9.71/9.86 1548 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1460,a,1435,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1521,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A). [resolve(1548,b,1525,a)].
% 9.71/9.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1548,b,1526,a)].
% 9.71/9.86 1549 -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(1471,b,1462,a)].
% 9.71/9.86 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(1549,a,1499,a)].
% 9.71/9.86 1550 -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(1471,b,1463,a)].
% 9.71/9.86 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(1550,a,1499,a)].
% 9.71/9.86 1551 -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(1471,b,1464,a)].
% 9.71/9.86 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(1551,a,1499,a)].
% 9.71/9.86 1552 -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(1471,b,1465,a)].
% 9.71/9.86 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(1552,a,1499,a)].
% 9.71/9.86 1553 -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(1471,b,1466,a)].
% 9.71/9.86 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(1553,a,1499,a)].
% 9.71/9.86 1554 -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(1471,b,1467,a)].
% 9.71/9.86 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(1554,a,1499,a)].
% 9.71/9.86 1555 -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(1471,b,1468,a)].
% 9.71/9.86 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(1555,a,1499,a)].
% 9.71/9.86 1556 -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(1471,b,1469,a)].
% 9.71/9.86 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(1556,a,1499,a)].
% 9.71/9.86 1557 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1476,a,1471,b)].
% 9.71/9.86 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1557,b,1499,a)].
% 9.71/9.86 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1557,b,1534,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1557,b,1535,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1557,b,1536,b)].
% 9.81/9.99 1558 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1477,a,1471,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1558,b,1499,a)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1558,b,1534,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1558,b,1535,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1558,b,1536,b)].
% 9.81/9.99 1559 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1478,a,1471,b)].
% 9.81/9.99 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1559,b,1534,b)].
% 9.81/9.99 1560 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1479,a,1471,b)].
% 9.81/9.99 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1560,b,1534,b)].
% 9.81/9.99 1561 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1488,a,1471,b)].
% 9.81/9.99 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1561,c,1499,a)].
% 9.81/9.99 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1561,c,1534,b)].
% 9.81/9.99 1562 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1489,a,1471,b)].
% 9.81/9.99 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1562,c,1499,a)].
% 9.81/9.99 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1562,c,1534,b)].
% 9.81/9.99 1563 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1490,b,1471,b)].
% 9.81/9.99 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1563,b,1534,b)].
% 9.81/9.99 1564 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,b,1471,b)].
% 9.81/9.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1564,b,1534,b)].
% 9.81/9.99 1565 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 9.81/9.99 1566 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 9.81/9.99 1567 -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].
% 9.81/9.99 1568 -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].
% 9.81/9.99 1569 -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].
% 9.81/9.99 1570 -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].
% 9.81/9.99 1571 -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].
% 9.81/9.99 1572 -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].
% 9.81/9.99 1573 -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].
% 9.85/10.01 1574 -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].
% 9.85/10.01 1575 -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].
% 9.85/10.01 1576 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 9.85/10.01 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1565,a,1566,a)].
% 9.85/10.01 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1567,a)].
% 9.85/10.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1565,a,1568,a)].
% 9.85/10.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1569,a)].
% 9.85/10.01 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(1565,a,1570,a)].
% 9.85/10.01 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(1565,a,1571,a)].
% 9.85/10.01 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(1565,a,1572,a)].
% 9.85/10.01 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(1565,a,1573,a)].
% 9.85/10.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1574,a)].
% 9.85/10.01 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(1565,a,1575,a)].
% 9.85/10.01 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1565,a,1576,a)].
% 9.85/10.01 1577 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 9.85/10.01 Derived: -c_less(A,A,tc_nat). [resolve(1577,a,1566,a)].
% 9.85/10.01 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1567,a)].
% 9.85/10.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1577,a,1568,a)].
% 9.85/10.01 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1569,a)].
% 9.85/10.01 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(1577,a,1570,a)].
% 9.85/10.01 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(1577,a,1571,a)].
% 9.85/10.01 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(1577,a,1572,a)].
% 9.85/10.01 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(1577,a,1573,a)].
% 9.85/10.01 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1574,a)].
% 9.85/10.01 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(1577,a,1575,a)].
% 9.85/10.01 Derived: c_lessequals(A,A,tc_nat). [resolve(1577,a,1576,a)].
% 9.85/10.01 1578 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 9.85/10.01 Derived: -c_less(A,A,tc_set(B)). [resolve(1578,a,1566,a)].
% 9.85/10.01 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1567,a)].
% 9.85/10.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(1578,a,1568,a)].
% 9.85/10.01 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1569,a)].
% 9.85/10.02 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(1578,a,1570,a)].
% 9.85/10.02 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(1578,a,1571,a)].
% 9.85/10.02 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(1578,a,1572,a)].
% 9.85/10.02 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(1578,a,1573,a)].
% 9.85/10.02 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1574,a)].
% 9.85/10.02 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(1578,a,1575,a)].
% 9.85/10.02 Derived: c_lessequals(A,A,tc_set(B)). [resolve(1578,a,1576,a)].
% 9.85/10.02 1579 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1579,b,1566,a)].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1567,a)].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1579,b,1568,a)].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1579,b,1569,a)].
% 9.85/10.02 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(1579,b,1570,a)].
% 9.85/10.02 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(1579,b,1571,a)].
% 9.85/10.02 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(1579,b,1572,a)].
% 9.85/10.02 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(1579,b,1573,a)].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1574,a)].
% 9.85/10.02 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(1579,b,1575,a)].
% 9.85/10.02 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1579,b,1576,a)].
% 9.85/10.02 1580 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 9.85/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1580,b,1566,a)].
% 9.85/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1580,b,1567,a)].
% 9.85/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1580,b,1568,a)].
% 9.85/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1580,b,1569,a)].
% 9.85/10.02 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(1580,b,1570,a)].
% 9.85/10.02 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(1580,b,1571,a)].
% 9.85/10.02 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(1580,b,1572,a)].
% 9.85/10.02 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(1580,b,1573,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1580,b,1574,a)].
% 9.85/10.03 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(1580,b,1575,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1580,b,1576,a)].
% 9.85/10.03 1581 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1581,b,1566,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1581,b,1567,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1581,b,1568,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1581,b,1569,a)].
% 9.85/10.03 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(1581,b,1570,a)].
% 9.85/10.03 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(1581,b,1571,a)].
% 9.85/10.03 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(1581,b,1572,a)].
% 9.85/10.03 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(1581,b,1573,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1581,b,1574,a)].
% 9.85/10.03 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(1581,b,1575,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1581,b,1576,a)].
% 9.85/10.03 1582 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 9.85/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1582,b,1566,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1582,b,1567,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1582,b,1568,a)].
% 9.85/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1582,b,1569,a)].
% 9.85/10.03 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(1582,b,1570,a)].
% 9.85/10.03 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(1582,b,1571,a)].
% 9.85/10.03 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(1582,b,1572,a)].
% 9.85/10.03 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(1582,b,1573,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1582,b,1574,a)].
% 9.90/10.04 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(1582,b,1575,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1582,b,1576,a)].
% 9.90/10.04 1583 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A). [resolve(1583,b,1566,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1583,b,1567,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1583,b,1568,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1583,b,1569,a)].
% 9.90/10.04 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(1583,b,1570,a)].
% 9.90/10.04 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(1583,b,1571,a)].
% 9.90/10.04 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(1583,b,1572,a)].
% 9.90/10.04 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(1583,b,1573,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1583,b,1574,a)].
% 9.90/10.04 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(1583,b,1575,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(1583,b,1576,a)].
% 9.90/10.04 1584 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1584,b,1566,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1584,b,1567,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1584,b,1568,a)].
% 9.90/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1584,b,1569,a)].
% 9.90/10.04 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(1584,b,1570,a)].
% 9.90/10.04 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(1584,b,1571,a)].
% 9.90/10.04 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(1584,b,1572,a)].
% 9.90/10.04 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(1584,b,1573,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1584,b,1574,a)].
% 9.90/10.05 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(1584,b,1575,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1584,b,1576,a)].
% 9.90/10.05 1585 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1585,b,1566,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1585,b,1567,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1585,b,1568,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1585,b,1569,a)].
% 9.90/10.05 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(1585,b,1570,a)].
% 9.90/10.05 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(1585,b,1571,a)].
% 9.90/10.05 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(1585,b,1572,a)].
% 9.90/10.05 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(1585,b,1573,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1585,b,1574,a)].
% 9.90/10.05 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(1585,b,1575,a)].
% 9.90/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1585,b,1576,a)].
% 9.90/10.05 1586 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 9.90/10.05 Derived: class_Orderings_Oord(tc_set(A)). [resolve(1586,a,1578,a)].
% 9.90/10.05 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1586,a,1584,b)].
% 9.90/10.05 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1586,a,1585,b)].
% 9.90/10.05 1587 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 9.90/10.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1587,b,1566,a)].
% 9.90/10.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1587,b,1567,a)].
% 9.90/10.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1587,b,1568,a)].
% 9.90/10.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1587,b,1569,a)].
% 9.90/10.05 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(1587,b,1570,a)].
% 9.90/10.05 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(1587,b,1571,a)].
% 9.90/10.07 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(1587,b,1572,a)].
% 9.90/10.07 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(1587,b,1573,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1587,b,1574,a)].
% 9.90/10.07 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(1587,b,1575,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1587,b,1576,a)].
% 9.90/10.07 1588 -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].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1588,b,1566,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1588,b,1567,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1588,b,1568,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1588,b,1569,a)].
% 9.90/10.07 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(1588,b,1570,a)].
% 9.90/10.07 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(1588,b,1571,a)].
% 9.90/10.07 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(1588,b,1572,a)].
% 9.90/10.07 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(1588,b,1573,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1588,b,1574,a)].
% 9.90/10.07 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(1588,b,1575,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1588,b,1576,a)].
% 9.90/10.07 1589 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A). [resolve(1589,b,1566,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1589,b,1567,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1589,b,1568,a)].
% 9.90/10.07 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1589,b,1569,a)].
% 9.90/10.07 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(1589,b,1570,a)].
% 9.90/10.07 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(1589,b,1571,a)].
% 9.90/10.07 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(1589,b,1572,a)].
% 9.90/10.08 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(1589,b,1573,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1589,b,1574,a)].
% 9.90/10.08 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(1589,b,1575,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(1589,b,1576,a)].
% 9.90/10.08 1590 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A). [resolve(1590,b,1566,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1590,b,1567,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1590,b,1568,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1590,b,1569,a)].
% 9.90/10.08 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(1590,b,1570,a)].
% 9.90/10.08 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(1590,b,1571,a)].
% 9.90/10.08 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(1590,b,1572,a)].
% 9.90/10.08 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(1590,b,1573,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1590,b,1574,a)].
% 9.90/10.08 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(1590,b,1575,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(1590,b,1576,a)].
% 9.90/10.08 1591 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom). [assumption].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1591,b,1566,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1591,b,1567,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1591,b,1568,a)].
% 9.90/10.08 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1591,b,1569,a)].
% 9.90/10.08 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(1591,b,1570,a)].
% 9.90/10.08 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(1591,b,1571,a)].
% 9.90/10.08 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(1591,b,1572,a)].
% 9.90/10.08 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(1591,b,1573,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1591,b,1574,a)].
% 9.90/10.09 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(1591,b,1575,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1591,b,1576,a)].
% 9.90/10.09 1592 -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].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1592,b,1566,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1592,b,1567,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1592,b,1568,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1592,b,1569,a)].
% 9.90/10.09 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(1592,b,1570,a)].
% 9.90/10.09 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(1592,b,1571,a)].
% 9.90/10.09 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(1592,b,1572,a)].
% 9.90/10.09 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(1592,b,1573,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1592,b,1574,a)].
% 9.90/10.09 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(1592,b,1575,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1592,b,1576,a)].
% 9.90/10.09 1593 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom). [assumption].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1593,b,1566,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1593,b,1567,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1593,b,1568,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1593,b,1569,a)].
% 9.90/10.09 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(1593,b,1570,a)].
% 9.90/10.09 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(1593,b,1571,a)].
% 9.90/10.09 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(1593,b,1572,a)].
% 9.90/10.09 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(1593,b,1573,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1593,b,1574,a)].
% 9.90/10.10 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(1593,b,1575,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1593,b,1576,a)].
% 9.90/10.10 1594 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom). [assumption].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A). [resolve(1594,b,1566,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1567,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1594,b,1568,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1594,b,1569,a)].
% 9.90/10.10 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(1594,b,1570,a)].
% 9.90/10.10 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(1594,b,1571,a)].
% 9.90/10.10 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(1594,b,1572,a)].
% 9.90/10.10 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(1594,b,1573,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1574,a)].
% 9.90/10.10 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(1594,b,1575,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(1594,b,1576,a)].
% 9.90/10.10 1595 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom). [assumption].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1595,b,1566,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1567,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1568,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1569,a)].
% 9.90/10.10 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(1595,b,1570,a)].
% 9.90/10.10 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(1595,b,1571,a)].
% 9.90/10.10 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(1595,b,1572,a)].
% 9.90/10.10 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(1595,b,1573,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1574,a)].
% 9.90/10.11 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(1595,b,1575,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1595,b,1576,a)].
% 9.90/10.11 1596 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1596,b,1566,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1567,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1568,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1569,a)].
% 9.90/10.11 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(1596,b,1570,a)].
% 9.90/10.11 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(1596,b,1571,a)].
% 9.90/10.11 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(1596,b,1572,a)].
% 9.90/10.11 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(1596,b,1573,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1574,a)].
% 9.90/10.11 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(1596,b,1575,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1596,b,1576,a)].
% 9.90/10.11 1597 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1597,b,1566,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1567,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1568,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1569,a)].
% 9.90/10.11 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(1597,b,1570,a)].
% 9.90/10.11 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(1597,b,1571,a)].
% 9.90/10.11 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(1597,b,1572,a)].
% 9.90/10.11 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(1597,b,1573,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1574,a)].
% 9.90/10.11 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(1597,b,1575,a)].
% 10.21/10.36 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1597,b,1576,a)].
% 10.21/10.36 1598 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1598,b,1566,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1567,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1568,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1569,a)].
% 10.21/10.36 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(1598,b,1570,a)].
% 10.21/10.36 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(1598,b,1571,a)].
% 10.21/10.36 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(1598,b,1572,a)].
% 10.21/10.36 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(1598,b,1573,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1574,a)].
% 10.21/10.36 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(1598,b,1575,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1598,b,1576,a)].
% 10.21/10.36 1599 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(886,a,821,a)].
% 10.21/10.36 1600 class_Orderings_Oorder(tc_nat). [resolve(886,a,880,a)].
% 10.21/10.36 1601 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(886,a,881,b)].
% 10.21/10.36 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1601,a,1586,a)].
% 10.21/10.36 1602 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(893,b,886,a)].
% 10.21/10.36 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1602,b,1586,a)].
% 10.21/10.36 1603 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1072,b,1071,a)].
% 10.21/10.36 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1603,b,1586,a)].
% 10.21/10.36 1604 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1078,b,1071,a)].
% 10.21/10.36 1605 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1139,b)].
% 10.21/10.36 1606 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1140,b)].
% 10.21/10.36 1607 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1458,a,1440,a)].
% 10.21/10.36 1608 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1459,a,1440,a)].
% 10.21/10.36 1609 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1460,a,1440,a)].
% 10.21/10.36 1610 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1478,a,1472,b)].
% 10.21/10.36 1611 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1478,a,1473,b)].
% 10.21/10.36 1612 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1478,a,1475,b)].
% 10.21/10.36 1613 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1487,b,1478,a)].
% 10.21/10.36 1614 class_Orderings_Oorder(tc_nat). [resolve(1493,a,1478,a)].
% 10.21/10.36 1615 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1496,a,1478,a)].
% 10.21/10.36 1616 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1497,b,1478,a)].
% 10.38/10.53 1617 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1498,b,1478,a)].
% 10.38/10.53 1618 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1559,b,1534,b)].
% 10.38/10.53 1619 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 10.38/10.53 1620 -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].
% 10.38/10.53 1621 -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].
% 10.38/10.53 1622 -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].
% 10.38/10.53 1623 -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].
% 10.38/10.53 1624 -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].
% 10.38/10.53 1625 -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].
% 10.38/10.53 1626 -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].
% 10.38/10.53 1627 -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].
% 10.38/10.53 1628 -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].
% 10.38/10.53 1629 -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].
% 10.38/10.53 1630 -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].
% 10.38/10.53 1631 -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].
% 10.38/10.53 1632 -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].
% 10.38/10.53 1633 -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].
% 10.38/10.53 1634 -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].
% 10.38/10.53 1635 -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].
% 10.38/10.53 1636 -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].
% 10.38/10.53 1637 -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].
% 10.38/10.53 1638 -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].
% 10.38/10.53 1639 -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].
% 10.38/10.53 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1619,a,1620,a)].
% 10.38/10.53 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1619,a,1621,a)].
% 10.38/10.54 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(1619,a,1622,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1619,a,1623,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1619,a,1624,a)].
% 10.38/10.54 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(1619,a,1625,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1619,a,1626,a)].
% 10.38/10.54 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1619,a,1627,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1619,a,1628,a)].
% 10.38/10.54 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1619,a,1629,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1619,a,1630,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1619,a,1631,a)].
% 10.38/10.54 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(1619,a,1632,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1619,a,1633,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1619,a,1634,a)].
% 10.38/10.54 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(1619,a,1635,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1619,a,1636,a)].
% 10.38/10.54 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1619,a,1637,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1619,a,1638,a)].
% 10.38/10.54 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1619,a,1639,a)].
% 10.38/10.54 1640 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1640,a,1620,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1640,a,1621,a)].
% 10.38/10.54 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(1640,a,1622,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1640,a,1623,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1640,a,1624,a)].
% 10.38/10.54 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(1640,a,1625,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1640,a,1626,a)].
% 10.38/10.54 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1640,a,1627,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1640,a,1628,a)].
% 10.38/10.54 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1640,a,1629,a)].
% 10.38/10.54 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1640,a,1630,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1640,a,1631,a)].
% 10.38/10.56 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(1640,a,1632,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1640,a,1633,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1640,a,1634,a)].
% 10.38/10.56 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(1640,a,1635,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1640,a,1636,a)].
% 10.38/10.56 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1640,a,1637,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1640,a,1638,a)].
% 10.38/10.56 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1640,a,1639,a)].
% 10.38/10.56 1641 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1641,a,1620,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1641,a,1621,a)].
% 10.38/10.56 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(1641,a,1622,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1641,a,1623,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1641,a,1624,a)].
% 10.38/10.56 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(1641,a,1625,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1641,a,1626,a)].
% 10.38/10.56 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1641,a,1627,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1641,a,1628,a)].
% 10.38/10.56 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1641,a,1629,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1641,a,1630,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1641,a,1631,a)].
% 10.38/10.56 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(1641,a,1632,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1641,a,1633,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1641,a,1634,a)].
% 10.38/10.56 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(1641,a,1635,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1641,a,1636,a)].
% 10.38/10.56 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1641,a,1637,a)].
% 10.38/10.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1641,a,1638,a)].
% 10.38/10.56 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1641,a,1639,a)].
% 10.38/10.56 1642 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 10.38/10.56 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1620,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1642,b,1621,a)].
% 10.38/10.57 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(1642,b,1622,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1623,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1642,b,1624,a)].
% 10.38/10.57 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(1642,b,1625,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1626,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1642,b,1627,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1642,b,1628,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1642,b,1629,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1642,b,1630,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1642,b,1631,a)].
% 10.38/10.57 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(1642,b,1632,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1642,b,1633,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1642,b,1634,a)].
% 10.38/10.57 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(1642,b,1635,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1642,b,1636,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1642,b,1637,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1642,b,1638,a)].
% 10.38/10.57 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1642,b,1639,a)].
% 10.38/10.57 1643 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1620,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1643,b,1621,a)].
% 10.38/10.57 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(1643,b,1622,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1623,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1643,b,1624,a)].
% 10.38/10.57 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(1643,b,1625,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1626,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1643,b,1627,a)].
% 10.38/10.57 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1643,b,1628,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1643,b,1629,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1643,b,1630,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1643,b,1631,a)].
% 10.44/10.58 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(1643,b,1632,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1643,b,1633,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1643,b,1634,a)].
% 10.44/10.58 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(1643,b,1635,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1643,b,1636,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1643,b,1637,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1643,b,1638,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1643,b,1639,a)].
% 10.44/10.58 1644 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1620,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1621,a)].
% 10.44/10.58 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(1644,b,1622,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1623,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1624,a)].
% 10.44/10.58 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(1644,b,1625,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1626,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1644,b,1627,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1644,b,1628,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1644,b,1629,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1630,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1631,a)].
% 10.44/10.58 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(1644,b,1632,a)].
% 10.44/10.58 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1633,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1634,a)].
% 10.44/10.59 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(1644,b,1635,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1644,b,1636,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1644,b,1637,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1644,b,1638,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1644,b,1639,a)].
% 10.44/10.59 1645 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 10.44/10.59 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(1645,b,1620,a)].
% 10.44/10.59 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(1645,b,1621,a)].
% 10.44/10.59 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(1645,b,1622,a)].
% 10.44/10.59 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(1645,b,1623,a)].
% 10.44/10.59 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(1645,b,1624,a)].
% 10.44/10.59 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(1645,b,1625,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1626,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1645,b,1627,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1645,b,1628,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1645,b,1629,a)].
% 10.44/10.59 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(1645,b,1630,a)].
% 10.44/10.59 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(1645,b,1631,a)].
% 10.44/10.59 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(1645,b,1632,a)].
% 10.44/10.59 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(1645,b,1633,a)].
% 10.44/10.59 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(1645,b,1634,a)].
% 10.44/10.59 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(1645,b,1635,a)].
% 10.44/10.59 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1645,b,1636,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1645,b,1637,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1645,b,1638,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1645,b,1639,a)].
% 10.44/10.60 1646 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1620,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1621,a)].
% 10.44/10.60 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(1646,b,1622,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1623,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1624,a)].
% 10.44/10.60 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(1646,b,1625,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1626,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1646,b,1627,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1646,b,1628,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1646,b,1629,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1630,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1631,a)].
% 10.44/10.60 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(1646,b,1632,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1633,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1634,a)].
% 10.44/10.60 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(1646,b,1635,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1646,b,1636,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1646,b,1637,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1646,b,1638,a)].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1646,b,1639,a)].
% 10.44/10.60 1647 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 10.44/10.60 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1620,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1621,a)].
% 10.44/10.62 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(1647,b,1622,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1623,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1624,a)].
% 10.44/10.62 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(1647,b,1625,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1626,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1647,b,1627,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1647,b,1628,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1647,b,1629,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1630,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1631,a)].
% 10.44/10.62 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(1647,b,1632,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1633,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1634,a)].
% 10.44/10.62 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(1647,b,1635,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1647,b,1636,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1647,b,1637,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1647,b,1638,a)].
% 10.44/10.62 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1647,b,1639,a)].
% 10.44/10.62 1648 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 10.44/10.62 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(1648,b,1620,a)].
% 10.44/10.62 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(1648,b,1621,a)].
% 10.44/10.62 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(1648,b,1622,a)].
% 10.44/10.62 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(1648,b,1623,a)].
% 10.44/10.62 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(1648,b,1624,a)].
% 10.44/10.63 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(1648,b,1625,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1626,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1648,b,1627,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1648,b,1628,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1648,b,1629,a)].
% 10.44/10.63 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(1648,b,1630,a)].
% 10.44/10.63 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(1648,b,1631,a)].
% 10.44/10.63 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(1648,b,1632,a)].
% 10.44/10.63 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(1648,b,1633,a)].
% 10.44/10.63 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(1648,b,1634,a)].
% 10.44/10.63 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(1648,b,1635,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1648,b,1636,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1648,b,1637,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1648,b,1638,a)].
% 10.44/10.63 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1648,b,1639,a)].
% 10.44/10.63 1649 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 10.44/10.63 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(1649,b,1620,a)].
% 10.44/10.63 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(1649,b,1621,a)].
% 10.44/10.63 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(1649,b,1622,a)].
% 10.44/10.63 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(1649,b,1623,a)].
% 10.44/10.63 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(1649,b,1624,a)].
% 10.44/10.63 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(1649,b,1625,a)].
% 10.44/10.63 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1626,a)].
% 10.44/10.63 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1649,b,1627,a)].
% 10.44/10.63 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1649,b,1628,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1649,b,1629,a)].
% 10.44/10.64 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(1649,b,1630,a)].
% 10.44/10.64 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(1649,b,1631,a)].
% 10.44/10.64 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(1649,b,1632,a)].
% 10.44/10.64 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(1649,b,1633,a)].
% 10.44/10.64 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(1649,b,1634,a)].
% 10.44/10.64 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(1649,b,1635,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1649,b,1636,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1649,b,1637,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1649,b,1638,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1649,b,1639,a)].
% 10.44/10.64 1650 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1620,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1621,a)].
% 10.44/10.64 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(1650,b,1622,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1623,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1624,a)].
% 10.44/10.64 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(1650,b,1625,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1626,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1650,b,1627,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1650,b,1628,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1650,b,1629,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1630,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1631,a)].
% 10.44/10.64 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(1650,b,1632,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1633,a)].
% 10.44/10.64 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1634,a)].
% 10.44/10.65 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(1650,b,1635,a)].
% 10.44/10.65 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1650,b,1636,a)].
% 10.44/10.65 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1650,b,1637,a)].
% 10.44/10.65 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1650,b,1638,a)].
% 10.44/10.65 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1650,b,1639,a)].
% 10.44/10.65 1651 -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].
% 10.44/10.65 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(1651,b,1620,a)].
% 10.44/10.65 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(1651,b,1621,a)].
% 10.44/10.65 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(1651,b,1622,a)].
% 10.44/10.65 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(1651,b,1623,a)].
% 10.44/10.65 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(1651,b,1624,a)].
% 10.44/10.65 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(1651,b,1625,a)].
% 10.44/10.65 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(1651,b,1626,a)].
% 10.44/10.65 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(1651,b,1627,a)].
% 10.44/10.65 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(1651,b,1628,a)].
% 10.44/10.65 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(1651,b,1629,a)].
% 10.44/10.65 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(1651,b,1630,a)].
% 10.44/10.65 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(1651,b,1631,a)].
% 10.44/10.65 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(1651,b,1632,a)].
% 10.44/10.65 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(1651,b,1633,a)].
% 10.44/10.65 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(1651,b,1634,a)].
% 10.44/10.65 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(1651,b,1635,a)].
% 10.44/10.65 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(1651,b,1636,a)].
% 10.44/10.65 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(1651,b,1637,a)].
% 10.44/10.65 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(1651,b,1638,a)].
% 10.53/10.67 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(1651,b,1639,a)].
% 10.53/10.67 1652 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1620,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1621,a)].
% 10.53/10.67 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(1652,b,1622,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1623,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1624,a)].
% 10.53/10.67 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(1652,b,1625,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1626,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1652,b,1627,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1652,b,1628,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1652,b,1629,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1630,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1631,a)].
% 10.53/10.67 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(1652,b,1632,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1633,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1634,a)].
% 10.53/10.67 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(1652,b,1635,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1652,b,1636,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1652,b,1637,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1652,b,1638,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1652,b,1639,a)].
% 10.53/10.67 1653 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1653,b,1620,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1653,b,1621,a)].
% 10.53/10.67 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(1653,b,1622,a)].
% 10.53/10.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1653,b,1623,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1653,b,1624,a)].
% 10.56/10.68 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(1653,b,1625,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1653,b,1626,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1653,b,1627,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1653,b,1628,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1653,b,1629,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1653,b,1630,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1653,b,1631,a)].
% 10.56/10.68 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(1653,b,1632,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1653,b,1633,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1653,b,1634,a)].
% 10.56/10.68 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(1653,b,1635,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1653,b,1636,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1653,b,1637,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1653,b,1638,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1653,b,1639,a)].
% 10.56/10.68 1654 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 10.56/10.68 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(1654,b,1620,a)].
% 10.56/10.68 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(1654,b,1621,a)].
% 10.56/10.68 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(1654,b,1622,a)].
% 10.56/10.68 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(1654,b,1623,a)].
% 10.56/10.68 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(1654,b,1624,a)].
% 10.56/10.68 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(1654,b,1625,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1626,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1654,b,1627,a)].
% 10.56/10.68 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1654,b,1628,a)].
% 10.56/10.69 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1654,b,1629,a)].
% 10.56/10.69 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(1654,b,1630,a)].
% 10.56/10.69 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(1654,b,1631,a)].
% 10.56/10.69 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(1654,b,1632,a)].
% 10.56/10.69 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(1654,b,1633,a)].
% 10.56/10.69 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(1654,b,1634,a)].
% 10.56/10.69 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(1654,b,1635,a)].
% 10.56/10.69 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1654,b,1636,a)].
% 10.56/10.69 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1654,b,1637,a)].
% 10.56/10.69 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1654,b,1638,a)].
% 10.56/10.69 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1654,b,1639,a)].
% 10.56/10.69 1655 -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].
% 10.56/10.69 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(1655,b,1620,a)].
% 10.56/10.69 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(1655,b,1621,a)].
% 10.56/10.69 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(1655,b,1622,a)].
% 10.56/10.69 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(1655,b,1623,a)].
% 10.56/10.69 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(1655,b,1624,a)].
% 10.56/10.69 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(1655,b,1625,a)].
% 10.56/10.69 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(1655,b,1626,a)].
% 10.56/10.69 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(1655,b,1627,a)].
% 10.56/10.69 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(1655,b,1628,a)].
% 10.56/10.69 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(1655,b,1629,a)].
% 10.56/10.69 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(1655,b,1630,a)].
% 10.56/10.69 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(1655,b,1631,a)].
% 10.56/10.69 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(1655,b,1632,a)].
% 10.56/10.70 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(1655,b,1633,a)].
% 10.56/10.70 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(1655,b,1634,a)].
% 10.56/10.70 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(1655,b,1635,a)].
% 10.56/10.70 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(1655,b,1636,a)].
% 10.56/10.70 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(1655,b,1637,a)].
% 10.56/10.70 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(1655,b,1638,a)].
% 10.56/10.70 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(1655,b,1639,a)].
% 10.56/10.70 1656 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 10.56/10.70 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(1656,b,1620,a)].
% 10.56/10.70 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(1656,b,1621,a)].
% 10.56/10.70 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(1656,b,1622,a)].
% 10.56/10.70 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(1656,b,1623,a)].
% 10.56/10.70 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(1656,b,1624,a)].
% 10.56/10.70 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(1656,b,1625,a)].
% 10.56/10.70 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1626,a)].
% 10.56/10.70 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1656,b,1627,a)].
% 10.56/10.70 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1656,b,1628,a)].
% 10.56/10.70 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1656,b,1629,a)].
% 10.56/10.70 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(1656,b,1630,a)].
% 10.56/10.70 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(1656,b,1631,a)].
% 10.56/10.70 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(1656,b,1632,a)].
% 10.56/10.70 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(1656,b,1633,a)].
% 10.56/10.70 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(1656,b,1634,a)].
% 10.56/10.70 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(1656,b,1635,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1656,b,1636,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1656,b,1637,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1656,b,1638,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1656,b,1639,a)].
% 10.56/10.72 1657 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 10.56/10.72 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(1657,b,1620,a)].
% 10.56/10.72 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(1657,b,1621,a)].
% 10.56/10.72 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(1657,b,1622,a)].
% 10.56/10.72 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(1657,b,1623,a)].
% 10.56/10.72 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(1657,b,1624,a)].
% 10.56/10.72 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(1657,b,1625,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1657,b,1626,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1657,b,1627,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1657,b,1628,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1657,b,1629,a)].
% 10.56/10.72 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(1657,b,1630,a)].
% 10.56/10.72 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(1657,b,1631,a)].
% 10.56/10.72 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(1657,b,1632,a)].
% 10.56/10.72 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(1657,b,1633,a)].
% 10.56/10.72 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(1657,b,1634,a)].
% 10.56/10.72 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(1657,b,1635,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1657,b,1636,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1657,b,1637,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1657,b,1638,a)].
% 10.56/10.72 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1657,b,1639,a)].
% 10.56/10.72 1658 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 10.60/10.73 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(1658,b,1620,a)].
% 10.60/10.73 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(1658,b,1621,a)].
% 10.60/10.73 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(1658,b,1622,a)].
% 10.60/10.73 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(1658,b,1623,a)].
% 10.60/10.73 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(1658,b,1624,a)].
% 10.60/10.73 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(1658,b,1625,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1626,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1658,b,1627,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1658,b,1628,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1658,b,1629,a)].
% 10.60/10.73 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(1658,b,1630,a)].
% 10.60/10.73 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(1658,b,1631,a)].
% 10.60/10.73 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(1658,b,1632,a)].
% 10.60/10.73 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(1658,b,1633,a)].
% 10.60/10.73 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(1658,b,1634,a)].
% 10.60/10.73 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(1658,b,1635,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1658,b,1636,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1658,b,1637,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1658,b,1638,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1658,b,1639,a)].
% 10.60/10.73 1659 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1620,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1621,a)].
% 10.60/10.73 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(1659,b,1622,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1623,a)].
% 10.60/10.73 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1624,a)].
% 10.62/10.74 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(1659,b,1625,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1626,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1627,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1628,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1629,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1630,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1631,a)].
% 10.62/10.74 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(1659,b,1632,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1633,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1634,a)].
% 10.62/10.74 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(1659,b,1635,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1636,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1637,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1638,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1639,a)].
% 10.62/10.74 1660 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1620,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1621,a)].
% 10.62/10.74 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(1660,b,1622,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1623,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1624,a)].
% 10.62/10.74 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(1660,b,1625,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1626,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1627,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1628,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1629,a)].
% 10.62/10.74 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1630,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1631,a)].
% 10.62/10.75 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(1660,b,1632,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1633,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1634,a)].
% 10.62/10.75 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(1660,b,1635,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1636,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1637,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1638,a)].
% 10.62/10.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1639,a)].
% 10.62/10.75 1661 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1620,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1621,a)].
% 10.62/10.75 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(1661,b,1622,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1623,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1624,a)].
% 10.62/10.75 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(1661,b,1625,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1626,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1627,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1628,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1629,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1630,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1631,a)].
% 10.62/10.75 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(1661,b,1632,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1633,a)].
% 10.62/10.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1634,a)].
% 10.62/10.75 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(1661,b,1635,a)].
% 11.75/11.90 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1636,a)].
% 11.75/11.90 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1637,a)].
% 11.75/11.90 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1638,a)].
% 11.75/11.90 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1639,a)].
% 11.75/11.90 1662 class_Orderings_Oord(tc_IntDef_Oint). [resolve(885,a,821,a)].
% 11.75/11.90 1663 class_Orderings_Oord(tc_nat). [resolve(885,a,880,a)].
% 11.75/11.90 1664 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(885,a,881,b)].
% 11.75/11.90 1665 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(893,b,885,a)].
% 11.75/11.90 1666 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1072,b,1070,a)].
% 11.75/11.90 1667 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1078,b,1070,a)].
% 11.75/11.90 1668 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1139,b)].
% 11.75/11.90 1669 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1140,b)].
% 11.75/11.90 1670 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1458,a,1441,a)].
% 11.75/11.90 1671 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1459,a,1441,a)].
% 11.75/11.90 1672 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1460,a,1441,a)].
% 11.75/11.90 1673 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1479,a,1472,b)].
% 11.75/11.90 1674 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1479,a,1473,b)].
% 11.75/11.90 1675 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1479,a,1475,b)].
% 11.75/11.90 1676 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1487,b,1479,a)].
% 11.75/11.90 1677 class_Orderings_Oord(tc_nat). [resolve(1493,a,1479,a)].
% 11.75/11.90 1678 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1496,a,1479,a)].
% 11.75/11.90 1679 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1497,b,1479,a)].
% 11.75/11.90 1680 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1498,b,1479,a)].
% 11.75/11.90 1681 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1560,b,1534,b)].
% 11.75/11.90 1682 class_Orderings_Oord(tc_set(A)). [resolve(1586,a,1578,a)].
% 11.75/11.90 1683 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1586,a,1584,b)].
% 11.75/11.90 1684 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1586,a,1585,b)].
% 11.75/11.90 1685 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1601,a,1586,a)].
% 11.75/11.90 1686 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1602,b,1586,a)].
% 11.75/11.90 1687 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1603,b,1586,a)].
% 11.75/11.90 1688 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1072,b,1068,a)].
% 11.75/11.90 1689 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 11.75/11.90 1690 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 11.75/11.90 1691 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 11.75/11.90 1692 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 11.75/11.90 1693 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 11.75/11.90 1694 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 11.75/11.90 1695 -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].
% 11.91/12.03 1696 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 11.91/12.03 1697 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 11.91/12.03 1698 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 11.91/12.03 1699 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 11.91/12.03 1700 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(882,a,821,a)].
% 11.91/12.03 1701 class_LOrder_Olorder(tc_nat). [resolve(882,a,880,a)].
% 11.91/12.03 1702 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(882,a,881,b)].
% 11.91/12.03 1703 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(893,b,882,a)].
% 11.91/12.03 1704 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1093,b,1091,a)].
% 11.91/12.03 1705 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1151,a,1139,b)].
% 11.91/12.03 1706 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1151,a,1140,b)].
% 11.91/12.03 1707 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1458,a,1439,a)].
% 11.91/12.03 1708 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1459,a,1439,a)].
% 11.91/12.03 1709 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1460,a,1439,a)].
% 11.91/12.03 1710 -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1579,b,1566,a)].
% 11.91/12.03 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1710,a,1689,a)].
% 11.91/12.03 Derived: -c_less(A,A,tc_nat). [resolve(1710,a,1690,a)].
% 11.91/12.03 1711 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1567,a)].
% 11.91/12.03 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1711,a,1689,a)].
% 11.91/12.03 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1711,a,1690,a)].
% 11.91/12.03 1712 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1579,b,1568,a)].
% 11.91/12.03 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1712,a,1689,a)].
% 11.91/12.03 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1712,a,1690,a)].
% 11.91/12.03 1713 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1579,b,1569,a)].
% 11.91/12.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1713,a,1689,a)].
% 11.91/12.03 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1713,a,1690,a)].
% 11.91/12.03 1714 -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(1579,b,1570,a)].
% 11.91/12.03 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(1714,a,1689,a)].
% 11.91/12.03 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(1714,a,1690,a)].
% 11.91/12.03 1715 -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(1579,b,1571,a)].
% 11.91/12.03 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(1715,a,1689,a)].
% 11.91/12.03 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(1715,a,1690,a)].
% 11.91/12.03 1716 -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(1579,b,1572,a)].
% 11.95/12.08 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(1716,a,1689,a)].
% 11.95/12.08 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(1716,a,1690,a)].
% 11.95/12.08 1717 -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(1579,b,1573,a)].
% 11.95/12.08 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(1717,a,1689,a)].
% 11.95/12.08 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(1717,a,1690,a)].
% 11.95/12.08 1718 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1574,a)].
% 11.95/12.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1718,a,1689,a)].
% 11.95/12.08 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1718,a,1690,a)].
% 11.95/12.08 1719 -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(1579,b,1575,a)].
% 11.95/12.08 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(1719,a,1689,a)].
% 11.95/12.08 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(1719,a,1690,a)].
% 11.95/12.08 1720 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1579,b,1576,a)].
% 11.95/12.08 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1720,a,1689,a)].
% 11.95/12.08 Derived: c_lessequals(A,A,tc_nat). [resolve(1720,a,1690,a)].
% 11.95/12.08 1721 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1620,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1721,a,1689,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1721,a,1690,a)].
% 11.95/12.08 1722 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1642,b,1621,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1722,a,1689,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1722,a,1690,a)].
% 11.95/12.08 1723 -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(1642,b,1622,a)].
% 11.95/12.08 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(1723,a,1689,a)].
% 11.95/12.08 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(1723,a,1690,a)].
% 11.95/12.08 1724 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1623,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1724,a,1689,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1724,a,1690,a)].
% 11.95/12.08 1725 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1642,b,1624,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1725,a,1689,a)].
% 11.95/12.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1725,a,1690,a)].
% 11.95/12.09 1726 -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(1642,b,1625,a)].
% 11.95/12.09 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(1726,a,1689,a)].
% 11.95/12.09 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(1726,a,1690,a)].
% 11.95/12.09 1727 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1642,b,1626,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1727,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1727,a,1690,a)].
% 11.95/12.09 1728 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1642,b,1627,a)].
% 11.95/12.09 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1728,a,1689,a)].
% 11.95/12.09 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1728,a,1690,a)].
% 11.95/12.09 1729 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1642,b,1628,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1729,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1729,a,1690,a)].
% 11.95/12.09 1730 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1642,b,1629,a)].
% 11.95/12.09 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1730,a,1689,a)].
% 11.95/12.09 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1730,a,1690,a)].
% 11.95/12.09 1731 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1642,b,1630,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1731,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1731,a,1690,a)].
% 11.95/12.09 1732 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1642,b,1631,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1732,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1732,a,1690,a)].
% 11.95/12.09 1733 -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(1642,b,1632,a)].
% 11.95/12.09 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(1733,a,1689,a)].
% 11.95/12.09 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(1733,a,1690,a)].
% 11.95/12.09 1734 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1642,b,1633,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1734,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1734,a,1690,a)].
% 11.95/12.09 1735 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1642,b,1634,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1735,a,1689,a)].
% 11.95/12.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1735,a,1690,a)].
% 11.95/12.09 1736 -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(1642,b,1635,a)].
% 12.16/12.29 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(1736,a,1689,a)].
% 12.16/12.29 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(1736,a,1690,a)].
% 12.16/12.29 1737 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1642,b,1636,a)].
% 12.16/12.29 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1737,a,1689,a)].
% 12.16/12.29 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1737,a,1690,a)].
% 12.16/12.29 1738 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1642,b,1637,a)].
% 12.16/12.29 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1738,a,1689,a)].
% 12.16/12.29 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1738,a,1690,a)].
% 12.16/12.29 1739 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1642,b,1638,a)].
% 12.16/12.29 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1739,a,1689,a)].
% 12.16/12.29 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1739,a,1690,a)].
% 12.16/12.29 1740 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1642,b,1639,a)].
% 12.16/12.29 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1740,a,1689,a)].
% 12.16/12.29 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1740,a,1690,a)].
% 12.16/12.29 1741 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 12.16/12.29 1742 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 12.16/12.29 1743 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 12.16/12.29 1744 -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].
% 12.16/12.29 1745 -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].
% 12.16/12.29 1746 -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].
% 12.16/12.29 1747 -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].
% 12.16/12.29 1748 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom). [assumption].
% 12.16/12.29 1749 -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].
% 12.16/12.29 1750 -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].
% 12.16/12.29 1751 -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].
% 12.16/12.29 1752 -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].
% 12.37/12.53 1753 -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].
% 12.37/12.53 1754 -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].
% 12.37/12.53 1755 -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].
% 12.37/12.53 1756 -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].
% 12.37/12.53 1757 -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].
% 12.37/12.53 1758 -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].
% 12.37/12.53 1759 -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].
% 12.37/12.53 1760 -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].
% 12.37/12.53 1761 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1113,a)].
% 12.37/12.53 1762 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1158,a,1138,a)].
% 12.37/12.53 1763 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1139,b)].
% 12.37/12.53 1764 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1140,b)].
% 12.37/12.53 1765 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1448,a)].
% 12.37/12.53 1766 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1459,a,1448,a)].
% 12.37/12.53 1767 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1460,a,1448,a)].
% 12.37/12.53 1768 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1477,a,1472,b)].
% 12.37/12.53 1769 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1477,a,1473,b)].
% 12.37/12.53 1770 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1477,a,1474,b)].
% 12.37/12.53 1771 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1477,a,1475,b)].
% 12.37/12.53 1772 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1487,b,1477,a)].
% 12.37/12.53 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1772,b,1741,a)].
% 12.37/12.53 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1772,b,1748,a)].
% 12.37/12.53 1773 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1558,b,1499,a)].
% 12.37/12.53 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1773,a,1741,a)].
% 12.37/12.53 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1773,a,1748,a)].
% 12.37/12.53 1774 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1558,b,1534,b)].
% 12.37/12.53 1775 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1558,b,1535,b)].
% 12.37/12.53 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1775,a,1741,a)].
% 12.37/12.53 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1775,a,1748,a)].
% 12.37/12.53 1776 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1558,b,1536,b)].
% 12.37/12.55 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1776,a,1741,a)].
% 12.37/12.55 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1776,a,1748,a)].
% 12.37/12.55 1777 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1584,b,1566,a)].
% 12.37/12.55 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1777,a,1744,b)].
% 12.37/12.55 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1777,a,1745,b)].
% 12.37/12.55 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1777,a,1746,b)].
% 12.37/12.55 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1777,a,1747,b)].
% 12.37/12.55 1778 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1584,b,1567,a)].
% 12.37/12.55 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1778,a,1744,b)].
% 12.44/12.55 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1778,a,1745,b)].
% 12.44/12.55 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1778,a,1746,b)].
% 12.44/12.55 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1778,a,1747,b)].
% 12.44/12.55 1779 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1584,b,1568,a)].
% 12.44/12.55 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1779,a,1744,b)].
% 12.44/12.55 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1779,a,1745,b)].
% 12.44/12.55 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1779,a,1746,b)].
% 12.44/12.55 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1779,a,1747,b)].
% 12.44/12.55 1780 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1584,b,1569,a)].
% 12.44/12.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1744,b)].
% 12.44/12.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1745,b)].
% 12.44/12.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1746,b)].
% 12.44/12.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1780,a,1747,b)].
% 12.44/12.55 1781 -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(1584,b,1570,a)].
% 12.44/12.55 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(1781,a,1744,b)].
% 12.44/12.55 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(1781,a,1745,b)].
% 12.44/12.55 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(1781,a,1746,b)].
% 12.44/12.55 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(1781,a,1747,b)].
% 12.44/12.56 1782 -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(1584,b,1571,a)].
% 12.44/12.56 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(1782,a,1744,b)].
% 12.44/12.56 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(1782,a,1745,b)].
% 12.44/12.56 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(1782,a,1746,b)].
% 12.44/12.56 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(1782,a,1747,b)].
% 12.44/12.56 1783 -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(1584,b,1572,a)].
% 12.44/12.56 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(1783,a,1744,b)].
% 12.44/12.56 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(1783,a,1745,b)].
% 12.44/12.56 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(1783,a,1746,b)].
% 12.44/12.56 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(1783,a,1747,b)].
% 12.44/12.56 1784 -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(1584,b,1573,a)].
% 12.44/12.56 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(1784,a,1744,b)].
% 12.44/12.56 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(1784,a,1745,b)].
% 12.44/12.56 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(1784,a,1746,b)].
% 12.44/12.56 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(1784,a,1747,b)].
% 12.44/12.56 1785 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1584,b,1574,a)].
% 12.44/12.56 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1785,a,1744,b)].
% 12.44/12.56 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1785,a,1745,b)].
% 12.44/12.56 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1785,a,1746,b)].
% 12.44/12.56 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1785,a,1747,b)].
% 12.44/12.56 1786 -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(1584,b,1575,a)].
% 12.44/12.56 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(1786,a,1744,b)].
% 12.46/12.61 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(1786,a,1745,b)].
% 12.46/12.61 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(1786,a,1746,b)].
% 12.46/12.61 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(1786,a,1747,b)].
% 12.46/12.61 1787 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1584,b,1576,a)].
% 12.46/12.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1787,a,1744,b)].
% 12.46/12.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1787,a,1745,b)].
% 12.46/12.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1787,a,1746,b)].
% 12.46/12.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1787,a,1747,b)].
% 12.46/12.61 1788 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1620,a)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1788,a,1744,b)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1788,a,1745,b)].
% 12.46/12.61 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(1788,a,1746,b)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1788,a,1747,b)].
% 12.46/12.61 1789 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1621,a)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1789,a,1744,b)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1789,a,1745,b)].
% 12.46/12.61 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(1789,a,1746,b)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1789,a,1747,b)].
% 12.46/12.61 1790 -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(1647,b,1622,a)].
% 12.46/12.61 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(1790,a,1744,b)].
% 12.46/12.61 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(1790,a,1745,b)].
% 12.46/12.61 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(1790,a,1746,b)].
% 12.46/12.61 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(1790,a,1747,b)].
% 12.46/12.61 1791 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1623,a)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1791,a,1744,b)].
% 12.46/12.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1791,a,1745,b)].
% 12.50/12.62 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(1791,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1791,a,1747,b)].
% 12.50/12.62 1792 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1624,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1792,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1792,a,1745,b)].
% 12.50/12.62 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(1792,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1792,a,1747,b)].
% 12.50/12.62 1793 -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(1647,b,1625,a)].
% 12.50/12.62 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(1793,a,1744,b)].
% 12.50/12.62 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(1793,a,1745,b)].
% 12.50/12.62 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(1793,a,1746,b)].
% 12.50/12.62 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(1793,a,1747,b)].
% 12.50/12.62 1794 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1626,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1794,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1794,a,1745,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1794,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1794,a,1747,b)].
% 12.50/12.62 1795 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1647,b,1627,a)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1795,a,1744,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1795,a,1745,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1795,a,1746,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1795,a,1747,b)].
% 12.50/12.62 1796 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1647,b,1628,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1796,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1796,a,1745,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1796,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1796,a,1747,b)].
% 12.50/12.62 1797 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1647,b,1629,a)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1797,a,1744,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1797,a,1745,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1797,a,1746,b)].
% 12.50/12.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1797,a,1747,b)].
% 12.50/12.62 1798 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1630,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1798,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1798,a,1745,b)].
% 12.50/12.62 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(1798,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1798,a,1747,b)].
% 12.50/12.62 1799 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1631,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1799,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1799,a,1745,b)].
% 12.50/12.62 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(1799,a,1746,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1799,a,1747,b)].
% 12.50/12.62 1800 -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(1647,b,1632,a)].
% 12.50/12.62 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(1800,a,1744,b)].
% 12.50/12.62 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(1800,a,1745,b)].
% 12.50/12.62 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(1800,a,1746,b)].
% 12.50/12.62 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(1800,a,1747,b)].
% 12.50/12.62 1801 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1633,a)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1801,a,1744,b)].
% 12.50/12.62 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1801,a,1745,b)].
% 12.50/12.62 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(1801,a,1746,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1801,a,1747,b)].
% 12.50/12.63 1802 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1634,a)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1802,a,1744,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1802,a,1745,b)].
% 12.50/12.63 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(1802,a,1746,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1802,a,1747,b)].
% 12.50/12.63 1803 -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(1647,b,1635,a)].
% 12.50/12.63 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(1803,a,1744,b)].
% 12.50/12.63 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(1803,a,1745,b)].
% 12.50/12.63 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(1803,a,1746,b)].
% 12.50/12.63 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(1803,a,1747,b)].
% 12.50/12.63 1804 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1647,b,1636,a)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1804,a,1744,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1804,a,1745,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1804,a,1746,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1804,a,1747,b)].
% 12.50/12.63 1805 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1647,b,1637,a)].
% 12.50/12.63 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1744,b)].
% 12.50/12.63 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1745,b)].
% 12.50/12.63 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1746,b)].
% 12.50/12.63 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1805,a,1747,b)].
% 12.50/12.63 1806 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1647,b,1638,a)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1806,a,1744,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1806,a,1745,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1806,a,1746,b)].
% 12.50/12.63 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1806,a,1747,b)].
% 12.75/12.91 1807 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1647,b,1639,a)].
% 12.75/12.91 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1807,a,1744,b)].
% 12.75/12.91 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1807,a,1745,b)].
% 12.75/12.91 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1807,a,1746,b)].
% 12.75/12.91 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1807,a,1747,b)].
% 12.75/12.91 1808 -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].
% 12.75/12.91 1809 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 12.75/12.91 1810 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 12.75/12.91 1811 -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].
% 12.75/12.91 1812 -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].
% 12.75/12.91 1813 -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].
% 12.75/12.91 1814 -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].
% 12.75/12.91 1815 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # label(axiom). [assumption].
% 12.75/12.91 1816 -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].
% 12.75/12.91 1817 -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].
% 12.75/12.91 1818 -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].
% 12.75/12.91 1819 -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].
% 12.75/12.91 1820 -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].
% 12.75/12.91 1821 -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].
% 12.75/12.91 1822 -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)].
% 12.75/12.91 1823 -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)].
% 12.75/12.91 1824 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 12.75/12.91 1825 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 12.75/12.91 1826 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(765,b,724,a)].
% 13.00/13.11 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1826,a,1817,b)].
% 13.00/13.11 1827 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(765,b,731,a)].
% 13.00/13.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1827,a,1817,b)].
% 13.00/13.11 1828 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1153,a,1113,a)].
% 13.00/13.11 1829 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1153,a,1138,a)].
% 13.00/13.11 1830 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1153,a,1139,b)].
% 13.00/13.11 1831 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1140,b)].
% 13.00/13.11 1832 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1447,a)].
% 13.00/13.11 1833 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1459,a,1447,a)].
% 13.00/13.11 1834 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1460,a,1447,a)].
% 13.00/13.11 1835 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1476,a,1472,b)].
% 13.00/13.11 1836 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1476,a,1473,b)].
% 13.00/13.11 1837 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1476,a,1474,b)].
% 13.00/13.11 1838 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1476,a,1475,b)].
% 13.00/13.11 1839 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1557,b,1499,a)].
% 13.00/13.11 1840 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1557,b,1534,b)].
% 13.00/13.11 1841 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1557,b,1535,b)].
% 13.00/13.11 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1841,a,1822,a)].
% 13.00/13.11 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1841,a,1823,a)].
% 13.00/13.11 1842 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1557,b,1536,b)].
% 13.00/13.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1842,a,1822,a)].
% 13.00/13.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1842,a,1823,a)].
% 13.00/13.11 1843 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1585,b,1566,a)].
% 13.00/13.11 1844 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1585,b,1567,a)].
% 13.00/13.11 1845 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1585,b,1568,a)].
% 13.00/13.11 1846 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1585,b,1569,a)].
% 13.00/13.11 1847 -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(1585,b,1570,a)].
% 13.00/13.11 1848 -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(1585,b,1571,a)].
% 13.00/13.11 1849 -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(1585,b,1572,a)].
% 13.00/13.11 1850 -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(1585,b,1573,a)].
% 13.26/13.37 1851 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1585,b,1574,a)].
% 13.26/13.37 1852 -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(1585,b,1575,a)].
% 13.26/13.37 1853 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1585,b,1576,a)].
% 13.26/13.37 1854 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1620,a)].
% 13.26/13.37 1855 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1648,b,1621,a)].
% 13.26/13.37 1856 -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(1648,b,1622,a)].
% 13.26/13.37 1857 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1623,a)].
% 13.26/13.37 1858 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1648,b,1624,a)].
% 13.26/13.37 1859 -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(1648,b,1625,a)].
% 13.26/13.37 1860 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1626,a)].
% 13.26/13.37 1861 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1648,b,1627,a)].
% 13.26/13.37 1862 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1648,b,1628,a)].
% 13.26/13.37 1863 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1648,b,1629,a)].
% 13.26/13.37 1864 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1648,b,1630,a)].
% 13.26/13.37 1865 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1648,b,1631,a)].
% 13.26/13.37 1866 -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(1648,b,1632,a)].
% 13.26/13.37 1867 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1648,b,1633,a)].
% 13.26/13.37 1868 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1648,b,1634,a)].
% 13.26/13.37 1869 -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(1648,b,1635,a)].
% 13.26/13.37 1870 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1648,b,1636,a)].
% 13.26/13.37 1871 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1648,b,1637,a)].
% 13.26/13.37 1872 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1648,b,1638,a)].
% 13.26/13.37 1873 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1648,b,1639,a)].
% 13.26/13.37 1874 -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].
% 13.34/13.46 1875 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 13.34/13.46 1876 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 13.34/13.46 1877 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) # label(axiom). [assumption].
% 13.34/13.46 1878 -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].
% 13.34/13.46 1879 -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].
% 13.34/13.46 1880 -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].
% 13.34/13.46 1881 -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].
% 13.34/13.46 1882 -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)].
% 13.34/13.46 1883 -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)].
% 13.34/13.46 1884 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 13.34/13.46 1885 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 13.34/13.46 1886 -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(881,b,822,a)].
% 13.34/13.46 1887 -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(881,b,823,a)].
% 13.34/13.46 1888 -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(881,b,824,a)].
% 13.34/13.46 1889 -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(881,b,825,a)].
% 13.34/13.46 1890 -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(881,b,826,a)].
% 13.34/13.46 1891 -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(881,b,827,a)].
% 13.34/13.46 1892 -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(881,b,828,a)].
% 13.34/13.46 1893 -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(881,b,829,a)].
% 13.34/13.46 1894 -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(881,b,830,a)].
% 13.34/13.46 1895 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(881,b,831,a)].
% 13.34/13.46 1896 -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(881,b,832,a)].
% 13.34/13.47 1897 -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(881,b,833,a)].
% 13.34/13.47 1898 -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(881,b,834,a)].
% 13.34/13.47 1899 -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(881,b,835,a)].
% 13.34/13.47 1900 -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(881,b,836,a)].
% 13.34/13.47 1901 -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(881,b,837,a)].
% 13.34/13.47 1902 -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(881,b,838,a)].
% 13.34/13.47 1903 -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(881,b,839,a)].
% 13.34/13.47 1904 -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(881,b,840,a)].
% 13.34/13.47 1905 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(881,b,841,a)].
% 13.34/13.47 1906 -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(881,b,842,a)].
% 13.34/13.47 1907 -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(881,b,843,a)].
% 13.34/13.47 1908 -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(881,b,844,a)].
% 13.34/13.47 1909 -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(881,b,845,b)].
% 13.34/13.47 1910 -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(881,b,846,b)].
% 13.34/13.47 1911 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(881,b,847,a)].
% 13.34/13.47 1912 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(881,b,848,a)].
% 13.34/13.47 1913 -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(881,b,849,a)].
% 13.34/13.47 1914 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(881,b,850,a)].
% 13.34/13.47 1915 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(881,b,851,a)].
% 13.34/13.47 1916 -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(881,b,852,a)].
% 13.34/13.47 1917 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(881,b,853,a)].
% 13.34/13.48 1918 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(881,b,854,a)].
% 13.34/13.48 1919 -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(881,b,855,a)].
% 13.34/13.48 1920 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(881,b,856,a)].
% 13.34/13.48 1921 -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(881,b,857,a)].
% 13.34/13.48 1922 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(881,b,858,a)].
% 13.34/13.48 1923 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(881,b,859,a)].
% 13.34/13.48 1924 -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(881,b,860,a)].
% 13.34/13.48 1925 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(881,b,861,a)].
% 13.34/13.48 1926 -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(881,b,862,a)].
% 13.34/13.48 1927 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(881,b,863,a)].
% 13.34/13.48 1928 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(881,b,864,a)].
% 13.34/13.48 1929 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(881,b,865,a)].
% 13.34/13.48 1930 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(881,b,866,a)].
% 13.34/13.48 1931 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(881,b,867,a)].
% 13.34/13.48 1932 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(881,b,868,a)].
% 13.34/13.48 1933 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(881,b,869,a)].
% 13.34/13.48 1934 -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(881,b,870,a)].
% 13.34/13.48 1935 -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(881,b,871,a)].
% 13.34/13.48 1936 -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(881,b,872,a)].
% 13.34/13.48 1937 -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(881,b,873,a)].
% 13.34/13.48 1938 -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(881,b,874,a)].
% 13.34/13.48 1939 -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(881,b,875,a)].
% 13.34/13.48 1940 -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(881,b,876,a)].
% 13.50/13.62 1941 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(881,b,877,a)].
% 13.50/13.62 1942 -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(881,b,878,a)].
% 13.50/13.62 1943 -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(881,b,879,a)].
% 13.50/13.62 1944 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1077,b,1068,a)].
% 13.50/13.62 1945 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1100,b,1091,a)].
% 13.50/13.62 1946 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1150,a,1113,a)].
% 13.50/13.62 1947 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1150,a,1138,a)].
% 13.50/13.62 1948 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1150,a,1139,b)].
% 13.50/13.62 1949 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1150,a,1140,b)].
% 13.50/13.62 1950 -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(1474,b,1462,a)].
% 13.50/13.62 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1950,a,1876,a)].
% 13.50/13.62 1951 -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(1474,b,1463,a)].
% 13.50/13.62 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1951,a,1876,a)].
% 13.50/13.62 1952 -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(1474,b,1464,a)].
% 13.50/13.62 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1952,a,1876,a)].
% 13.50/13.62 1953 -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(1474,b,1465,a)].
% 13.50/13.62 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1953,a,1876,a)].
% 13.50/13.62 1954 -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(1474,b,1466,a)].
% 13.50/13.62 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1954,a,1876,a)].
% 13.50/13.62 1955 -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(1474,b,1467,a)].
% 13.50/13.62 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1955,a,1876,a)].
% 13.50/13.62 1956 -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(1474,b,1468,a)].
% 13.50/13.62 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1956,a,1876,a)].
% 13.50/13.62 1957 -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(1474,b,1469,a)].
% 13.50/13.62 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1957,a,1876,a)].
% 13.50/13.62 1958 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1488,a,1474,b)].
% 13.50/13.62 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1958,c,1878,b)].
% 13.50/13.62 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1958,c,1881,b)].
% 13.50/13.62 1959 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1489,a,1474,b)].
% 13.56/13.69 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1959,c,1878,b)].
% 13.56/13.69 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1959,c,1881,b)].
% 13.56/13.69 1960 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1490,b,1474,b)].
% 13.56/13.69 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1960,b,1876,a)].
% 13.56/13.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1960,b,1881,b)].
% 13.56/13.69 1961 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,b,1474,b)].
% 13.56/13.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1961,b,1881,b)].
% 13.56/13.69 1962 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1582,b,1566,a)].
% 13.56/13.69 1963 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1582,b,1567,a)].
% 13.56/13.69 1964 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1582,b,1568,a)].
% 13.56/13.69 1965 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1582,b,1569,a)].
% 13.56/13.69 1966 -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(1582,b,1570,a)].
% 13.56/13.69 1967 -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(1582,b,1571,a)].
% 13.56/13.69 1968 -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(1582,b,1572,a)].
% 13.56/13.69 1969 -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(1582,b,1573,a)].
% 13.56/13.69 1970 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1582,b,1574,a)].
% 13.56/13.69 1971 -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(1582,b,1575,a)].
% 13.56/13.69 1972 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1582,b,1576,a)].
% 13.56/13.69 1973 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1620,a)].
% 13.56/13.69 1974 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1621,a)].
% 13.56/13.69 1975 -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(1645,b,1622,a)].
% 13.56/13.69 1976 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1623,a)].
% 13.56/13.69 1977 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1624,a)].
% 13.56/13.69 1978 -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(1645,b,1625,a)].
% 13.56/13.69 1979 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1626,a)].
% 13.56/13.69 1980 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1645,b,1627,a)].
% 13.64/13.76 1981 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1645,b,1628,a)].
% 13.64/13.76 1982 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1645,b,1629,a)].
% 13.64/13.76 1983 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1630,a)].
% 13.64/13.76 1984 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1631,a)].
% 13.64/13.76 1985 -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(1645,b,1632,a)].
% 13.64/13.76 1986 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1633,a)].
% 13.64/13.76 1987 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1634,a)].
% 13.64/13.76 1988 -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(1645,b,1635,a)].
% 13.64/13.76 1989 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1645,b,1636,a)].
% 13.64/13.76 1990 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1645,b,1637,a)].
% 13.64/13.76 1991 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1645,b,1638,a)].
% 13.64/13.76 1992 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1645,b,1639,a)].
% 13.64/13.76 1993 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1777,a,1746,b)].
% 13.64/13.76 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1993,b,1875,a)].
% 13.64/13.76 Derived: -c_less(A,A,tc_nat). [resolve(1993,b,1876,a)].
% 13.64/13.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1993,b,1878,b)].
% 13.64/13.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1993,b,1879,b)].
% 13.64/13.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1993,b,1880,b)].
% 13.64/13.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1993,b,1881,b)].
% 13.64/13.76 1994 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1778,a,1746,b)].
% 13.64/13.76 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1994,c,1875,a)].
% 13.64/13.76 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1994,c,1876,a)].
% 13.64/13.76 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1994,c,1878,b)].
% 13.64/13.76 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1994,c,1879,b)].
% 13.64/13.76 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1994,c,1880,b)].
% 13.64/13.76 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1994,c,1881,b)].
% 13.64/13.76 1995 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1779,a,1746,b)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1995,b,1875,a)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1995,b,1876,a)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1995,b,1878,b)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1995,b,1879,b)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1995,b,1880,b)].
% 13.64/13.76 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1995,b,1881,b)].
% 13.64/13.76 1996 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1746,b)].
% 13.64/13.76 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1996,c,1875,a)].
% 13.64/13.76 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1996,c,1876,a)].
% 13.64/13.76 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1996,c,1878,b)].
% 13.64/13.76 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1996,c,1879,b)].
% 13.64/13.76 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1996,c,1880,b)].
% 13.64/13.76 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1996,c,1881,b)].
% 13.64/13.76 1997 -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(1781,a,1746,b)].
% 13.64/13.76 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(1997,c,1875,a)].
% 13.64/13.76 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(1997,c,1876,a)].
% 13.64/13.76 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(1997,c,1878,b)].
% 13.64/13.76 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(1997,c,1879,b)].
% 13.64/13.76 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(1997,c,1880,b)].
% 13.64/13.76 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(1997,c,1881,b)].
% 13.64/13.76 1998 -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(1782,a,1746,b)].
% 13.64/13.76 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(1998,c,1875,a)].
% 13.64/13.76 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(1998,c,1876,a)].
% 13.64/13.76 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(1998,c,1878,b)].
% 13.64/13.76 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(1998,c,1879,b)].
% 13.64/13.76 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(1998,c,1880,b)].
% 13.64/13.76 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(1998,c,1881,b)].
% 13.64/13.77 1999 -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(1783,a,1746,b)].
% 13.64/13.77 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(1999,c,1875,a)].
% 13.64/13.77 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(1999,c,1876,a)].
% 13.64/13.77 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(1999,c,1878,b)].
% 13.64/13.77 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(1999,c,1879,b)].
% 13.64/13.77 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(1999,c,1880,b)].
% 13.64/13.77 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(1999,c,1881,b)].
% 13.64/13.77 2000 -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(1784,a,1746,b)].
% 13.64/13.77 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(2000,c,1875,a)].
% 13.64/13.77 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(2000,c,1876,a)].
% 13.64/13.77 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(2000,c,1878,b)].
% 13.64/13.77 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(2000,c,1879,b)].
% 13.64/13.77 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(2000,c,1880,b)].
% 13.64/13.77 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(2000,c,1881,b)].
% 13.64/13.77 2001 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1785,a,1746,b)].
% 13.64/13.77 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2001,c,1875,a)].
% 13.64/13.77 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2001,c,1876,a)].
% 13.64/13.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2001,c,1878,b)].
% 13.64/13.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2001,c,1879,b)].
% 13.64/13.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2001,c,1880,b)].
% 13.64/13.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2001,c,1881,b)].
% 13.64/13.77 2002 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(1786,a,1746,b)].
% 13.64/13.77 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(2002,b,1875,a)].
% 13.64/13.77 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(2002,b,1876,a)].
% 13.64/13.77 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2002,b,1878,b)].
% 13.64/13.77 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2002,b,1879,b)].
% 13.64/13.77 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2002,b,1880,b)].
% 13.64/13.77 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2002,b,1881,b)].
% 13.64/13.77 2003 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1787,a,1746,b)].
% 13.64/13.77 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2003,b,1875,a)].
% 13.64/13.77 Derived: c_lessequals(A,A,tc_nat). [resolve(2003,b,1876,a)].
% 13.64/13.77 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2003,b,1878,b)].
% 13.64/13.77 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2003,b,1879,b)].
% 13.64/13.77 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2003,b,1880,b)].
% 13.64/13.77 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2003,b,1881,b)].
% 13.64/13.77 2004 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1788,a,1746,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2004,c,1875,a)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2004,c,1876,a)].
% 13.64/13.77 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(2004,c,1878,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2004,c,1879,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2004,c,1880,b)].
% 13.64/13.77 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(2004,c,1881,b)].
% 13.64/13.77 2005 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1789,a,1746,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2005,c,1875,a)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2005,c,1876,a)].
% 13.64/13.77 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(2005,c,1878,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2005,c,1879,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2005,c,1880,b)].
% 13.64/13.77 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(2005,c,1881,b)].
% 13.64/13.77 2006 -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(1790,a,1746,b)].
% 13.64/13.77 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(2006,d,1875,a)].
% 13.64/13.77 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(2006,d,1876,a)].
% 13.64/13.77 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(2006,d,1878,b)].
% 13.64/13.77 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(2006,d,1879,b)].
% 13.64/13.77 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(2006,d,1880,b)].
% 13.64/13.77 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(2006,d,1881,b)].
% 13.64/13.77 2007 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1791,a,1746,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2007,c,1875,a)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2007,c,1876,a)].
% 13.64/13.77 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(2007,c,1878,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2007,c,1879,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2007,c,1880,b)].
% 13.64/13.77 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(2007,c,1881,b)].
% 13.64/13.77 2008 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1792,a,1746,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2008,c,1875,a)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2008,c,1876,a)].
% 13.64/13.77 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(2008,c,1878,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2008,c,1879,b)].
% 13.64/13.77 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2008,c,1880,b)].
% 13.64/13.77 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(2008,c,1881,b)].
% 13.64/13.77 2009 -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(1793,a,1746,b)].
% 13.64/13.77 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(2009,d,1875,a)].
% 13.64/13.77 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(2009,d,1876,a)].
% 13.64/13.77 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(2009,d,1878,b)].
% 13.64/13.77 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(2009,d,1879,b)].
% 13.64/13.77 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(2009,d,1880,b)].
% 13.64/13.78 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(2009,d,1881,b)].
% 13.64/13.78 2010 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1794,a,1746,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2010,c,1875,a)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2010,c,1876,a)].
% 13.64/13.78 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(2010,c,1878,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2010,c,1879,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2010,c,1880,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2010,c,1881,b)].
% 13.64/13.78 2011 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1795,a,1746,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2011,c,1875,a)].
% 13.64/13.78 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2011,c,1876,a)].
% 13.64/13.78 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(2011,c,1878,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2011,c,1879,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2011,c,1880,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2011,c,1881,b)].
% 13.64/13.78 2012 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1796,a,1746,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2012,c,1875,a)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2012,c,1876,a)].
% 13.64/13.78 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(2012,c,1878,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2012,c,1879,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2012,c,1880,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2012,c,1881,b)].
% 13.64/13.78 2013 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1797,a,1746,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2013,c,1875,a)].
% 13.64/13.78 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2013,c,1876,a)].
% 13.64/13.78 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(2013,c,1878,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2013,c,1879,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2013,c,1880,b)].
% 13.64/13.78 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2013,c,1881,b)].
% 13.64/13.78 2014 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1798,a,1746,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2014,c,1875,a)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2014,c,1876,a)].
% 13.64/13.78 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(2014,c,1878,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2014,c,1879,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2014,c,1880,b)].
% 13.64/13.78 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(2014,c,1881,b)].
% 13.64/13.78 2015 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1799,a,1746,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2015,c,1875,a)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2015,c,1876,a)].
% 13.64/13.78 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(2015,c,1878,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2015,c,1879,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2015,c,1880,b)].
% 13.64/13.78 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(2015,c,1881,b)].
% 13.64/13.78 2016 -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(1800,a,1746,b)].
% 13.64/13.78 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(2016,d,1875,a)].
% 13.64/13.78 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(2016,d,1876,a)].
% 13.64/13.78 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(2016,d,1878,b)].
% 13.64/13.78 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(2016,d,1879,b)].
% 13.64/13.78 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(2016,d,1880,b)].
% 13.64/13.78 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(2016,d,1881,b)].
% 13.64/13.78 2017 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1801,a,1746,b)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2017,c,1875,a)].
% 13.64/13.78 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2017,c,1876,a)].
% 13.64/13.78 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(2017,c,1878,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2017,c,1879,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2017,c,1880,b)].
% 13.64/13.79 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(2017,c,1881,b)].
% 13.64/13.79 2018 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1802,a,1746,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2018,c,1875,a)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2018,c,1876,a)].
% 13.64/13.79 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(2018,c,1878,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2018,c,1879,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2018,c,1880,b)].
% 13.64/13.79 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(2018,c,1881,b)].
% 13.64/13.79 2019 -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(1803,a,1746,b)].
% 13.64/13.79 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(2019,d,1875,a)].
% 13.64/13.79 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(2019,d,1876,a)].
% 13.64/13.79 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(2019,d,1878,b)].
% 13.64/13.79 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(2019,d,1879,b)].
% 13.64/13.79 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(2019,d,1880,b)].
% 13.64/13.79 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(2019,d,1881,b)].
% 13.64/13.79 2020 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1804,a,1746,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2020,c,1875,a)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2020,c,1876,a)].
% 13.64/13.79 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(2020,c,1878,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2020,c,1879,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2020,c,1880,b)].
% 13.64/13.79 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2020,c,1881,b)].
% 13.64/13.79 2021 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1746,b)].
% 13.64/13.79 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2021,c,1875,a)].
% 13.64/13.79 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2021,c,1876,a)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2021,c,1878,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2021,c,1879,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2021,c,1880,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2021,c,1881,b)].
% 13.81/13.95 2022 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1806,a,1746,b)].
% 13.81/13.95 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2022,c,1875,a)].
% 13.81/13.95 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2022,c,1876,a)].
% 13.81/13.95 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(2022,c,1878,b)].
% 13.81/13.95 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2022,c,1879,b)].
% 13.81/13.95 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2022,c,1880,b)].
% 13.81/13.95 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2022,c,1881,b)].
% 13.81/13.95 2023 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1807,a,1746,b)].
% 13.81/13.95 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2023,c,1875,a)].
% 13.81/13.95 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2023,c,1876,a)].
% 13.81/13.95 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(2023,c,1878,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2023,c,1879,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2023,c,1880,b)].
% 13.81/13.95 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2023,c,1881,b)].
% 13.81/13.95 2024 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 13.81/13.95 2025 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 13.81/13.95 2026 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 13.81/13.95 2027 -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].
% 13.81/13.95 2028 -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].
% 13.81/13.95 2029 -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].
% 13.81/13.95 2030 -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].
% 13.81/13.95 2031 -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].
% 13.81/13.95 2032 -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].
% 13.81/13.96 2033 -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].
% 13.81/13.96 2034 -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].
% 13.81/13.96 2035 -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].
% 13.81/13.96 2036 -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].
% 13.81/13.96 2037 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom). [assumption].
% 13.81/13.96 2038 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 13.81/13.96 2039 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 13.81/13.96 2040 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom). [assumption].
% 13.81/13.96 2041 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom). [assumption].
% 13.81/13.96 2042 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(c_0,D,A) | c_lessequals(c_times(D,B,A),c_times(D,C,A),A) # label(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) # label(axiom). [assumption].
% 13.81/13.96 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(C,A,tc_IntDef_Oint),c_times(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2042,a,2025,a)].
% 13.81/13.96 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(C,A,tc_nat),c_times(C,B,tc_nat),tc_nat). [resolve(2042,a,2026,a)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2042,a,2027,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2042,a,2028,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2042,a,2029,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2042,a,2030,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2042,a,2031,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2042,a,2032,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2042,a,2033,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2042,a,2034,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2042,a,2035,b)].
% 13.81/13.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2042,a,2036,b)].
% 13.87/13.99 2043 -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(161,b,133,b)].
% 13.87/13.99 2044 -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(161,b,135,b)].
% 13.87/13.99 2045 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,161,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2045,b,2035,b)].
% 13.87/13.99 2046 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,161,b)].
% 13.87/13.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2046,b,2035,b)].
% 13.87/13.99 2047 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(167,a,161,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2047,b,2028,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2047,b,2031,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2047,b,2032,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2047,b,2033,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2047,b,2035,b)].
% 13.87/13.99 2048 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(168,a,161,b)].
% 13.87/13.99 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2048,b,2028,b)].
% 13.87/13.99 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2048,b,2031,b)].
% 13.87/13.99 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2048,b,2032,b)].
% 13.87/13.99 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2048,b,2033,b)].
% 13.87/13.99 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2048,b,2035,b)].
% 13.87/13.99 2049 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2049,b,2028,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2049,b,2031,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2049,b,2032,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2049,b,2033,b)].
% 13.87/13.99 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2049,b,2035,b)].
% 13.87/13.99 2050 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 13.87/13.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2050,b,2028,b)].
% 13.87/13.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2050,b,2031,b)].
% 13.87/13.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2050,b,2032,b)].
% 13.87/13.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2050,b,2033,b)].
% 13.87/13.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2050,b,2035,b)].
% 13.87/13.99 2051 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(245,a,233,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2051,c,2028,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2051,c,2031,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2051,c,2032,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2051,c,2033,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2051,c,2035,b)].
% 13.98/14.11 2052 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(246,a,233,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2052,c,2028,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2052,c,2031,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2052,c,2032,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2052,c,2033,b)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2052,c,2035,b)].
% 13.98/14.11 2053 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1157,a,1113,a)].
% 13.98/14.11 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2053,a,2024,a)].
% 13.98/14.11 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2053,a,2037,a)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2053,a,2043,a)].
% 13.98/14.11 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2053,a,2044,a)].
% 13.98/14.11 2054 class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1157,a,1138,a)].
% 13.98/14.11 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2054,a,2024,a)].
% 13.98/14.11 Derived: class_HOL_Otimes(tc_nat). [resolve(2054,a,2037,a)].
% 14.12/14.23 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2054,a,2038,a)].
% 14.12/14.23 Derived: class_HOL_Ozero(tc_nat). [resolve(2054,a,2041,a)].
% 14.12/14.23 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(2054,a,2043,a)].
% 14.12/14.23 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(2054,a,2044,a)].
% 14.12/14.23 2055 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1139,b)].
% 14.12/14.23 2056 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1140,b)].
% 14.12/14.23 2057 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1597,b,1566,a)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2057,a,2027,b)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2057,a,2032,b)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2057,a,2033,b)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2057,a,2034,b)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2057,a,2035,b)].
% 14.12/14.23 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2057,a,2036,b)].
% 14.12/14.23 2058 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1567,a)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2058,a,2027,b)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2058,a,2032,b)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2058,a,2033,b)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2058,a,2034,b)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2058,a,2035,b)].
% 14.12/14.23 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2058,a,2036,b)].
% 14.12/14.23 2059 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1568,a)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2059,a,2027,b)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2059,a,2032,b)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2059,a,2033,b)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2059,a,2034,b)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2059,a,2035,b)].
% 14.12/14.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2059,a,2036,b)].
% 14.12/14.23 2060 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1569,a)].
% 14.12/14.23 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2060,a,2027,b)].
% 14.12/14.24 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2060,a,2032,b)].
% 14.12/14.24 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2060,a,2033,b)].
% 14.12/14.24 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2060,a,2034,b)].
% 14.12/14.24 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2060,a,2035,b)].
% 14.12/14.24 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2060,a,2036,b)].
% 14.12/14.24 2061 -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(1597,b,1570,a)].
% 14.12/14.24 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(2061,a,2027,b)].
% 14.12/14.24 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(2061,a,2032,b)].
% 14.12/14.24 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(2061,a,2033,b)].
% 14.12/14.24 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(2061,a,2034,b)].
% 14.12/14.24 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(2061,a,2035,b)].
% 14.12/14.24 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(2061,a,2036,b)].
% 14.12/14.24 2062 -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(1597,b,1571,a)].
% 14.12/14.24 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(2062,a,2027,b)].
% 14.12/14.24 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(2062,a,2032,b)].
% 14.12/14.24 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(2062,a,2033,b)].
% 14.12/14.24 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(2062,a,2034,b)].
% 14.12/14.24 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(2062,a,2035,b)].
% 14.12/14.24 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(2062,a,2036,b)].
% 14.12/14.24 2063 -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(1597,b,1572,a)].
% 14.12/14.24 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(2063,a,2027,b)].
% 14.12/14.24 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(2063,a,2032,b)].
% 14.12/14.25 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(2063,a,2033,b)].
% 14.12/14.25 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(2063,a,2034,b)].
% 14.12/14.25 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(2063,a,2035,b)].
% 14.12/14.25 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(2063,a,2036,b)].
% 14.12/14.25 2064 -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(1597,b,1573,a)].
% 14.12/14.25 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(2064,a,2027,b)].
% 14.12/14.25 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(2064,a,2032,b)].
% 14.12/14.25 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(2064,a,2033,b)].
% 14.12/14.25 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(2064,a,2034,b)].
% 14.12/14.25 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(2064,a,2035,b)].
% 14.12/14.25 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(2064,a,2036,b)].
% 14.12/14.25 2065 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1574,a)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2065,a,2027,b)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2065,a,2032,b)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2065,a,2033,b)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2065,a,2034,b)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2065,a,2035,b)].
% 14.12/14.25 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2065,a,2036,b)].
% 14.12/14.25 2066 -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(1597,b,1575,a)].
% 14.12/14.25 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(2066,a,2027,b)].
% 14.12/14.25 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(2066,a,2032,b)].
% 14.12/14.25 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(2066,a,2033,b)].
% 14.12/14.25 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(2066,a,2034,b)].
% 14.19/14.30 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__semiring(B). [resolve(2066,a,2035,b)].
% 14.19/14.30 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__ring(B). [resolve(2066,a,2036,b)].
% 14.19/14.30 2067 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1597,b,1576,a)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2067,a,2027,b)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2067,a,2032,b)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2067,a,2033,b)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2067,a,2034,b)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2067,a,2035,b)].
% 14.19/14.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2067,a,2036,b)].
% 14.19/14.30 2068 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1620,a)].
% 14.19/14.30 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2068,a,2027,b)].
% 14.19/14.30 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(2068,a,2032,b)].
% 14.19/14.30 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(2068,a,2033,b)].
% 14.19/14.30 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(2068,a,2034,b)].
% 14.19/14.30 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(2068,a,2035,b)].
% 14.19/14.30 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2068,a,2036,b)].
% 14.19/14.30 2069 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1621,a)].
% 14.19/14.30 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2069,a,2027,b)].
% 14.19/14.30 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(2069,a,2032,b)].
% 14.19/14.30 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(2069,a,2033,b)].
% 14.19/14.30 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(2069,a,2034,b)].
% 14.19/14.30 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(2069,a,2035,b)].
% 14.19/14.30 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2069,a,2036,b)].
% 14.19/14.30 2070 -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(1660,b,1622,a)].
% 14.19/14.30 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(2070,a,2027,b)].
% 14.19/14.30 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(2070,a,2032,b)].
% 14.19/14.30 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(2070,a,2033,b)].
% 14.19/14.31 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(2070,a,2034,b)].
% 14.19/14.31 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(2070,a,2035,b)].
% 14.19/14.31 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(2070,a,2036,b)].
% 14.19/14.31 2071 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1623,a)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2071,a,2027,b)].
% 14.19/14.31 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(2071,a,2032,b)].
% 14.19/14.31 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(2071,a,2033,b)].
% 14.19/14.31 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(2071,a,2034,b)].
% 14.19/14.31 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(2071,a,2035,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2071,a,2036,b)].
% 14.19/14.31 2072 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1624,a)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2072,a,2027,b)].
% 14.19/14.31 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(2072,a,2032,b)].
% 14.19/14.31 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(2072,a,2033,b)].
% 14.19/14.31 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(2072,a,2034,b)].
% 14.19/14.31 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(2072,a,2035,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2072,a,2036,b)].
% 14.19/14.31 2073 -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(1660,b,1625,a)].
% 14.19/14.31 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(2073,a,2027,b)].
% 14.19/14.31 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(2073,a,2032,b)].
% 14.19/14.31 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(2073,a,2033,b)].
% 14.19/14.31 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(2073,a,2034,b)].
% 14.19/14.31 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(2073,a,2035,b)].
% 14.19/14.31 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(2073,a,2036,b)].
% 14.19/14.31 2074 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1626,a)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2074,a,2027,b)].
% 14.19/14.31 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(2074,a,2032,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2074,a,2033,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2074,a,2034,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2074,a,2035,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2074,a,2036,b)].
% 14.19/14.31 2075 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1627,a)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2075,a,2027,b)].
% 14.19/14.31 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(2075,a,2032,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2075,a,2033,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2075,a,2034,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2075,a,2035,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2075,a,2036,b)].
% 14.19/14.31 2076 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1628,a)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2076,a,2027,b)].
% 14.19/14.31 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(2076,a,2032,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2076,a,2033,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2076,a,2034,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2076,a,2035,b)].
% 14.19/14.31 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2076,a,2036,b)].
% 14.19/14.31 2077 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1629,a)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2027,b)].
% 14.19/14.31 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(2077,a,2032,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2033,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2077,a,2034,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2035,b)].
% 14.19/14.31 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2036,b)].
% 14.19/14.32 2078 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1630,a)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2078,a,2027,b)].
% 14.19/14.32 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(2078,a,2032,b)].
% 14.19/14.32 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(2078,a,2033,b)].
% 14.19/14.32 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(2078,a,2034,b)].
% 14.19/14.32 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(2078,a,2035,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2078,a,2036,b)].
% 14.19/14.32 2079 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1631,a)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2079,a,2027,b)].
% 14.19/14.32 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(2079,a,2032,b)].
% 14.19/14.32 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(2079,a,2033,b)].
% 14.19/14.32 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(2079,a,2034,b)].
% 14.19/14.32 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(2079,a,2035,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2079,a,2036,b)].
% 14.19/14.32 2080 -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(1660,b,1632,a)].
% 14.19/14.32 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_Olordered__ring(C). [resolve(2080,a,2027,b)].
% 14.19/14.32 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__cancel__comm__semiring(C). [resolve(2080,a,2032,b)].
% 14.19/14.32 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__cancel__semiring(C). [resolve(2080,a,2033,b)].
% 14.19/14.32 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(2080,a,2034,b)].
% 14.19/14.32 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__semiring(C). [resolve(2080,a,2035,b)].
% 14.19/14.32 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__ring(C). [resolve(2080,a,2036,b)].
% 14.19/14.32 2081 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1633,a)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2081,a,2027,b)].
% 14.19/14.32 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(2081,a,2032,b)].
% 14.19/14.32 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(2081,a,2033,b)].
% 14.19/14.32 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(2081,a,2034,b)].
% 14.19/14.32 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(2081,a,2035,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2081,a,2036,b)].
% 14.19/14.32 2082 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1634,a)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2082,a,2027,b)].
% 14.19/14.32 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(2082,a,2032,b)].
% 14.19/14.32 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(2082,a,2033,b)].
% 14.19/14.32 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(2082,a,2034,b)].
% 14.19/14.32 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(2082,a,2035,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2082,a,2036,b)].
% 14.19/14.32 2083 -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(1660,b,1635,a)].
% 14.19/14.32 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(2083,a,2027,b)].
% 14.19/14.32 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(2083,a,2032,b)].
% 14.19/14.32 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(2083,a,2033,b)].
% 14.19/14.32 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(2083,a,2034,b)].
% 14.19/14.32 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(2083,a,2035,b)].
% 14.19/14.32 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(2083,a,2036,b)].
% 14.19/14.32 2084 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1636,a)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2084,a,2027,b)].
% 14.19/14.32 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(2084,a,2032,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2084,a,2033,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2084,a,2034,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2084,a,2035,b)].
% 14.19/14.32 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2084,a,2036,b)].
% 14.19/14.32 2085 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1637,a)].
% 14.19/14.32 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2085,a,2027,b)].
% 14.44/14.56 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(2085,a,2032,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2085,a,2033,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2085,a,2034,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2085,a,2035,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2085,a,2036,b)].
% 14.44/14.56 2086 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1638,a)].
% 14.44/14.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2086,a,2027,b)].
% 14.44/14.56 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(2086,a,2032,b)].
% 14.44/14.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2086,a,2033,b)].
% 14.44/14.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2086,a,2034,b)].
% 14.44/14.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2086,a,2035,b)].
% 14.44/14.56 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2086,a,2036,b)].
% 14.44/14.56 2087 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1639,a)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2087,a,2027,b)].
% 14.44/14.56 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(2087,a,2032,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2087,a,2033,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2087,a,2034,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2087,a,2035,b)].
% 14.44/14.56 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2087,a,2036,b)].
% 14.44/14.56 2088 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_10) # label(axiom). [assumption].
% 14.44/14.56 2089 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 14.44/14.56 2090 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 14.44/14.56 2091 -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].
% 14.44/14.56 2092 -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].
% 14.44/14.56 2093 -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].
% 14.44/14.56 2094 -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].
% 14.44/14.56 2095 -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].
% 14.49/14.60 2096 -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].
% 14.49/14.60 2097 -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].
% 14.49/14.60 2098 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_4) # label(axiom). [assumption].
% 14.49/14.60 2099 -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].
% 14.49/14.60 2100 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # label(axiom). [assumption].
% 14.49/14.60 2101 -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].
% 14.49/14.60 2102 -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].
% 14.49/14.60 2103 -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)].
% 14.49/14.60 2104 -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)].
% 14.49/14.60 2105 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 14.49/14.60 2106 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 14.49/14.60 2107 -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(157,b,133,b)].
% 14.49/14.60 2108 -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(157,b,135,b)].
% 14.49/14.60 2109 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(167,a,157,b)].
% 14.49/14.60 2110 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(168,a,157,b)].
% 14.49/14.60 2111 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 14.49/14.60 2112 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 14.49/14.60 2113 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(245,a,229,b)].
% 14.49/14.60 2114 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(246,a,229,b)].
% 14.49/14.60 2115 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,286,a)].
% 14.49/14.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2115,a,2092,b)].
% 14.49/14.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2115,a,2095,b)].
% 14.49/14.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2115,a,2096,b)].
% 14.49/14.60 2116 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,288,a)].
% 14.49/14.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2116,a,2092,b)].
% 14.74/14.84 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2116,a,2095,b)].
% 14.74/14.84 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2116,a,2096,b)].
% 14.74/14.84 2117 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(320,a,307,b)].
% 14.74/14.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2117,c,2096,b)].
% 14.74/14.84 2118 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(321,a,307,b)].
% 14.74/14.84 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2118,c,2096,b)].
% 14.74/14.84 2119 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(324,a,307,b)].
% 14.74/14.84 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2119,b,2096,b)].
% 14.74/14.84 2120 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(780,a,724,a)].
% 14.74/14.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2120,a,2096,b)].
% 14.74/14.84 2121 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1155,a,1113,a)].
% 14.74/14.84 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2121,a,2115,a)].
% 14.74/14.84 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2121,a,2116,a)].
% 14.74/14.84 2122 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1155,a,1138,a)].
% 14.74/14.84 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2122,a,2115,a)].
% 14.74/14.84 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2122,a,2116,a)].
% 14.74/14.84 2123 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1155,a,1139,b)].
% 14.74/14.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(2123,a,2115,a)].
% 14.74/14.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(2123,a,2116,a)].
% 14.74/14.84 2124 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1155,a,1140,b)].
% 14.74/14.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(2124,a,2115,a)].
% 14.74/14.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(2124,a,2116,a)].
% 14.74/14.84 2125 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1593,b,1566,a)].
% 14.74/14.84 2126 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1593,b,1567,a)].
% 14.74/14.84 2127 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1593,b,1568,a)].
% 14.74/14.84 2128 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1593,b,1569,a)].
% 14.74/14.84 2129 -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(1593,b,1570,a)].
% 14.74/14.84 2130 -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(1593,b,1571,a)].
% 14.74/14.84 2131 -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(1593,b,1572,a)].
% 14.74/14.84 2132 -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(1593,b,1573,a)].
% 14.74/14.84 2133 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1593,b,1574,a)].
% 14.74/14.84 2134 -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(1593,b,1575,a)].
% 14.86/14.98 2135 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1593,b,1576,a)].
% 14.86/14.98 2136 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1620,a)].
% 14.86/14.98 2137 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1656,b,1621,a)].
% 14.86/14.98 2138 -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(1656,b,1622,a)].
% 14.86/14.98 2139 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1623,a)].
% 14.86/14.98 2140 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1656,b,1624,a)].
% 14.86/14.98 2141 -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(1656,b,1625,a)].
% 14.86/14.98 2142 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1626,a)].
% 14.86/14.98 2143 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1656,b,1627,a)].
% 14.86/14.98 2144 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1656,b,1628,a)].
% 14.86/14.98 2145 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1656,b,1629,a)].
% 14.86/14.98 2146 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1656,b,1630,a)].
% 14.86/14.98 2147 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1656,b,1631,a)].
% 14.86/14.98 2148 -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(1656,b,1632,a)].
% 14.86/14.98 2149 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1656,b,1633,a)].
% 14.86/14.98 2150 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1656,b,1634,a)].
% 14.86/14.98 2151 -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(1656,b,1635,a)].
% 14.86/14.98 2152 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1656,b,1636,a)].
% 14.86/14.98 2153 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1656,b,1637,a)].
% 14.86/14.98 2154 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1656,b,1638,a)].
% 14.86/14.98 2155 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1656,b,1639,a)].
% 14.86/14.98 2156 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2042,a,2033,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(C,A,tc_IntDef_Oint),c_times(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2156,d,2089,a)].
% 14.86/14.98 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(C,A,tc_nat),c_times(C,B,tc_nat),tc_nat). [resolve(2156,d,2090,a)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2156,d,2091,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2156,d,2092,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2156,d,2093,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2156,d,2094,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2156,d,2095,b)].
% 14.86/14.98 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2156,d,2096,b)].
% 14.86/14.98 2157 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2047,b,2033,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2157,b,2091,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2157,b,2092,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2157,b,2093,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2157,b,2094,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2157,b,2095,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2157,b,2096,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2157,b,2102,b)].
% 14.86/14.98 2158 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2048,b,2033,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2158,b,2091,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2158,b,2092,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2158,b,2093,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2158,b,2094,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2158,b,2095,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2158,b,2096,b)].
% 14.86/14.98 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2158,b,2102,b)].
% 14.86/14.98 2159 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2049,b,2033,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2159,b,2089,a)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2159,b,2091,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2159,b,2092,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2159,b,2093,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2159,b,2094,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2159,b,2095,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2159,b,2096,b)].
% 14.86/14.98 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2159,b,2102,b)].
% 14.86/14.98 2160 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2050,b,2033,b)].
% 14.86/14.98 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2160,b,2089,a)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2160,b,2091,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2160,b,2092,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2160,b,2093,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2160,b,2094,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2160,b,2095,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2160,b,2096,b)].
% 14.90/14.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2160,b,2102,b)].
% 14.90/14.98 2161 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2051,c,2033,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2161,c,2091,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2161,c,2092,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2161,c,2093,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2161,c,2094,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2161,c,2095,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,c,2096,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2161,c,2102,b)].
% 14.90/14.98 2162 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2052,c,2033,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2162,c,2091,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2162,c,2092,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2162,c,2093,b)].
% 14.90/14.98 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2162,c,2094,b)].
% 14.90/14.99 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2162,c,2095,b)].
% 14.90/14.99 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,c,2096,b)].
% 14.90/14.99 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2162,c,2102,b)].
% 14.90/14.99 2163 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2057,a,2033,b)].
% 14.90/14.99 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2163,b,2089,a)].
% 14.90/14.99 Derived: -c_less(A,A,tc_nat). [resolve(2163,b,2090,a)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2163,b,2091,b)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2163,b,2092,b)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2163,b,2093,b)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2163,b,2094,b)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2163,b,2095,b)].
% 14.90/14.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2163,b,2096,b)].
% 14.90/14.99 2164 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2058,a,2033,b)].
% 14.90/14.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2164,c,2089,a)].
% 14.90/14.99 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2164,c,2090,a)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2164,c,2091,b)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2164,c,2092,b)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2164,c,2093,b)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2164,c,2094,b)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2164,c,2095,b)].
% 14.90/14.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2164,c,2096,b)].
% 14.90/14.99 2165 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2059,a,2033,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2165,b,2089,a)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2165,b,2090,a)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2165,b,2091,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2165,b,2092,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2165,b,2093,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2165,b,2094,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2165,b,2095,b)].
% 14.90/14.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2165,b,2096,b)].
% 14.90/14.99 2166 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2060,a,2033,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2166,c,2089,a)].
% 14.90/14.99 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2166,c,2090,a)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2166,c,2091,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2166,c,2092,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2166,c,2093,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2166,c,2094,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2166,c,2095,b)].
% 14.90/14.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2166,c,2096,b)].
% 14.90/14.99 2167 -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(2061,a,2033,b)].
% 14.90/14.99 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2167,c,2089,a)].
% 14.90/14.99 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2167,c,2090,a)].
% 14.90/15.00 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(2167,c,2091,b)].
% 14.90/15.00 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(2167,c,2092,b)].
% 14.90/15.00 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(2167,c,2093,b)].
% 14.90/15.00 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(2167,c,2094,b)].
% 14.90/15.00 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(2167,c,2095,b)].
% 14.90/15.00 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(2167,c,2096,b)].
% 14.90/15.00 2168 -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(2062,a,2033,b)].
% 14.90/15.00 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(2168,c,2089,a)].
% 14.90/15.00 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(2168,c,2090,a)].
% 14.90/15.00 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(2168,c,2091,b)].
% 14.90/15.00 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(2168,c,2092,b)].
% 14.90/15.00 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(2168,c,2093,b)].
% 14.90/15.00 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(2168,c,2094,b)].
% 14.90/15.00 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(2168,c,2095,b)].
% 14.90/15.00 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(2168,c,2096,b)].
% 14.90/15.00 2169 -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(2063,a,2033,b)].
% 14.90/15.00 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(2169,c,2089,a)].
% 14.90/15.00 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(2169,c,2090,a)].
% 14.90/15.00 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(2169,c,2091,b)].
% 14.90/15.00 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(2169,c,2092,b)].
% 14.90/15.00 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(2169,c,2093,b)].
% 14.90/15.00 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(2169,c,2094,b)].
% 14.90/15.00 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(2169,c,2095,b)].
% 14.90/15.00 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(2169,c,2096,b)].
% 14.90/15.00 2170 -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(2064,a,2033,b)].
% 14.90/15.00 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(2170,c,2089,a)].
% 14.90/15.00 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(2170,c,2090,a)].
% 14.90/15.00 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(2170,c,2091,b)].
% 14.90/15.00 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(2170,c,2092,b)].
% 14.90/15.00 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(2170,c,2093,b)].
% 14.90/15.00 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(2170,c,2094,b)].
% 14.90/15.00 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(2170,c,2095,b)].
% 14.90/15.00 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(2170,c,2096,b)].
% 14.90/15.00 2171 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2065,a,2033,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2171,c,2089,a)].
% 14.90/15.00 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2171,c,2090,a)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2171,c,2091,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2171,c,2092,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2171,c,2093,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2171,c,2094,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2171,c,2095,b)].
% 14.90/15.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2171,c,2096,b)].
% 14.90/15.00 2172 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(2066,a,2033,b)].
% 14.90/15.00 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(2172,b,2089,a)].
% 14.90/15.00 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(2172,b,2090,a)].
% 14.90/15.00 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(2172,b,2091,b)].
% 14.90/15.00 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(2172,b,2092,b)].
% 14.90/15.00 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(2172,b,2093,b)].
% 14.90/15.00 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(2172,b,2094,b)].
% 14.90/15.00 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(2172,b,2095,b)].
% 14.90/15.00 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(2172,b,2096,b)].
% 14.90/15.00 2173 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2067,a,2033,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2173,b,2089,a)].
% 14.90/15.00 Derived: c_lessequals(A,A,tc_nat). [resolve(2173,b,2090,a)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2173,b,2091,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2173,b,2092,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2173,b,2093,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2173,b,2094,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2173,b,2095,b)].
% 14.90/15.00 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2173,b,2096,b)].
% 14.90/15.01 2174 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2068,a,2033,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2174,c,2089,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2174,c,2090,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2174,c,2091,b)].
% 14.90/15.01 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(2174,c,2092,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2174,c,2093,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2174,c,2094,b)].
% 14.90/15.01 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(2174,c,2095,b)].
% 14.90/15.01 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(2174,c,2096,b)].
% 14.90/15.01 2175 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2069,a,2033,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2175,c,2089,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2175,c,2090,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2175,c,2091,b)].
% 14.90/15.01 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(2175,c,2092,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2175,c,2093,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2175,c,2094,b)].
% 14.90/15.01 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(2175,c,2095,b)].
% 14.90/15.01 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(2175,c,2096,b)].
% 14.90/15.01 2176 -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(2070,a,2033,b)].
% 14.90/15.01 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(2176,d,2089,a)].
% 14.90/15.01 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(2176,d,2090,a)].
% 14.90/15.01 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(2176,d,2091,b)].
% 14.90/15.01 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(2176,d,2092,b)].
% 14.90/15.01 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(2176,d,2093,b)].
% 14.90/15.01 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(2176,d,2094,b)].
% 14.90/15.01 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(2176,d,2095,b)].
% 14.90/15.01 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(2176,d,2096,b)].
% 14.90/15.01 2177 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2071,a,2033,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2177,c,2089,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2177,c,2090,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2177,c,2091,b)].
% 14.90/15.01 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(2177,c,2092,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2177,c,2093,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2177,c,2094,b)].
% 14.90/15.01 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(2177,c,2095,b)].
% 14.90/15.01 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(2177,c,2096,b)].
% 14.90/15.01 2178 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2072,a,2033,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2178,c,2089,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2178,c,2090,a)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2178,c,2091,b)].
% 14.90/15.01 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(2178,c,2092,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2178,c,2093,b)].
% 14.90/15.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2178,c,2094,b)].
% 14.90/15.01 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(2178,c,2095,b)].
% 14.90/15.01 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(2178,c,2096,b)].
% 14.90/15.01 2179 -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(2073,a,2033,b)].
% 14.90/15.01 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(2179,d,2089,a)].
% 14.90/15.01 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(2179,d,2090,a)].
% 14.90/15.01 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(2179,d,2091,b)].
% 14.90/15.01 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(2179,d,2092,b)].
% 14.90/15.01 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(2179,d,2093,b)].
% 14.90/15.02 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(2179,d,2094,b)].
% 14.90/15.02 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(2179,d,2095,b)].
% 14.90/15.02 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(2179,d,2096,b)].
% 14.90/15.02 2180 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2074,a,2033,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2180,c,2089,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2180,c,2090,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2180,c,2091,b)].
% 14.90/15.02 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(2180,c,2092,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2180,c,2093,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2180,c,2094,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2180,c,2095,b)].
% 14.90/15.02 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(2180,c,2096,b)].
% 14.90/15.02 2181 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2075,a,2033,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2181,c,2089,a)].
% 14.90/15.02 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2181,c,2090,a)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2181,c,2091,b)].
% 14.90/15.02 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(2181,c,2092,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2181,c,2093,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2181,c,2094,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2181,c,2095,b)].
% 14.90/15.02 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(2181,c,2096,b)].
% 14.90/15.02 2182 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2076,a,2033,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2182,c,2089,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2182,c,2090,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2182,c,2091,b)].
% 14.90/15.02 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(2182,c,2092,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2182,c,2093,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2182,c,2094,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2182,c,2095,b)].
% 14.90/15.02 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(2182,c,2096,b)].
% 14.90/15.02 2183 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2033,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2183,c,2089,a)].
% 14.90/15.02 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2183,c,2090,a)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2183,c,2091,b)].
% 14.90/15.02 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(2183,c,2092,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2183,c,2093,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2183,c,2094,b)].
% 14.90/15.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2183,c,2095,b)].
% 14.90/15.02 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(2183,c,2096,b)].
% 14.90/15.02 2184 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2078,a,2033,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2184,c,2089,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2184,c,2090,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2184,c,2091,b)].
% 14.90/15.02 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(2184,c,2092,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2184,c,2093,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2184,c,2094,b)].
% 14.90/15.02 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(2184,c,2095,b)].
% 14.90/15.02 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(2184,c,2096,b)].
% 14.90/15.02 2185 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2079,a,2033,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2185,c,2089,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2185,c,2090,a)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2185,c,2091,b)].
% 14.90/15.02 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(2185,c,2092,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2185,c,2093,b)].
% 14.90/15.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2185,c,2094,b)].
% 14.90/15.03 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(2185,c,2095,b)].
% 14.90/15.03 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(2185,c,2096,b)].
% 14.90/15.03 2186 -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(2080,a,2033,b)].
% 14.90/15.03 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(2186,d,2089,a)].
% 14.90/15.03 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(2186,d,2090,a)].
% 14.90/15.03 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(2186,d,2091,b)].
% 14.90/15.03 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(2186,d,2092,b)].
% 14.90/15.03 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(2186,d,2093,b)].
% 14.90/15.03 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(2186,d,2094,b)].
% 14.90/15.03 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(2186,d,2095,b)].
% 14.90/15.03 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(2186,d,2096,b)].
% 14.90/15.03 2187 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2081,a,2033,b)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2187,c,2089,a)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2187,c,2090,a)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2187,c,2091,b)].
% 14.90/15.03 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(2187,c,2092,b)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2187,c,2093,b)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2187,c,2094,b)].
% 14.90/15.03 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(2187,c,2095,b)].
% 14.90/15.03 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(2187,c,2096,b)].
% 14.90/15.03 2188 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2082,a,2033,b)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2188,c,2089,a)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2188,c,2090,a)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2188,c,2091,b)].
% 14.90/15.03 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(2188,c,2092,b)].
% 14.90/15.03 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2188,c,2093,b)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2188,c,2094,b)].
% 14.90/15.04 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(2188,c,2095,b)].
% 14.90/15.04 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(2188,c,2096,b)].
% 14.90/15.04 2189 -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(2083,a,2033,b)].
% 14.90/15.04 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(2189,d,2089,a)].
% 14.90/15.04 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(2189,d,2090,a)].
% 14.90/15.04 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(2189,d,2091,b)].
% 14.90/15.04 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(2189,d,2092,b)].
% 14.90/15.04 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(2189,d,2093,b)].
% 14.90/15.04 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(2189,d,2094,b)].
% 14.90/15.04 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(2189,d,2095,b)].
% 14.90/15.04 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(2189,d,2096,b)].
% 14.90/15.04 2190 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2084,a,2033,b)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2190,c,2089,a)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2190,c,2090,a)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2190,c,2091,b)].
% 14.90/15.04 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(2190,c,2092,b)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2190,c,2093,b)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2190,c,2094,b)].
% 14.90/15.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2190,c,2095,b)].
% 14.90/15.04 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(2190,c,2096,b)].
% 14.90/15.04 2191 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2085,a,2033,b)].
% 14.90/15.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2191,c,2089,a)].
% 14.90/15.04 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2191,c,2090,a)].
% 14.90/15.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2191,c,2091,b)].
% 14.90/15.04 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(2191,c,2092,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2191,c,2093,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2191,c,2094,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2191,c,2095,b)].
% 15.15/15.24 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(2191,c,2096,b)].
% 15.15/15.24 2192 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2086,a,2033,b)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2192,c,2089,a)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2192,c,2090,a)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2192,c,2091,b)].
% 15.15/15.24 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(2192,c,2092,b)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2192,c,2093,b)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2192,c,2094,b)].
% 15.15/15.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2192,c,2095,b)].
% 15.15/15.24 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(2192,c,2096,b)].
% 15.15/15.24 2193 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2087,a,2033,b)].
% 15.15/15.24 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2193,c,2089,a)].
% 15.15/15.24 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2193,c,2090,a)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2193,c,2091,b)].
% 15.15/15.24 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(2193,c,2092,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2193,c,2093,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2193,c,2094,b)].
% 15.15/15.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2193,c,2095,b)].
% 15.15/15.24 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(2193,c,2096,b)].
% 15.15/15.24 2194 -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].
% 15.15/15.24 2195 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 15.15/15.24 2196 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 15.15/15.24 2197 -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].
% 15.15/15.24 2198 -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].
% 15.15/15.24 2199 -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].
% 15.19/15.33 2200 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_3) # label(axiom). [assumption].
% 15.19/15.33 2201 -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].
% 15.19/15.33 2202 -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].
% 15.19/15.33 2203 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_7) # label(axiom). [assumption].
% 15.19/15.33 2204 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_8) # label(axiom). [assumption].
% 15.19/15.33 2205 -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)].
% 15.19/15.33 2206 -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)].
% 15.19/15.33 2207 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 15.19/15.33 2208 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 15.19/15.33 2209 -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(155,b,133,b)].
% 15.19/15.33 2210 -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(155,b,135,b)].
% 15.19/15.33 2211 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(167,a,155,b)].
% 15.19/15.33 2212 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(168,a,155,b)].
% 15.19/15.33 2213 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 15.19/15.33 2214 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 15.19/15.33 2215 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(245,a,227,b)].
% 15.19/15.33 2216 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(246,a,227,b)].
% 15.19/15.33 2217 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,286,a)].
% 15.19/15.33 2218 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,288,a)].
% 15.19/15.33 2219 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(320,a,305,b)].
% 15.19/15.33 2220 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(321,a,305,b)].
% 15.19/15.33 2221 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(779,a,724,a)].
% 15.19/15.33 2222 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(779,a,731,a)].
% 15.19/15.33 2223 -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(892,b,822,a)].
% 15.19/15.33 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(2223,a,2197,b)].
% 15.19/15.33 2224 -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(892,b,823,a)].
% 15.26/15.34 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(2224,a,2197,b)].
% 15.26/15.34 2225 -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(892,b,824,a)].
% 15.26/15.34 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(2225,a,2197,b)].
% 15.26/15.34 2226 -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(892,b,825,a)].
% 15.26/15.34 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(2226,a,2197,b)].
% 15.26/15.34 2227 -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(892,b,826,a)].
% 15.26/15.34 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(2227,a,2197,b)].
% 15.26/15.34 2228 -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(892,b,827,a)].
% 15.26/15.34 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(2228,a,2197,b)].
% 15.26/15.34 2229 -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(892,b,828,a)].
% 15.26/15.34 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(2229,a,2197,b)].
% 15.26/15.34 2230 -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(892,b,829,a)].
% 15.26/15.34 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(2230,a,2197,b)].
% 15.26/15.34 2231 -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(892,b,830,a)].
% 15.26/15.34 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(2231,a,2197,b)].
% 15.26/15.34 2232 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(892,b,831,a)].
% 15.26/15.34 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2232,a,2197,b)].
% 15.26/15.34 2233 -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(892,b,832,a)].
% 15.26/15.35 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(2233,a,2197,b)].
% 15.26/15.35 2234 -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(892,b,833,a)].
% 15.26/15.35 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(2234,a,2197,b)].
% 15.26/15.35 2235 -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(892,b,834,a)].
% 15.26/15.35 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(2235,a,2197,b)].
% 15.26/15.35 2236 -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(892,b,835,a)].
% 15.26/15.35 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(2236,a,2197,b)].
% 15.26/15.35 2237 -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(892,b,836,a)].
% 15.26/15.35 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(2237,a,2197,b)].
% 15.26/15.35 2238 -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(892,b,837,a)].
% 15.26/15.35 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(2238,a,2197,b)].
% 15.26/15.35 2239 -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(892,b,838,a)].
% 15.26/15.35 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(2239,a,2197,b)].
% 15.26/15.35 2240 -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(892,b,839,a)].
% 15.26/15.35 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(2240,a,2197,b)].
% 15.26/15.35 2241 -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(892,b,840,a)].
% 15.26/15.35 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(2241,a,2197,b)].
% 15.26/15.35 2242 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(892,b,841,a)].
% 15.26/15.36 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2242,a,2197,b)].
% 15.26/15.36 2243 -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(892,b,842,a)].
% 15.26/15.36 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(2243,a,2197,b)].
% 15.26/15.36 2244 -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(892,b,843,a)].
% 15.26/15.36 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(2244,a,2197,b)].
% 15.26/15.36 2245 -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(892,b,844,a)].
% 15.26/15.36 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(2245,a,2197,b)].
% 15.26/15.36 2246 -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(892,b,845,b)].
% 15.26/15.36 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(2246,a,2197,b)].
% 15.26/15.36 2247 -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(892,b,846,b)].
% 15.26/15.36 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(2247,a,2197,b)].
% 15.26/15.36 2248 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(892,b,847,a)].
% 15.26/15.36 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(2248,a,2197,b)].
% 15.26/15.36 2249 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(892,b,848,a)].
% 15.26/15.36 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(2249,a,2197,b)].
% 15.26/15.36 2250 -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(892,b,849,a)].
% 15.26/15.36 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(2250,a,2197,b)].
% 15.26/15.36 2251 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(892,b,850,a)].
% 15.26/15.36 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(2251,a,2197,b)].
% 15.26/15.36 2252 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(892,b,851,a)].
% 15.26/15.36 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(2252,a,2197,b)].
% 15.26/15.36 2253 -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(892,b,852,a)].
% 15.26/15.36 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(2253,a,2197,b)].
% 15.26/15.36 2254 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(892,b,853,a)].
% 15.30/15.37 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(2254,a,2197,b)].
% 15.30/15.37 2255 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(892,b,854,a)].
% 15.30/15.37 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(2255,a,2197,b)].
% 15.30/15.37 2256 -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(892,b,855,a)].
% 15.30/15.37 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(2256,a,2197,b)].
% 15.30/15.37 2257 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(892,b,856,a)].
% 15.30/15.37 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2257,a,2197,b)].
% 15.30/15.37 2258 -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(892,b,857,a)].
% 15.30/15.37 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(2258,a,2197,b)].
% 15.30/15.37 2259 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(892,b,858,a)].
% 15.30/15.37 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(2259,a,2197,b)].
% 15.30/15.37 2260 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(892,b,859,a)].
% 15.30/15.37 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(2260,a,2197,b)].
% 15.30/15.37 2261 -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(892,b,860,a)].
% 15.30/15.37 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(2261,a,2197,b)].
% 15.30/15.37 2262 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(892,b,861,a)].
% 15.30/15.37 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2262,a,2197,b)].
% 15.30/15.37 2263 -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(892,b,862,a)].
% 15.30/15.37 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(2263,a,2197,b)].
% 15.30/15.37 2264 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(892,b,863,a)].
% 15.30/15.37 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(2264,a,2197,b)].
% 15.30/15.37 2265 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(892,b,864,a)].
% 15.30/15.37 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(2265,a,2197,b)].
% 15.30/15.37 2266 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(892,b,865,a)].
% 15.30/15.37 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(2266,a,2197,b)].
% 15.30/15.38 2267 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(892,b,866,a)].
% 15.30/15.38 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(2267,a,2197,b)].
% 15.30/15.38 2268 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(892,b,867,a)].
% 15.30/15.38 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2268,a,2197,b)].
% 15.30/15.38 2269 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(892,b,868,a)].
% 15.30/15.38 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2269,a,2197,b)].
% 15.30/15.38 2270 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(892,b,869,a)].
% 15.30/15.38 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2270,a,2197,b)].
% 15.30/15.38 2271 -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(892,b,870,a)].
% 15.30/15.38 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(2271,a,2197,b)].
% 15.30/15.38 2272 -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(892,b,871,a)].
% 15.30/15.38 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(2272,a,2197,b)].
% 15.30/15.38 2273 -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(892,b,872,a)].
% 15.30/15.38 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(2273,a,2197,b)].
% 15.30/15.38 2274 -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(892,b,873,a)].
% 15.30/15.38 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(2274,a,2197,b)].
% 15.30/15.38 2275 -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(892,b,874,a)].
% 15.30/15.38 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(2275,a,2197,b)].
% 15.30/15.38 2276 -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(892,b,875,a)].
% 15.30/15.38 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(2276,a,2197,b)].
% 15.30/15.38 2277 -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(892,b,876,a)].
% 15.38/15.50 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(2277,a,2197,b)].
% 15.38/15.50 2278 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(892,b,877,a)].
% 15.38/15.50 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2278,a,2197,b)].
% 15.38/15.50 2279 -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(892,b,878,a)].
% 15.38/15.50 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(2279,a,2197,b)].
% 15.38/15.50 2280 -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(892,b,879,a)].
% 15.38/15.50 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(2280,a,2197,b)].
% 15.38/15.50 2281 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1068,a)].
% 15.38/15.50 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2281,a,2197,b)].
% 15.38/15.50 2282 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1091,a)].
% 15.38/15.50 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2197,b)].
% 15.38/15.50 2283 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1149,a,1113,a)].
% 15.38/15.50 2284 class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1149,a,1138,a)].
% 15.38/15.50 2285 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1149,a,1139,b)].
% 15.38/15.50 2286 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1149,a,1140,b)].
% 15.38/15.50 2287 -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(1486,b,1462,a)].
% 15.38/15.50 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(2287,a,2197,b)].
% 15.38/15.50 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(2287,a,2198,b)].
% 15.38/15.50 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(2287,a,2199,b)].
% 15.38/15.50 2288 -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(1486,b,1463,a)].
% 15.38/15.50 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(2288,a,2197,b)].
% 15.38/15.50 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(2288,a,2198,b)].
% 15.38/15.50 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(2288,a,2199,b)].
% 15.38/15.50 2289 -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(1486,b,1464,a)].
% 15.38/15.50 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(2289,a,2197,b)].
% 15.38/15.50 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(2289,a,2198,b)].
% 15.47/15.55 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(2289,a,2199,b)].
% 15.47/15.55 2290 -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(1486,b,1465,a)].
% 15.47/15.55 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(2290,a,2197,b)].
% 15.47/15.55 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(2290,a,2198,b)].
% 15.47/15.55 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(2290,a,2199,b)].
% 15.47/15.55 2291 -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(1486,b,1466,a)].
% 15.47/15.55 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(2291,a,2197,b)].
% 15.47/15.55 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(2291,a,2198,b)].
% 15.47/15.55 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(2291,a,2199,b)].
% 15.47/15.55 2292 -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(1486,b,1467,a)].
% 15.47/15.55 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(2292,a,2197,b)].
% 15.47/15.55 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(2292,a,2198,b)].
% 15.47/15.55 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(2292,a,2199,b)].
% 15.47/15.55 2293 -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(1486,b,1468,a)].
% 15.47/15.55 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(2293,a,2197,b)].
% 15.47/15.55 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(2293,a,2198,b)].
% 15.47/15.55 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(2293,a,2199,b)].
% 15.47/15.55 2294 -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(1486,b,1469,a)].
% 15.47/15.55 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(2294,a,2197,b)].
% 15.47/15.55 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(2294,a,2198,b)].
% 15.47/15.55 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(2294,a,2199,b)].
% 15.47/15.55 2295 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1591,b,1566,a)].
% 15.47/15.55 2296 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1591,b,1567,a)].
% 15.47/15.55 2297 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1591,b,1568,a)].
% 15.47/15.55 2298 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1591,b,1569,a)].
% 15.47/15.55 2299 -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(1591,b,1570,a)].
% 15.47/15.55 2300 -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(1591,b,1571,a)].
% 15.51/15.65 2301 -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(1591,b,1572,a)].
% 15.51/15.65 2302 -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(1591,b,1573,a)].
% 15.51/15.65 2303 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1591,b,1574,a)].
% 15.51/15.65 2304 -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(1591,b,1575,a)].
% 15.51/15.65 2305 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1591,b,1576,a)].
% 15.51/15.65 2306 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1620,a)].
% 15.51/15.65 2307 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1654,b,1621,a)].
% 15.51/15.65 2308 -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(1654,b,1622,a)].
% 15.51/15.65 2309 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1623,a)].
% 15.51/15.65 2310 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1654,b,1624,a)].
% 15.51/15.65 2311 -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(1654,b,1625,a)].
% 15.51/15.65 2312 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1626,a)].
% 15.51/15.65 2313 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1654,b,1627,a)].
% 15.51/15.65 2314 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1654,b,1628,a)].
% 15.51/15.65 2315 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1654,b,1629,a)].
% 15.51/15.65 2316 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1654,b,1630,a)].
% 15.51/15.65 2317 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1654,b,1631,a)].
% 15.51/15.65 2318 -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(1654,b,1632,a)].
% 15.51/15.65 2319 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1654,b,1633,a)].
% 15.51/15.65 2320 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1654,b,1634,a)].
% 15.51/15.65 2321 -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(1654,b,1635,a)].
% 15.51/15.65 2322 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1654,b,1636,a)].
% 15.51/15.65 2323 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1654,b,1637,a)].
% 15.51/15.65 2324 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1654,b,1638,a)].
% 15.51/15.65 2325 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1654,b,1639,a)].
% 15.51/15.65 2326 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1958,c,1881,b)].
% 15.59/15.67 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2326,c,2195,a)].
% 15.59/15.67 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2326,c,2196,a)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2326,c,2197,b)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2326,c,2198,b)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2326,c,2199,b)].
% 15.59/15.67 2327 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1959,c,1881,b)].
% 15.59/15.67 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2327,c,2195,a)].
% 15.59/15.67 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2327,c,2196,a)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2327,c,2197,b)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2327,c,2198,b)].
% 15.59/15.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2327,c,2199,b)].
% 15.59/15.67 2328 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1960,b,1881,b)].
% 15.59/15.67 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2328,b,2195,a)].
% 15.59/15.67 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2328,b,2196,a)].
% 15.59/15.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2328,b,2197,b)].
% 15.59/15.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2328,b,2198,b)].
% 15.59/15.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2328,b,2199,b)].
% 15.59/15.67 2329 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1961,b,1881,b)].
% 15.59/15.67 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2329,b,2195,a)].
% 15.59/15.67 Derived: class_HOL_Oplus(tc_nat). [resolve(2329,b,2196,a)].
% 15.59/15.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2329,b,2197,b)].
% 15.59/15.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2329,b,2198,b)].
% 15.59/15.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2329,b,2199,b)].
% 15.59/15.67 2330 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1993,b,1881,b)].
% 15.59/15.67 2331 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1994,c,1881,b)].
% 15.59/15.67 2332 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1995,b,1881,b)].
% 15.59/15.67 2333 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1996,c,1881,b)].
% 15.59/15.67 2334 -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(1997,c,1881,b)].
% 15.59/15.67 2335 -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(1998,c,1881,b)].
% 15.59/15.67 2336 -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(1999,c,1881,b)].
% 15.59/15.67 2337 -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(2000,c,1881,b)].
% 15.59/15.67 2338 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2001,c,1881,b)].
% 15.59/15.67 2339 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(2002,b,1881,b)].
% 15.64/15.71 2340 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2003,b,1881,b)].
% 15.64/15.71 2341 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2004,c,1881,b)].
% 15.64/15.71 2342 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2005,c,1881,b)].
% 15.64/15.71 2343 -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(2006,d,1881,b)].
% 15.64/15.71 2344 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2007,c,1881,b)].
% 15.64/15.71 2345 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2008,c,1881,b)].
% 15.64/15.71 2346 -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(2009,d,1881,b)].
% 15.64/15.71 2347 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2010,c,1881,b)].
% 15.64/15.71 2348 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2011,c,1881,b)].
% 15.64/15.71 2349 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2012,c,1881,b)].
% 15.64/15.71 2350 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2013,c,1881,b)].
% 15.64/15.71 2351 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2014,c,1881,b)].
% 15.64/15.71 2352 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2015,c,1881,b)].
% 15.64/15.71 2353 -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(2016,d,1881,b)].
% 15.64/15.71 2354 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2017,c,1881,b)].
% 15.64/15.71 2355 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2018,c,1881,b)].
% 15.64/15.71 2356 -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(2019,d,1881,b)].
% 15.64/15.71 2357 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2020,c,1881,b)].
% 15.64/15.71 2358 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2021,c,1881,b)].
% 15.64/15.71 2359 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2022,c,1881,b)].
% 15.64/15.71 2360 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2023,c,1881,b)].
% 15.64/15.71 2361 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2042,a,2031,b)].
% 15.64/15.71 2362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2047,b,2031,b)].
% 15.64/15.71 2363 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2048,b,2031,b)].
% 15.64/15.71 2364 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2049,b,2031,b)].
% 15.64/15.71 2365 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2050,b,2031,b)].
% 15.64/15.71 2366 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2051,c,2031,b)].
% 15.67/15.75 2367 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2052,c,2031,b)].
% 15.67/15.75 2368 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2115,a,2095,b)].
% 15.67/15.75 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2368,b,2197,b)].
% 15.67/15.75 2369 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2116,a,2095,b)].
% 15.67/15.75 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2369,b,2197,b)].
% 15.67/15.75 2370 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2156,d,2095,b)].
% 15.67/15.75 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(C,A,tc_IntDef_Oint),c_times(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2370,d,2195,a)].
% 15.67/15.75 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(C,A,tc_nat),c_times(C,B,tc_nat),tc_nat). [resolve(2370,d,2196,a)].
% 15.67/15.75 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2370,d,2197,b)].
% 15.67/15.75 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2370,d,2198,b)].
% 15.67/15.75 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2370,d,2199,b)].
% 15.67/15.75 2371 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2157,b,2095,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2371,b,2195,a)].
% 15.67/15.75 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2371,b,2196,a)].
% 15.67/15.75 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2371,b,2197,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2371,b,2198,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2371,b,2199,b)].
% 15.67/15.75 2372 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2158,b,2095,b)].
% 15.67/15.75 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2372,b,2195,a)].
% 15.67/15.75 Derived: class_HOL_Otimes(tc_nat). [resolve(2372,b,2196,a)].
% 15.67/15.75 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2372,b,2197,b)].
% 15.67/15.75 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2372,b,2198,b)].
% 15.67/15.75 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2372,b,2199,b)].
% 15.67/15.75 2373 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2159,b,2095,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2373,b,2195,a)].
% 15.67/15.75 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2373,b,2196,a)].
% 15.67/15.75 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2373,b,2197,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2373,b,2198,b)].
% 15.67/15.75 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2373,b,2199,b)].
% 15.67/15.75 2374 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2160,b,2095,b)].
% 15.67/15.75 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2374,b,2195,a)].
% 15.67/15.76 Derived: class_HOL_Ozero(tc_nat). [resolve(2374,b,2196,a)].
% 15.67/15.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2374,b,2197,b)].
% 15.67/15.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2374,b,2198,b)].
% 15.67/15.76 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2374,b,2199,b)].
% 15.67/15.76 2375 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2161,c,2095,b)].
% 15.67/15.76 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(2375,c,2195,a)].
% 15.67/15.76 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(2375,c,2196,a)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2375,c,2197,b)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2375,c,2198,b)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2375,c,2199,b)].
% 15.67/15.76 2376 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2162,c,2095,b)].
% 15.67/15.76 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(2376,c,2195,a)].
% 15.67/15.76 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(2376,c,2196,a)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2376,c,2197,b)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2376,c,2198,b)].
% 15.67/15.76 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2376,c,2199,b)].
% 15.67/15.76 2377 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2163,b,2095,b)].
% 15.67/15.76 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2377,b,2195,a)].
% 15.67/15.76 Derived: -c_less(A,A,tc_nat). [resolve(2377,b,2196,a)].
% 15.67/15.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2377,b,2197,b)].
% 15.67/15.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2377,b,2198,b)].
% 15.67/15.76 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2377,b,2199,b)].
% 15.67/15.77 2378 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2164,c,2095,b)].
% 15.67/15.77 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2378,c,2195,a)].
% 15.67/15.77 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2378,c,2196,a)].
% 15.67/15.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2378,c,2197,b)].
% 15.67/15.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2378,c,2198,b)].
% 15.67/15.77 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2378,c,2199,b)].
% 15.67/15.77 2379 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2165,b,2095,b)].
% 15.67/15.77 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2379,b,2195,a)].
% 15.67/15.77 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2379,b,2196,a)].
% 15.67/15.77 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2379,b,2197,b)].
% 15.67/15.77 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2379,b,2198,b)].
% 15.67/15.77 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2379,b,2199,b)].
% 15.67/15.77 2380 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2166,c,2095,b)].
% 15.67/15.77 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2380,c,2195,a)].
% 15.67/15.77 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2380,c,2196,a)].
% 15.67/15.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2380,c,2197,b)].
% 15.67/15.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2380,c,2198,b)].
% 15.67/15.77 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2380,c,2199,b)].
% 15.67/15.77 2381 -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(2167,c,2095,b)].
% 15.67/15.77 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(2381,c,2195,a)].
% 15.67/15.77 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(2381,c,2196,a)].
% 15.67/15.77 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(2381,c,2197,b)].
% 15.67/15.77 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(2381,c,2198,b)].
% 15.67/15.77 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(2381,c,2199,b)].
% 15.67/15.77 2382 -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(2168,c,2095,b)].
% 15.67/15.77 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(2382,c,2195,a)].
% 15.67/15.78 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(2382,c,2196,a)].
% 15.67/15.78 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(2382,c,2197,b)].
% 15.67/15.78 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(2382,c,2198,b)].
% 15.67/15.78 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(2382,c,2199,b)].
% 15.67/15.78 2383 -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(2169,c,2095,b)].
% 15.67/15.78 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(2383,c,2195,a)].
% 15.67/15.78 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(2383,c,2196,a)].
% 15.67/15.78 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(2383,c,2197,b)].
% 15.67/15.78 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(2383,c,2198,b)].
% 15.67/15.78 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(2383,c,2199,b)].
% 15.67/15.78 2384 -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(2170,c,2095,b)].
% 15.67/15.78 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(2384,c,2195,a)].
% 15.67/15.78 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(2384,c,2196,a)].
% 15.67/15.78 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(2384,c,2197,b)].
% 15.67/15.78 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(2384,c,2198,b)].
% 15.67/15.78 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__idom(C). [resolve(2384,c,2199,b)].
% 15.67/15.78 2385 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2171,c,2095,b)].
% 15.67/15.78 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2385,c,2195,a)].
% 15.67/15.78 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2385,c,2196,a)].
% 15.67/15.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2385,c,2197,b)].
% 15.67/15.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2385,c,2198,b)].
% 15.67/15.78 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2385,c,2199,b)].
% 15.67/15.78 2386 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(2172,b,2095,b)].
% 15.67/15.78 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(2386,b,2195,a)].
% 15.67/15.78 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(2386,b,2196,a)].
% 15.67/15.78 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(2386,b,2197,b)].
% 15.67/15.78 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(2386,b,2198,b)].
% 15.67/15.78 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(2386,b,2199,b)].
% 15.67/15.78 2387 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2173,b,2095,b)].
% 15.67/15.78 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2387,b,2195,a)].
% 15.67/15.78 Derived: c_lessequals(A,A,tc_nat). [resolve(2387,b,2196,a)].
% 15.67/15.78 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2387,b,2197,b)].
% 15.67/15.78 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2387,b,2198,b)].
% 15.67/15.78 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2387,b,2199,b)].
% 15.67/15.78 2388 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2174,c,2095,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2388,c,2195,a)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2388,c,2196,a)].
% 15.67/15.78 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(2388,c,2197,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2388,c,2198,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2388,c,2199,b)].
% 15.67/15.78 2389 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2175,c,2095,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2389,c,2195,a)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2389,c,2196,a)].
% 15.67/15.78 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(2389,c,2197,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2389,c,2198,b)].
% 15.67/15.78 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2389,c,2199,b)].
% 15.67/15.78 2390 -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(2176,d,2095,b)].
% 15.67/15.78 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(2390,d,2195,a)].
% 15.67/15.78 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(2390,d,2196,a)].
% 15.67/15.78 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(2390,d,2197,b)].
% 15.67/15.78 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(2390,d,2198,b)].
% 15.67/15.79 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(2390,d,2199,b)].
% 15.67/15.79 2391 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2177,c,2095,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2391,c,2195,a)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2391,c,2196,a)].
% 15.67/15.79 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(2391,c,2197,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2391,c,2198,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2391,c,2199,b)].
% 15.67/15.79 2392 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2178,c,2095,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2392,c,2195,a)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2392,c,2196,a)].
% 15.67/15.79 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(2392,c,2197,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2392,c,2198,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2392,c,2199,b)].
% 15.67/15.79 2393 -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(2179,d,2095,b)].
% 15.67/15.79 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(2393,d,2195,a)].
% 15.67/15.79 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(2393,d,2196,a)].
% 15.67/15.79 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(2393,d,2197,b)].
% 15.67/15.79 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(2393,d,2198,b)].
% 15.67/15.79 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(2393,d,2199,b)].
% 15.67/15.79 2394 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2180,c,2095,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2394,c,2195,a)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2394,c,2196,a)].
% 15.67/15.79 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(2394,c,2197,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2394,c,2198,b)].
% 15.67/15.79 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2394,c,2199,b)].
% 15.67/15.79 2395 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2181,c,2095,b)].
% 15.67/15.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2395,c,2195,a)].
% 15.67/15.80 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2395,c,2196,a)].
% 15.67/15.80 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(2395,c,2197,b)].
% 15.67/15.80 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2395,c,2198,b)].
% 15.67/15.80 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2395,c,2199,b)].
% 15.67/15.80 2396 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2182,c,2095,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2396,c,2195,a)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2396,c,2196,a)].
% 15.67/15.80 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(2396,c,2197,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2396,c,2198,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2396,c,2199,b)].
% 15.67/15.80 2397 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2183,c,2095,b)].
% 15.67/15.80 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2397,c,2195,a)].
% 15.67/15.80 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2397,c,2196,a)].
% 15.67/15.80 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(2397,c,2197,b)].
% 15.67/15.80 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2397,c,2198,b)].
% 15.67/15.80 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2397,c,2199,b)].
% 15.67/15.80 2398 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2184,c,2095,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2398,c,2195,a)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2398,c,2196,a)].
% 15.67/15.80 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(2398,c,2197,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2398,c,2198,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2398,c,2199,b)].
% 15.67/15.80 2399 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2185,c,2095,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2399,c,2195,a)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2399,c,2196,a)].
% 15.67/15.80 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(2399,c,2197,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2399,c,2198,b)].
% 15.67/15.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2399,c,2199,b)].
% 15.67/15.81 2400 -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(2186,d,2095,b)].
% 15.67/15.81 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(2400,d,2195,a)].
% 15.67/15.81 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(2400,d,2196,a)].
% 15.67/15.81 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(2400,d,2197,b)].
% 15.67/15.81 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__field(C). [resolve(2400,d,2198,b)].
% 15.67/15.81 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__idom(C). [resolve(2400,d,2199,b)].
% 15.67/15.81 2401 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2187,c,2095,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2401,c,2195,a)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2401,c,2196,a)].
% 15.67/15.81 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(2401,c,2197,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2401,c,2198,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2401,c,2199,b)].
% 15.67/15.81 2402 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2188,c,2095,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2402,c,2195,a)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2402,c,2196,a)].
% 15.67/15.81 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(2402,c,2197,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2402,c,2198,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2402,c,2199,b)].
% 15.67/15.81 2403 -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(2189,d,2095,b)].
% 15.67/15.81 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(2403,d,2195,a)].
% 15.67/15.81 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(2403,d,2196,a)].
% 15.67/15.81 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(2403,d,2197,b)].
% 15.67/15.81 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(2403,d,2198,b)].
% 15.67/15.81 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(2403,d,2199,b)].
% 15.67/15.81 2404 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2190,c,2095,b)].
% 15.67/15.81 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2404,c,2195,a)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2404,c,2196,a)].
% 15.95/16.02 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(2404,c,2197,b)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2404,c,2198,b)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2404,c,2199,b)].
% 15.95/16.02 2405 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2191,c,2095,b)].
% 15.95/16.02 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2405,c,2195,a)].
% 15.95/16.02 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2405,c,2196,a)].
% 15.95/16.02 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(2405,c,2197,b)].
% 15.95/16.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2405,c,2198,b)].
% 15.95/16.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2405,c,2199,b)].
% 15.95/16.02 2406 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2192,c,2095,b)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2406,c,2195,a)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2406,c,2196,a)].
% 15.95/16.02 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(2406,c,2197,b)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2406,c,2198,b)].
% 15.95/16.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2406,c,2199,b)].
% 15.95/16.02 2407 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2193,c,2095,b)].
% 15.95/16.02 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2407,c,2195,a)].
% 15.95/16.02 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2407,c,2196,a)].
% 15.95/16.02 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(2407,c,2197,b)].
% 15.95/16.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2407,c,2198,b)].
% 15.95/16.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2407,c,2199,b)].
% 15.95/16.02 2408 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_10) # label(axiom). [assumption].
% 15.95/16.02 2409 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 15.95/16.02 2410 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 15.95/16.02 2411 -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].
% 15.95/16.02 2412 -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].
% 15.95/16.02 2413 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_41) # label(axiom). [assumption].
% 15.95/16.02 2414 -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].
% 16.00/16.14 2415 -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].
% 16.00/16.14 2416 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_11) # label(axiom). [assumption].
% 16.00/16.14 2417 -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].
% 16.00/16.14 2418 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_6) # label(axiom). [assumption].
% 16.00/16.14 2419 -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].
% 16.00/16.14 2420 -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].
% 16.00/16.14 2421 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(108,a,107,b)].
% 16.00/16.14 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2421,b,2411,b)].
% 16.00/16.14 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2421,b,2414,b)].
% 16.00/16.14 2422 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(109,a,107,b)].
% 16.00/16.14 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2422,b,2411,b)].
% 16.00/16.14 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2422,b,2414,b)].
% 16.00/16.14 2423 -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(159,b,133,b)].
% 16.00/16.14 2424 -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(159,b,135,b)].
% 16.00/16.14 2425 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,159,b)].
% 16.00/16.14 2426 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,159,b)].
% 16.00/16.14 2427 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(167,a,159,b)].
% 16.00/16.14 2428 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(168,a,159,b)].
% 16.00/16.14 2429 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 16.00/16.14 2430 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 16.00/16.14 2431 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(245,a,231,b)].
% 16.00/16.14 2432 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(246,a,231,b)].
% 16.00/16.14 2433 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1156,a,1113,a)].
% 16.00/16.14 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(2433,a,2421,b)].
% 16.00/16.14 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2433,a,2422,b)].
% 16.19/16.31 2434 class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1156,a,1138,a)].
% 16.19/16.31 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(2434,a,2421,b)].
% 16.19/16.31 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(2434,a,2422,b)].
% 16.19/16.31 2435 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1139,b)].
% 16.19/16.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) = c_times(C,B,A). [resolve(2435,a,2421,b)].
% 16.19/16.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A). [resolve(2435,a,2422,b)].
% 16.19/16.31 2436 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1140,b)].
% 16.19/16.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) = c_times(C,B,A). [resolve(2436,a,2421,b)].
% 16.19/16.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A). [resolve(2436,a,2422,b)].
% 16.19/16.31 2437 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1595,b,1566,a)].
% 16.19/16.31 2438 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1567,a)].
% 16.19/16.31 2439 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1568,a)].
% 16.19/16.31 2440 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1569,a)].
% 16.19/16.31 2441 -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(1595,b,1570,a)].
% 16.19/16.31 2442 -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(1595,b,1571,a)].
% 16.19/16.31 2443 -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(1595,b,1572,a)].
% 16.19/16.31 2444 -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(1595,b,1573,a)].
% 16.19/16.31 2445 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1574,a)].
% 16.19/16.31 2446 -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(1595,b,1575,a)].
% 16.19/16.31 2447 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1595,b,1576,a)].
% 16.19/16.31 2448 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1620,a)].
% 16.19/16.31 2449 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1658,b,1621,a)].
% 16.19/16.31 2450 -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(1658,b,1622,a)].
% 16.19/16.31 2451 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1623,a)].
% 16.19/16.31 2452 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1658,b,1624,a)].
% 16.19/16.31 2453 -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(1658,b,1625,a)].
% 16.19/16.31 2454 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1626,a)].
% 16.19/16.31 2455 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1658,b,1627,a)].
% 16.28/16.38 2456 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1658,b,1628,a)].
% 16.28/16.38 2457 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1658,b,1629,a)].
% 16.28/16.38 2458 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1658,b,1630,a)].
% 16.28/16.38 2459 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1658,b,1631,a)].
% 16.28/16.38 2460 -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(1658,b,1632,a)].
% 16.28/16.38 2461 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1658,b,1633,a)].
% 16.28/16.38 2462 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1658,b,1634,a)].
% 16.28/16.38 2463 -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(1658,b,1635,a)].
% 16.28/16.38 2464 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1658,b,1636,a)].
% 16.28/16.38 2465 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1658,b,1637,a)].
% 16.28/16.38 2466 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1658,b,1638,a)].
% 16.28/16.38 2467 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1658,b,1639,a)].
% 16.28/16.38 2468 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2042,a,2035,b)].
% 16.28/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2468,d,2415,b)].
% 16.28/16.38 2469 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2045,b,2035,b)].
% 16.28/16.38 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2469,b,2415,b)].
% 16.28/16.38 2470 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2046,b,2035,b)].
% 16.28/16.38 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2470,b,2415,b)].
% 16.28/16.38 2471 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2047,b,2035,b)].
% 16.28/16.38 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2471,b,2415,b)].
% 16.28/16.38 2472 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2048,b,2035,b)].
% 16.28/16.38 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2472,b,2415,b)].
% 16.28/16.38 2473 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2049,b,2035,b)].
% 16.28/16.38 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2473,b,2415,b)].
% 16.28/16.38 2474 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2050,b,2035,b)].
% 16.28/16.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2474,b,2415,b)].
% 16.28/16.38 2475 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2051,c,2035,b)].
% 16.28/16.38 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2475,c,2415,b)].
% 16.33/16.40 2476 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2052,c,2035,b)].
% 16.33/16.40 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2476,c,2415,b)].
% 16.33/16.40 2477 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2057,a,2035,b)].
% 16.33/16.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2477,b,2415,b)].
% 16.33/16.40 2478 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2058,a,2035,b)].
% 16.33/16.40 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2478,c,2415,b)].
% 16.33/16.40 2479 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2059,a,2035,b)].
% 16.33/16.40 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2479,b,2415,b)].
% 16.33/16.40 2480 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2060,a,2035,b)].
% 16.33/16.40 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2480,c,2415,b)].
% 16.33/16.40 2481 -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(2061,a,2035,b)].
% 16.33/16.40 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(2481,c,2415,b)].
% 16.33/16.40 2482 -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(2062,a,2035,b)].
% 16.33/16.40 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(2482,c,2415,b)].
% 16.33/16.40 2483 -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(2063,a,2035,b)].
% 16.33/16.40 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(2483,c,2415,b)].
% 16.33/16.40 2484 -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(2064,a,2035,b)].
% 16.33/16.40 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(2484,c,2415,b)].
% 16.33/16.40 2485 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2065,a,2035,b)].
% 16.33/16.40 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2485,c,2415,b)].
% 16.33/16.40 2486 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(2066,a,2035,b)].
% 16.33/16.40 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(2486,b,2415,b)].
% 16.33/16.40 2487 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2067,a,2035,b)].
% 16.33/16.42 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2487,b,2415,b)].
% 16.33/16.42 2488 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2068,a,2035,b)].
% 16.33/16.42 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(2488,c,2415,b)].
% 16.33/16.42 2489 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2069,a,2035,b)].
% 16.33/16.42 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(2489,c,2415,b)].
% 16.33/16.42 2490 -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(2070,a,2035,b)].
% 16.33/16.42 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(2490,d,2415,b)].
% 16.33/16.42 2491 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2071,a,2035,b)].
% 16.33/16.42 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(2491,c,2415,b)].
% 16.33/16.42 2492 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2072,a,2035,b)].
% 16.33/16.42 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(2492,c,2415,b)].
% 16.33/16.42 2493 -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(2073,a,2035,b)].
% 16.33/16.42 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(2493,d,2415,b)].
% 16.33/16.42 2494 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2074,a,2035,b)].
% 16.33/16.42 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2494,c,2415,b)].
% 16.33/16.42 2495 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2075,a,2035,b)].
% 16.33/16.42 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2495,c,2415,b)].
% 16.33/16.42 2496 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2076,a,2035,b)].
% 16.33/16.42 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2496,c,2415,b)].
% 16.33/16.42 2497 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2035,b)].
% 16.33/16.42 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2497,c,2415,b)].
% 16.33/16.42 2498 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2078,a,2035,b)].
% 16.33/16.42 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(2498,c,2415,b)].
% 16.33/16.42 2499 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2079,a,2035,b)].
% 16.33/16.42 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(2499,c,2415,b)].
% 16.33/16.42 2500 -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(2080,a,2035,b)].
% 16.59/16.68 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(2500,d,2415,b)].
% 16.59/16.68 2501 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2081,a,2035,b)].
% 16.59/16.68 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(2501,c,2415,b)].
% 16.59/16.68 2502 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2082,a,2035,b)].
% 16.59/16.68 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(2502,c,2415,b)].
% 16.59/16.68 2503 -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(2083,a,2035,b)].
% 16.59/16.68 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(2503,d,2415,b)].
% 16.59/16.68 2504 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2084,a,2035,b)].
% 16.59/16.68 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2504,c,2415,b)].
% 16.59/16.68 2505 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2085,a,2035,b)].
% 16.59/16.68 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2505,c,2415,b)].
% 16.59/16.68 2506 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2086,a,2035,b)].
% 16.59/16.68 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2506,c,2415,b)].
% 16.59/16.68 2507 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2087,a,2035,b)].
% 16.59/16.68 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2507,c,2415,b)].
% 16.59/16.68 2508 -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].
% 16.59/16.68 2509 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 16.59/16.68 2510 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 16.59/16.68 2511 -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].
% 16.59/16.68 2512 -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].
% 16.59/16.68 2513 -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].
% 16.59/16.68 2514 -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].
% 16.59/16.68 2515 -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].
% 16.59/16.68 2516 -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].
% 16.59/16.68 2517 -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].
% 16.79/16.92 2518 -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].
% 16.79/16.92 2519 -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)].
% 16.79/16.92 2520 -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)].
% 16.79/16.92 2521 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 16.79/16.92 2522 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 16.79/16.92 2523 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(108,a,105,b)].
% 16.79/16.92 2524 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(109,a,105,b)].
% 16.79/16.92 2525 -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(156,b,133,b)].
% 16.79/16.92 2526 -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(156,b,135,b)].
% 16.79/16.92 2527 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(167,a,156,b)].
% 16.79/16.92 2528 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(168,a,156,b)].
% 16.79/16.92 2529 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(203,b,195,b)].
% 16.79/16.92 2530 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(204,b,195,b)].
% 16.79/16.92 2531 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 16.79/16.92 2532 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 16.79/16.92 2533 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(245,a,228,b)].
% 16.79/16.92 2534 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(246,a,228,b)].
% 16.79/16.92 2535 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,286,a)].
% 16.79/16.92 2536 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,288,a)].
% 16.79/16.92 2537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(320,a,306,b)].
% 16.79/16.92 2538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(321,a,306,b)].
% 16.79/16.92 2539 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1154,a,1113,a)].
% 16.79/16.92 2540 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1154,a,1138,a)].
% 16.79/16.92 2541 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1154,a,1139,b)].
% 16.79/16.92 2542 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1154,a,1140,b)].
% 16.79/16.92 2543 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1592,b,1566,a)].
% 16.79/16.92 2544 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1592,b,1567,a)].
% 16.88/16.97 2545 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1592,b,1568,a)].
% 16.88/16.97 2546 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1592,b,1569,a)].
% 16.88/16.97 2547 -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(1592,b,1570,a)].
% 16.88/16.97 2548 -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(1592,b,1571,a)].
% 16.88/16.97 2549 -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(1592,b,1572,a)].
% 16.88/16.97 2550 -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(1592,b,1573,a)].
% 16.88/16.97 2551 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1592,b,1574,a)].
% 16.88/16.97 2552 -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(1592,b,1575,a)].
% 16.88/16.97 2553 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1592,b,1576,a)].
% 16.88/16.97 2554 -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(1655,b,1620,a)].
% 16.88/16.97 2555 -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(1655,b,1621,a)].
% 16.88/16.97 2556 -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(1655,b,1622,a)].
% 16.88/16.97 2557 -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(1655,b,1623,a)].
% 16.88/16.97 2558 -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(1655,b,1624,a)].
% 16.88/16.97 2559 -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(1655,b,1625,a)].
% 16.88/16.97 2560 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1655,b,1626,a)].
% 16.88/16.97 2561 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1655,b,1627,a)].
% 16.88/16.97 2562 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1655,b,1628,a)].
% 16.88/16.97 2563 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1655,b,1629,a)].
% 16.88/16.97 2564 -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(1655,b,1630,a)].
% 16.88/16.97 2565 -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(1655,b,1631,a)].
% 16.88/16.97 2566 -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(1655,b,1632,a)].
% 16.88/16.97 2567 -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(1655,b,1633,a)].
% 16.88/16.97 2568 -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(1655,b,1634,a)].
% 16.94/17.05 2569 -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(1655,b,1635,a)].
% 16.94/17.05 2570 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1655,b,1636,a)].
% 16.94/17.05 2571 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1655,b,1637,a)].
% 16.94/17.05 2572 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1655,b,1638,a)].
% 16.94/17.05 2573 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1655,b,1639,a)].
% 16.94/17.05 2574 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2042,a,2032,b)].
% 16.94/17.05 2575 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2047,b,2032,b)].
% 16.94/17.05 2576 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2048,b,2032,b)].
% 16.94/17.05 2577 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2049,b,2032,b)].
% 16.94/17.05 2578 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2050,b,2032,b)].
% 16.94/17.05 2579 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2051,c,2032,b)].
% 16.94/17.05 2580 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2052,c,2032,b)].
% 16.94/17.05 2581 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2057,a,2032,b)].
% 16.94/17.05 2582 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2058,a,2032,b)].
% 16.94/17.05 2583 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2059,a,2032,b)].
% 16.94/17.05 2584 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2060,a,2032,b)].
% 16.94/17.05 2585 -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(2061,a,2032,b)].
% 16.94/17.05 2586 -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(2062,a,2032,b)].
% 16.94/17.05 2587 -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(2063,a,2032,b)].
% 16.94/17.05 2588 -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(2064,a,2032,b)].
% 16.94/17.05 2589 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2065,a,2032,b)].
% 16.94/17.05 2590 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(2066,a,2032,b)].
% 16.94/17.05 2591 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2067,a,2032,b)].
% 16.94/17.05 2592 -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(2068,a,2032,b)].
% 17.01/17.08 2593 -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(2069,a,2032,b)].
% 17.01/17.08 2594 -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(2070,a,2032,b)].
% 17.01/17.08 2595 -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(2071,a,2032,b)].
% 17.01/17.08 2596 -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(2072,a,2032,b)].
% 17.01/17.08 2597 -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(2073,a,2032,b)].
% 17.01/17.08 2598 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2074,a,2032,b)].
% 17.01/17.08 2599 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2075,a,2032,b)].
% 17.01/17.08 2600 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2076,a,2032,b)].
% 17.01/17.08 2601 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2032,b)].
% 17.01/17.08 2602 -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(2078,a,2032,b)].
% 17.01/17.08 2603 -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(2079,a,2032,b)].
% 17.01/17.08 2604 -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(2080,a,2032,b)].
% 17.01/17.08 2605 -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(2081,a,2032,b)].
% 17.01/17.08 2606 -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(2082,a,2032,b)].
% 17.01/17.08 2607 -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(2083,a,2032,b)].
% 17.01/17.08 2608 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2084,a,2032,b)].
% 17.01/17.08 2609 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2085,a,2032,b)].
% 17.01/17.08 2610 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2086,a,2032,b)].
% 17.01/17.08 2611 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2087,a,2032,b)].
% 17.01/17.08 2612 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2115,a,2096,b)].
% 17.01/17.08 2613 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2116,a,2096,b)].
% 17.01/17.08 2614 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2117,c,2096,b)].
% 17.01/17.08 2615 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2118,c,2096,b)].
% 17.01/17.08 2616 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2119,b,2096,b)].
% 17.01/17.08 2617 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2120,a,2096,b)].
% 17.01/17.08 2618 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2156,d,2096,b)].
% 17.05/17.12 2619 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2157,b,2096,b)].
% 17.05/17.12 2620 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2158,b,2096,b)].
% 17.05/17.12 2621 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2159,b,2096,b)].
% 17.05/17.12 2622 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2160,b,2096,b)].
% 17.05/17.12 2623 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,c,2096,b)].
% 17.05/17.12 2624 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,c,2096,b)].
% 17.05/17.12 2625 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2163,b,2096,b)].
% 17.05/17.12 2626 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2164,c,2096,b)].
% 17.05/17.12 2627 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2165,b,2096,b)].
% 17.05/17.12 2628 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2166,c,2096,b)].
% 17.05/17.12 2629 -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(2167,c,2096,b)].
% 17.05/17.12 2630 -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(2168,c,2096,b)].
% 17.05/17.12 2631 -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(2169,c,2096,b)].
% 17.05/17.12 2632 -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(2170,c,2096,b)].
% 17.05/17.12 2633 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2171,c,2096,b)].
% 17.05/17.12 2634 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(2172,b,2096,b)].
% 17.05/17.12 2635 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2173,b,2096,b)].
% 17.05/17.12 2636 -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(2174,c,2096,b)].
% 17.05/17.12 2637 -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(2175,c,2096,b)].
% 17.05/17.12 2638 -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(2176,d,2096,b)].
% 17.05/17.12 2639 -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(2177,c,2096,b)].
% 17.05/17.12 2640 -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(2178,c,2096,b)].
% 17.05/17.12 2641 -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(2179,d,2096,b)].
% 17.05/17.12 2642 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2180,c,2096,b)].
% 17.25/17.34 2643 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2181,c,2096,b)].
% 17.25/17.34 2644 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2182,c,2096,b)].
% 17.25/17.34 2645 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2183,c,2096,b)].
% 17.25/17.34 2646 -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(2184,c,2096,b)].
% 17.25/17.34 2647 -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(2185,c,2096,b)].
% 17.25/17.34 2648 -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(2186,d,2096,b)].
% 17.25/17.34 2649 -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(2187,c,2096,b)].
% 17.25/17.34 2650 -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(2188,c,2096,b)].
% 17.25/17.34 2651 -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(2189,d,2096,b)].
% 17.25/17.34 2652 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2190,c,2096,b)].
% 17.25/17.34 2653 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2191,c,2096,b)].
% 17.25/17.34 2654 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2192,c,2096,b)].
% 17.25/17.34 2655 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2193,c,2096,b)].
% 17.25/17.34 2656 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2421,b,2414,b)].
% 17.25/17.34 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2656,b,2511,b)].
% 17.25/17.34 2657 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2422,b,2414,b)].
% 17.25/17.34 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2657,b,2511,b)].
% 17.25/17.34 2658 -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].
% 17.25/17.34 2659 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 17.25/17.34 2660 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 17.25/17.34 2661 -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].
% 17.25/17.34 2662 -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].
% 17.25/17.34 2663 -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].
% 17.25/17.34 2664 -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].
% 17.25/17.34 2665 -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].
% 17.32/17.41 2666 -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].
% 17.32/17.41 2667 -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].
% 17.32/17.41 2668 -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)].
% 17.32/17.41 2669 -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)].
% 17.32/17.41 2670 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 17.32/17.41 2671 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 17.32/17.41 2672 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(108,a,101,b)].
% 17.32/17.41 2673 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(109,a,101,b)].
% 17.32/17.41 2674 -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(150,b,133,b)].
% 17.32/17.41 2675 -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(150,b,135,b)].
% 17.32/17.41 2676 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(167,a,150,b)].
% 17.32/17.41 2677 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(168,a,150,b)].
% 17.32/17.41 2678 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(203,b,191,b)].
% 17.32/17.41 2679 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(204,b,191,b)].
% 17.32/17.41 2680 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 17.32/17.41 2681 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 17.32/17.41 2682 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(245,a,222,b)].
% 17.32/17.41 2683 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(246,a,222,b)].
% 17.32/17.41 2684 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,286,a)].
% 17.32/17.41 2685 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,288,a)].
% 17.32/17.41 2686 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(320,a,300,b)].
% 17.32/17.41 2687 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(321,a,300,b)].
% 17.32/17.41 2688 -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(887,b,822,a)].
% 17.32/17.41 2689 -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(887,b,823,a)].
% 17.32/17.41 2690 -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(887,b,824,a)].
% 17.32/17.42 2691 -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(887,b,825,a)].
% 17.32/17.42 2692 -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(887,b,826,a)].
% 17.32/17.42 2693 -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(887,b,827,a)].
% 17.32/17.42 2694 -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(887,b,828,a)].
% 17.32/17.42 2695 -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(887,b,829,a)].
% 17.32/17.42 2696 -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(887,b,830,a)].
% 17.32/17.42 2697 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(887,b,831,a)].
% 17.32/17.42 2698 -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(887,b,832,a)].
% 17.32/17.42 2699 -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(887,b,833,a)].
% 17.32/17.42 2700 -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(887,b,834,a)].
% 17.32/17.42 2701 -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(887,b,835,a)].
% 17.32/17.42 2702 -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(887,b,836,a)].
% 17.32/17.42 2703 -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(887,b,837,a)].
% 17.32/17.42 2704 -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(887,b,838,a)].
% 17.32/17.42 2705 -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(887,b,839,a)].
% 17.32/17.42 2706 -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(887,b,840,a)].
% 17.32/17.42 2707 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(887,b,841,a)].
% 17.32/17.42 2708 -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(887,b,842,a)].
% 17.32/17.42 2709 -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(887,b,843,a)].
% 17.32/17.42 2710 -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(887,b,844,a)].
% 17.32/17.42 2711 -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(887,b,845,b)].
% 17.32/17.42 2712 -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(887,b,846,b)].
% 17.32/17.42 2713 -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(887,b,847,a)].
% 17.32/17.42 2714 -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(887,b,848,a)].
% 17.32/17.42 2715 -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(887,b,849,a)].
% 17.32/17.42 2716 -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(887,b,850,a)].
% 17.32/17.42 2717 -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(887,b,851,a)].
% 17.32/17.42 2718 -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(887,b,852,a)].
% 17.32/17.42 2719 -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(887,b,853,a)].
% 17.32/17.42 2720 -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(887,b,854,a)].
% 17.32/17.42 2721 -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(887,b,855,a)].
% 17.32/17.42 2722 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(887,b,856,a)].
% 17.32/17.42 2723 -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(887,b,857,a)].
% 17.32/17.42 2724 -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(887,b,858,a)].
% 17.32/17.42 2725 -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(887,b,859,a)].
% 17.32/17.42 2726 -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(887,b,860,a)].
% 17.32/17.42 2727 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(887,b,861,a)].
% 17.32/17.42 2728 -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(887,b,862,a)].
% 17.32/17.42 2729 -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(887,b,863,a)].
% 17.32/17.42 2730 -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(887,b,864,a)].
% 17.32/17.42 2731 -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(887,b,865,a)].
% 17.32/17.42 2732 -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(887,b,866,a)].
% 17.32/17.42 2733 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(887,b,867,a)].
% 17.48/17.55 2734 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(887,b,868,a)].
% 17.48/17.55 2735 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(887,b,869,a)].
% 17.48/17.55 2736 -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(887,b,870,a)].
% 17.48/17.55 2737 -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(887,b,871,a)].
% 17.48/17.55 2738 -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(887,b,872,a)].
% 17.48/17.55 2739 -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(887,b,873,a)].
% 17.48/17.55 2740 -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(887,b,874,a)].
% 17.48/17.55 2741 -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(887,b,875,a)].
% 17.48/17.55 2742 -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(887,b,876,a)].
% 17.48/17.55 2743 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(887,b,877,a)].
% 17.48/17.55 2744 -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(887,b,878,a)].
% 17.48/17.55 2745 -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(887,b,879,a)].
% 17.48/17.55 2746 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1079,b,1068,a)].
% 17.48/17.55 2747 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1102,b,1091,a)].
% 17.48/17.55 2748 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1148,a,1113,a)].
% 17.48/17.55 2749 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1148,a,1138,a)].
% 17.48/17.55 2750 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1148,a,1139,b)].
% 17.48/17.55 2751 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1148,a,1140,b)].
% 17.48/17.55 2752 -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(1483,b,1462,a)].
% 17.48/17.55 2753 -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(1483,b,1463,a)].
% 17.48/17.55 2754 -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(1483,b,1464,a)].
% 17.48/17.55 2755 -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(1483,b,1465,a)].
% 17.48/17.55 2756 -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(1483,b,1466,a)].
% 17.48/17.55 2757 -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(1483,b,1467,a)].
% 17.55/17.62 2758 -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(1483,b,1468,a)].
% 17.55/17.62 2759 -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(1483,b,1469,a)].
% 17.55/17.62 2760 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1588,b,1566,a)].
% 17.55/17.62 2761 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1588,b,1567,a)].
% 17.55/17.62 2762 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1588,b,1568,a)].
% 17.55/17.62 2763 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1588,b,1569,a)].
% 17.55/17.62 2764 -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(1588,b,1570,a)].
% 17.55/17.62 2765 -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(1588,b,1571,a)].
% 17.55/17.62 2766 -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(1588,b,1572,a)].
% 17.55/17.62 2767 -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(1588,b,1573,a)].
% 17.55/17.62 2768 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1588,b,1574,a)].
% 17.55/17.62 2769 -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(1588,b,1575,a)].
% 17.55/17.62 2770 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1588,b,1576,a)].
% 17.55/17.62 2771 -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(1651,b,1620,a)].
% 17.55/17.62 2772 -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(1651,b,1621,a)].
% 17.55/17.62 2773 -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(1651,b,1622,a)].
% 17.55/17.62 2774 -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(1651,b,1623,a)].
% 17.55/17.62 2775 -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(1651,b,1624,a)].
% 17.55/17.62 2776 -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(1651,b,1625,a)].
% 17.55/17.62 2777 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1651,b,1626,a)].
% 17.55/17.62 2778 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1651,b,1627,a)].
% 17.55/17.62 2779 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1651,b,1628,a)].
% 17.55/17.62 2780 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1651,b,1629,a)].
% 17.55/17.62 2781 -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(1651,b,1630,a)].
% 17.55/17.62 2782 -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(1651,b,1631,a)].
% 17.62/17.68 2783 -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(1651,b,1632,a)].
% 17.62/17.68 2784 -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(1651,b,1633,a)].
% 17.62/17.68 2785 -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(1651,b,1634,a)].
% 17.62/17.68 2786 -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(1651,b,1635,a)].
% 17.62/17.68 2787 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1651,b,1636,a)].
% 17.62/17.68 2788 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1651,b,1637,a)].
% 17.62/17.68 2789 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1651,b,1638,a)].
% 17.62/17.68 2790 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1651,b,1639,a)].
% 17.62/17.68 2791 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1826,a,1817,b)].
% 17.62/17.68 2792 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1827,a,1817,b)].
% 17.62/17.68 2793 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1958,c,1878,b)].
% 17.62/17.68 2794 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1959,c,1878,b)].
% 17.62/17.68 2795 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1993,b,1878,b)].
% 17.62/17.68 2796 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1994,c,1878,b)].
% 17.62/17.68 2797 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1995,b,1878,b)].
% 17.62/17.68 2798 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1996,c,1878,b)].
% 17.62/17.68 2799 -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(1997,c,1878,b)].
% 17.62/17.68 2800 -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(1998,c,1878,b)].
% 17.62/17.68 2801 -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(1999,c,1878,b)].
% 17.62/17.68 2802 -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(2000,c,1878,b)].
% 17.62/17.68 2803 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2001,c,1878,b)].
% 17.62/17.68 2804 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(2002,b,1878,b)].
% 17.62/17.68 2805 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2003,b,1878,b)].
% 17.62/17.68 2806 -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(2004,c,1878,b)].
% 17.62/17.68 2807 -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(2005,c,1878,b)].
% 17.62/17.70 2808 -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(2006,d,1878,b)].
% 17.62/17.70 2809 -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(2007,c,1878,b)].
% 17.62/17.70 2810 -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(2008,c,1878,b)].
% 17.62/17.70 2811 -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(2009,d,1878,b)].
% 17.62/17.70 2812 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2010,c,1878,b)].
% 17.62/17.70 2813 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2011,c,1878,b)].
% 17.62/17.70 2814 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2012,c,1878,b)].
% 17.62/17.70 2815 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2013,c,1878,b)].
% 17.62/17.70 2816 -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(2014,c,1878,b)].
% 17.62/17.70 2817 -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(2015,c,1878,b)].
% 17.62/17.70 2818 -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(2016,d,1878,b)].
% 17.62/17.70 2819 -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(2017,c,1878,b)].
% 17.62/17.70 2820 -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(2018,c,1878,b)].
% 17.62/17.70 2821 -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(2019,d,1878,b)].
% 17.62/17.70 2822 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2020,c,1878,b)].
% 17.62/17.70 2823 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2021,c,1878,b)].
% 17.62/17.70 2824 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2022,c,1878,b)].
% 17.62/17.70 2825 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2023,c,1878,b)].
% 17.62/17.70 2826 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2042,a,2028,b)].
% 17.62/17.70 2827 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2047,b,2028,b)].
% 17.62/17.70 2828 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2048,b,2028,b)].
% 17.62/17.70 2829 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2049,b,2028,b)].
% 17.62/17.70 2830 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2050,b,2028,b)].
% 17.62/17.70 2831 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2051,c,2028,b)].
% 17.62/17.70 2832 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2052,c,2028,b)].
% 17.62/17.75 2833 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2115,a,2092,b)].
% 17.62/17.75 2834 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2116,a,2092,b)].
% 17.62/17.75 2835 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2156,d,2092,b)].
% 17.62/17.75 2836 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2157,b,2092,b)].
% 17.62/17.75 2837 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2158,b,2092,b)].
% 17.62/17.75 2838 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2159,b,2092,b)].
% 17.62/17.75 2839 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2160,b,2092,b)].
% 17.62/17.75 2840 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2161,c,2092,b)].
% 17.62/17.75 2841 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2162,c,2092,b)].
% 17.62/17.75 2842 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2163,b,2092,b)].
% 17.62/17.75 2843 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2164,c,2092,b)].
% 17.62/17.75 2844 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2165,b,2092,b)].
% 17.62/17.75 2845 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2166,c,2092,b)].
% 17.62/17.75 2846 -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(2167,c,2092,b)].
% 17.62/17.75 2847 -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(2168,c,2092,b)].
% 17.62/17.75 2848 -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(2169,c,2092,b)].
% 17.62/17.75 2849 -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(2170,c,2092,b)].
% 17.62/17.75 2850 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2171,c,2092,b)].
% 17.62/17.75 2851 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(2172,b,2092,b)].
% 17.62/17.75 2852 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2173,b,2092,b)].
% 17.62/17.75 2853 -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(2174,c,2092,b)].
% 17.62/17.75 2854 -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(2175,c,2092,b)].
% 17.62/17.75 2855 -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(2176,d,2092,b)].
% 17.62/17.75 2856 -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(2177,c,2092,b)].
% 17.71/17.77 2857 -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(2178,c,2092,b)].
% 17.71/17.77 2858 -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(2179,d,2092,b)].
% 17.71/17.77 2859 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2180,c,2092,b)].
% 17.71/17.77 2860 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2181,c,2092,b)].
% 17.71/17.77 2861 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2182,c,2092,b)].
% 17.71/17.77 2862 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2183,c,2092,b)].
% 17.71/17.77 2863 -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(2184,c,2092,b)].
% 17.71/17.77 2864 -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(2185,c,2092,b)].
% 17.71/17.77 2865 -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(2186,d,2092,b)].
% 17.71/17.77 2866 -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(2187,c,2092,b)].
% 17.71/17.77 2867 -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(2188,c,2092,b)].
% 17.71/17.77 2868 -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(2189,d,2092,b)].
% 17.71/17.77 2869 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2190,c,2092,b)].
% 17.71/17.77 2870 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2191,c,2092,b)].
% 17.71/17.77 2871 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2192,c,2092,b)].
% 17.71/17.77 2872 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2193,c,2092,b)].
% 17.71/17.77 2873 -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(2223,a,2197,b)].
% 17.71/17.77 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(2873,e,2659,a)].
% 17.71/17.77 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(2873,e,2660,a)].
% 17.71/17.77 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(2873,e,2666,b)].
% 17.71/17.77 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(2873,e,2667,b)].
% 17.71/17.77 2874 -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(2224,a,2197,b)].
% 17.71/17.77 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(2874,d,2659,a)].
% 17.71/17.77 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(2874,d,2660,a)].
% 17.71/17.77 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(2874,d,2666,b)].
% 17.71/17.77 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(2874,d,2667,b)].
% 17.71/17.77 2875 -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(2225,a,2197,b)].
% 17.71/17.77 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(2875,d,2659,a)].
% 17.71/17.77 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(2875,d,2660,a)].
% 17.71/17.77 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(2875,d,2666,b)].
% 17.71/17.77 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(2875,d,2667,b)].
% 17.71/17.77 2876 -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(2226,a,2197,b)].
% 17.71/17.77 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(2876,f,2659,a)].
% 17.71/17.77 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(2876,f,2660,a)].
% 17.71/17.77 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(2876,f,2666,b)].
% 17.71/17.77 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(2876,f,2667,b)].
% 17.71/17.77 2877 -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(2227,a,2197,b)].
% 17.71/17.77 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(2877,e,2659,a)].
% 17.71/17.77 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(2877,e,2660,a)].
% 17.71/17.77 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(2877,e,2666,b)].
% 17.71/17.77 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(2877,e,2667,b)].
% 17.71/17.77 2878 -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(2228,a,2197,b)].
% 17.71/17.77 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(2878,e,2659,a)].
% 17.71/17.78 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(2878,e,2660,a)].
% 17.71/17.78 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(2878,e,2666,b)].
% 17.71/17.78 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(2878,e,2667,b)].
% 17.71/17.78 2879 -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(2229,a,2197,b)].
% 17.71/17.78 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(2879,f,2659,a)].
% 17.71/17.78 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(2879,f,2660,a)].
% 17.71/17.78 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(2879,f,2666,b)].
% 17.71/17.78 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(2879,f,2667,b)].
% 17.71/17.78 2880 -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(2230,a,2197,b)].
% 17.71/17.78 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(2880,e,2659,a)].
% 17.71/17.78 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(2880,e,2660,a)].
% 17.71/17.78 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(2880,e,2666,b)].
% 17.71/17.78 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(2880,e,2667,b)].
% 17.71/17.78 2881 -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(2231,a,2197,b)].
% 17.71/17.78 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(2881,e,2659,a)].
% 17.71/17.78 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(2881,e,2660,a)].
% 17.71/17.78 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(2881,e,2666,b)].
% 17.71/17.78 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(2881,e,2667,b)].
% 17.71/17.78 2882 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2232,a,2197,b)].
% 17.71/17.78 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2882,b,2659,a)].
% 17.71/17.78 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2882,b,2660,a)].
% 17.71/17.78 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2882,b,2666,b)].
% 17.71/17.78 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2882,b,2667,b)].
% 17.71/17.78 2883 -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(2233,a,2197,b)].
% 17.71/17.78 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(2883,f,2659,a)].
% 17.71/17.78 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(2883,f,2660,a)].
% 17.71/17.78 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(2883,f,2666,b)].
% 17.71/17.78 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(2883,f,2667,b)].
% 17.71/17.78 2884 -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(2234,a,2197,b)].
% 17.71/17.78 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(2884,e,2659,a)].
% 17.71/17.78 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(2884,e,2660,a)].
% 17.71/17.78 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(2884,e,2666,b)].
% 17.71/17.78 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(2884,e,2667,b)].
% 17.71/17.78 2885 -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(2235,a,2197,b)].
% 17.71/17.78 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(2885,e,2659,a)].
% 17.71/17.78 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(2885,e,2660,a)].
% 17.71/17.78 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(2885,e,2666,b)].
% 17.71/17.78 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(2885,e,2667,b)].
% 17.71/17.78 2886 -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(2236,a,2197,b)].
% 17.71/17.78 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(2886,f,2659,a)].
% 17.71/17.78 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(2886,f,2660,a)].
% 17.71/17.78 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(2886,f,2666,b)].
% 17.71/17.78 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(2886,f,2667,b)].
% 17.71/17.78 2887 -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(2237,a,2197,b)].
% 17.71/17.78 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(2887,e,2659,a)].
% 17.71/17.78 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(2887,e,2660,a)].
% 17.71/17.78 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(2887,e,2666,b)].
% 17.71/17.78 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(2887,e,2667,b)].
% 17.71/17.78 2888 -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(2238,a,2197,b)].
% 17.71/17.78 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(2888,e,2659,a)].
% 17.71/17.78 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(2888,e,2660,a)].
% 17.71/17.78 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(2888,e,2666,b)].
% 17.71/17.78 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(2888,e,2667,b)].
% 17.71/17.78 2889 -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(2239,a,2197,b)].
% 17.71/17.78 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(2889,d,2659,a)].
% 17.71/17.78 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(2889,d,2660,a)].
% 17.71/17.78 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(2889,d,2666,b)].
% 17.71/17.79 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(2889,d,2667,b)].
% 17.71/17.79 2890 -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(2240,a,2197,b)].
% 17.71/17.79 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(2890,d,2659,a)].
% 17.71/17.79 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(2890,d,2660,a)].
% 17.71/17.79 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(2890,d,2666,b)].
% 17.71/17.79 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(2890,d,2667,b)].
% 17.71/17.79 2891 -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(2241,a,2197,b)].
% 17.71/17.79 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2891,e,2659,a)].
% 17.71/17.79 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(2891,e,2660,a)].
% 17.71/17.79 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(2891,e,2666,b)].
% 17.71/17.79 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(2891,e,2667,b)].
% 17.71/17.79 2892 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2242,a,2197,b)].
% 17.71/17.79 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2892,b,2659,a)].
% 17.71/17.79 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2892,b,2660,a)].
% 17.71/17.79 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2892,b,2666,b)].
% 17.71/17.79 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2892,b,2667,b)].
% 17.71/17.79 2893 -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(2243,a,2197,b)].
% 17.71/17.79 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(2893,d,2659,a)].
% 17.71/17.79 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(2893,d,2660,a)].
% 17.71/17.79 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(2893,d,2666,b)].
% 17.71/17.79 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(2893,d,2667,b)].
% 17.71/17.79 2894 -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(2244,a,2197,b)].
% 17.75/17.79 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(2894,e,2659,a)].
% 17.75/17.79 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(2894,e,2660,a)].
% 17.75/17.79 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(2894,e,2666,b)].
% 17.75/17.79 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(2894,e,2667,b)].
% 17.75/17.79 2895 -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(2245,a,2197,b)].
% 17.75/17.79 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(2895,e,2659,a)].
% 17.75/17.79 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(2895,e,2660,a)].
% 17.75/17.79 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(2895,e,2666,b)].
% 17.75/17.79 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(2895,e,2667,b)].
% 17.75/17.79 2896 -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(2246,a,2197,b)].
% 17.75/17.79 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(2896,d,2659,a)].
% 17.75/17.79 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(2896,d,2660,a)].
% 17.75/17.79 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(2896,d,2666,b)].
% 17.75/17.79 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(2896,d,2667,b)].
% 17.75/17.79 2897 -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(2247,a,2197,b)].
% 17.75/17.79 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(2897,d,2659,a)].
% 17.75/17.79 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(2897,d,2660,a)].
% 17.75/17.79 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(2897,d,2666,b)].
% 17.75/17.79 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(2897,d,2667,b)].
% 17.75/17.79 2898 -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(2248,a,2197,b)].
% 17.75/17.79 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2898,c,2659,a)].
% 17.75/17.79 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2898,c,2660,a)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2898,c,2666,b)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2898,c,2667,b)].
% 17.75/17.80 2899 -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(2249,a,2197,b)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2899,c,2659,a)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2899,c,2660,a)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2899,c,2666,b)].
% 17.75/17.80 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2899,c,2667,b)].
% 17.75/17.80 2900 -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(2250,a,2197,b)].
% 17.75/17.80 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2900,d,2659,a)].
% 17.75/17.80 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2900,d,2660,a)].
% 17.75/17.80 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2900,d,2666,b)].
% 17.75/17.80 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2900,d,2667,b)].
% 17.75/17.80 2901 -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(2251,a,2197,b)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2901,c,2659,a)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2901,c,2660,a)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2901,c,2666,b)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2901,c,2667,b)].
% 17.75/17.80 2902 -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(2252,a,2197,b)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2902,c,2659,a)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2902,c,2660,a)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2902,c,2666,b)].
% 17.75/17.80 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2902,c,2667,b)].
% 17.75/17.80 2903 -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(2253,a,2197,b)].
% 17.75/17.80 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(2903,d,2659,a)].
% 17.75/17.80 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(2903,d,2660,a)].
% 17.75/17.80 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(2903,d,2666,b)].
% 17.75/17.80 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(2903,d,2667,b)].
% 17.75/17.80 2904 -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(2254,a,2197,b)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2904,c,2659,a)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2904,c,2660,a)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2904,c,2666,b)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2904,c,2667,b)].
% 17.75/17.80 2905 -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(2255,a,2197,b)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2905,c,2659,a)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2905,c,2660,a)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2905,c,2666,b)].
% 17.75/17.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2905,c,2667,b)].
% 17.75/17.80 2906 -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(2256,a,2197,b)].
% 17.75/17.80 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(2906,d,2659,a)].
% 17.75/17.80 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(2906,d,2660,a)].
% 17.75/17.80 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(2906,d,2666,b)].
% 17.75/17.80 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(2906,d,2667,b)].
% 17.75/17.80 2907 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2257,a,2197,b)].
% 17.75/17.80 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2907,b,2659,a)].
% 17.75/17.80 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2907,b,2660,a)].
% 17.75/17.80 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2907,b,2666,b)].
% 17.75/17.80 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2907,b,2667,b)].
% 17.75/17.80 2908 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(2258,a,2197,b)].
% 17.75/17.80 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(2908,b,2659,a)].
% 17.75/17.80 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2908,b,2660,a)].
% 17.75/17.80 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(2908,b,2666,b)].
% 17.75/17.80 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(2908,b,2667,b)].
% 17.75/17.80 2909 -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(2259,a,2197,b)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2909,c,2659,a)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2909,c,2660,a)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2909,c,2666,b)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2909,c,2667,b)].
% 17.75/17.80 2910 -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(2260,a,2197,b)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2910,c,2659,a)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2910,c,2660,a)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2910,c,2666,b)].
% 17.75/17.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2910,c,2667,b)].
% 17.75/17.80 2911 -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(2261,a,2197,b)].
% 17.75/17.80 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(2911,d,2659,a)].
% 17.75/17.80 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(2911,d,2660,a)].
% 17.75/17.80 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(2911,d,2666,b)].
% 17.75/17.80 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(2911,d,2667,b)].
% 17.75/17.80 2912 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2262,a,2197,b)].
% 17.75/17.80 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2912,b,2659,a)].
% 17.75/17.80 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2912,b,2660,a)].
% 17.75/17.80 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2912,b,2666,b)].
% 17.75/17.80 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2912,b,2667,b)].
% 17.75/17.80 2913 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(2263,a,2197,b)].
% 17.75/17.80 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(2913,b,2659,a)].
% 17.75/17.80 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(2913,b,2660,a)].
% 17.75/17.80 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(2913,b,2666,b)].
% 17.75/17.80 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(2913,b,2667,b)].
% 17.75/17.80 2914 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(2264,a,2197,b)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(2914,b,2659,a)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2914,b,2660,a)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2914,b,2666,b)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2914,b,2667,b)].
% 17.75/17.80 2915 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(2265,a,2197,b)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(2915,b,2659,a)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2915,b,2660,a)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2915,b,2666,b)].
% 17.75/17.80 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2915,b,2667,b)].
% 17.75/17.81 2916 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(2266,a,2197,b)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(2916,b,2659,a)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2916,b,2660,a)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2916,b,2666,b)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2916,b,2667,b)].
% 17.75/17.81 2917 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(2267,a,2197,b)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(2917,b,2659,a)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2917,b,2660,a)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2917,b,2666,b)].
% 17.75/17.81 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2917,b,2667,b)].
% 17.75/17.81 2918 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2268,a,2197,b)].
% 17.75/17.81 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2918,c,2659,a)].
% 17.75/17.81 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2918,c,2660,a)].
% 17.75/17.81 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2918,c,2666,b)].
% 17.75/17.81 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2918,c,2667,b)].
% 17.75/17.81 2919 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2269,a,2197,b)].
% 17.75/17.81 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2919,c,2659,a)].
% 17.75/17.81 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2919,c,2660,a)].
% 17.75/17.81 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2919,c,2666,b)].
% 17.75/17.81 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2919,c,2667,b)].
% 17.75/17.81 2920 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2270,a,2197,b)].
% 17.75/17.81 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2920,c,2659,a)].
% 17.75/17.81 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2920,c,2660,a)].
% 17.75/17.81 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2920,c,2666,b)].
% 17.75/17.81 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2920,c,2667,b)].
% 17.75/17.81 2921 -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(2271,a,2197,b)].
% 17.75/17.81 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(2921,c,2659,a)].
% 17.75/17.81 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(2921,c,2660,a)].
% 17.75/17.81 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(2921,c,2666,b)].
% 17.75/17.81 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(2921,c,2667,b)].
% 17.75/17.81 2922 -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(2272,a,2197,b)].
% 17.75/17.81 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(2922,c,2659,a)].
% 17.75/17.81 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(2922,c,2660,a)].
% 17.75/17.81 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(2922,c,2666,b)].
% 17.75/17.81 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(2922,c,2667,b)].
% 17.75/17.81 2923 -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(2273,a,2197,b)].
% 17.75/17.81 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(2923,c,2659,a)].
% 17.75/17.81 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(2923,c,2660,a)].
% 17.75/17.81 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(2923,c,2666,b)].
% 17.75/17.81 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(2923,c,2667,b)].
% 17.75/17.81 2924 -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(2274,a,2197,b)].
% 17.75/17.81 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(2924,d,2659,a)].
% 17.75/17.81 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(2924,d,2660,a)].
% 17.75/17.81 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(2924,d,2666,b)].
% 17.75/17.81 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(2924,d,2667,b)].
% 17.75/17.81 2925 -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(2275,a,2197,b)].
% 17.75/17.82 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(2925,d,2659,a)].
% 17.75/17.82 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(2925,d,2660,a)].
% 17.75/17.82 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(2925,d,2666,b)].
% 17.75/17.82 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(2925,d,2667,b)].
% 17.75/17.82 2926 -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(2276,a,2197,b)].
% 17.75/17.82 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(2926,c,2659,a)].
% 17.75/17.82 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(2926,c,2660,a)].
% 17.75/17.82 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(2926,c,2666,b)].
% 17.75/17.82 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(2926,c,2667,b)].
% 17.75/17.82 2927 -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(2277,a,2197,b)].
% 17.75/17.82 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(2927,d,2659,a)].
% 17.75/17.82 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(2927,d,2660,a)].
% 17.75/17.82 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(2927,d,2666,b)].
% 17.75/17.82 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(2927,d,2667,b)].
% 17.75/17.82 2928 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2278,a,2197,b)].
% 17.75/17.82 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2928,c,2659,a)].
% 17.75/17.82 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2928,c,2660,a)].
% 17.75/17.82 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2928,c,2666,b)].
% 17.75/17.82 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2928,c,2667,b)].
% 17.75/17.82 2929 -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(2279,a,2197,b)].
% 17.75/17.82 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(2929,c,2659,a)].
% 17.75/17.82 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(2929,c,2660,a)].
% 17.75/17.82 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(2929,c,2666,b)].
% 17.75/17.82 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(2929,c,2667,b)].
% 17.75/17.82 2930 -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(2280,a,2197,b)].
% 17.75/17.82 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(2930,c,2659,a)].
% 17.75/17.82 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(2930,c,2660,a)].
% 17.75/17.82 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(2930,c,2666,b)].
% 17.75/17.82 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(2930,c,2667,b)].
% 17.75/17.82 2931 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2281,a,2197,b)].
% 17.75/17.82 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2931,b,2659,a)].
% 17.75/17.82 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2931,b,2660,a)].
% 17.75/17.82 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2931,b,2666,b)].
% 17.75/17.82 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2931,b,2667,b)].
% 17.75/17.82 2932 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2197,b)].
% 17.75/17.82 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2932,b,2659,a)].
% 17.75/17.82 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2932,b,2660,a)].
% 17.75/17.82 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2932,b,2666,b)].
% 17.75/17.82 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2932,b,2667,b)].
% 17.75/17.82 2933 -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(2287,a,2197,b)].
% 17.75/17.82 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(2933,c,2659,a)].
% 17.75/17.82 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2933,c,2660,a)].
% 17.75/17.82 2934 -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(2288,a,2197,b)].
% 17.75/17.82 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(2934,c,2659,a)].
% 17.75/17.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2934,c,2660,a)].
% 17.75/17.82 2935 -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(2289,a,2197,b)].
% 17.75/17.82 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(2935,c,2659,a)].
% 17.75/17.82 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2935,c,2660,a)].
% 17.75/17.82 2936 -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(2290,a,2197,b)].
% 17.75/17.83 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(2936,c,2659,a)].
% 17.75/17.83 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2936,c,2660,a)].
% 17.75/17.83 2937 -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(2291,a,2197,b)].
% 17.75/17.83 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(2937,c,2659,a)].
% 17.75/17.83 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(2937,c,2660,a)].
% 17.75/17.83 2938 -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(2292,a,2197,b)].
% 17.75/17.83 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(2938,c,2659,a)].
% 17.75/17.83 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2938,c,2660,a)].
% 17.75/17.83 2939 -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(2293,a,2197,b)].
% 17.75/17.83 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(2939,c,2659,a)].
% 17.75/17.83 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2939,c,2660,a)].
% 17.75/17.83 2940 -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(2294,a,2197,b)].
% 17.75/17.83 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(2940,c,2659,a)].
% 17.75/17.83 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2940,c,2660,a)].
% 17.75/17.83 2941 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2326,c,2197,b)].
% 17.75/17.83 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2941,c,2659,a)].
% 17.75/17.83 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2941,c,2660,a)].
% 17.75/17.83 2942 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2327,c,2197,b)].
% 17.75/17.83 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2942,c,2659,a)].
% 17.75/17.83 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2942,c,2660,a)].
% 17.75/17.83 2943 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2328,b,2197,b)].
% 17.75/17.83 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2943,b,2659,a)].
% 17.75/17.83 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2943,b,2660,a)].
% 17.75/17.83 2944 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2329,b,2197,b)].
% 17.75/17.83 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2944,b,2659,a)].
% 17.75/17.83 Derived: class_HOL_Oplus(tc_nat). [resolve(2944,b,2660,a)].
% 17.75/17.83 2945 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2368,b,2197,b)].
% 17.75/17.83 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2945,b,2659,a)].
% 17.75/17.83 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2945,b,2660,a)].
% 17.75/17.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2945,b,2666,b)].
% 17.75/17.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2945,b,2667,b)].
% 17.75/17.83 2946 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2369,b,2197,b)].
% 17.75/17.83 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2946,b,2659,a)].
% 17.75/17.83 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2946,b,2660,a)].
% 17.75/17.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2946,b,2666,b)].
% 17.75/17.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2946,b,2667,b)].
% 17.75/17.83 2947 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2370,d,2197,b)].
% 17.80/17.85 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(C,A,tc_IntDef_Oint),c_times(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2947,d,2659,a)].
% 17.80/17.85 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(C,A,tc_nat),c_times(C,B,tc_nat),tc_nat). [resolve(2947,d,2660,a)].
% 17.80/17.85 2948 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2371,b,2197,b)].
% 17.80/17.85 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2948,b,2659,a)].
% 17.80/17.85 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2948,b,2660,a)].
% 17.80/17.85 2949 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2372,b,2197,b)].
% 17.80/17.85 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2949,b,2659,a)].
% 17.80/17.85 Derived: class_HOL_Otimes(tc_nat). [resolve(2949,b,2660,a)].
% 17.80/17.85 2950 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2373,b,2197,b)].
% 17.80/17.85 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2950,b,2659,a)].
% 17.80/17.85 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2950,b,2660,a)].
% 17.80/17.85 2951 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2374,b,2197,b)].
% 17.80/17.85 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2951,b,2659,a)].
% 17.80/17.85 Derived: class_HOL_Ozero(tc_nat). [resolve(2951,b,2660,a)].
% 17.80/17.85 2952 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2375,c,2197,b)].
% 17.80/17.85 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2952,c,2659,a)].
% 17.80/17.85 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(2952,c,2660,a)].
% 17.80/17.85 2953 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2376,c,2197,b)].
% 17.80/17.85 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2953,c,2659,a)].
% 17.80/17.85 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(2953,c,2660,a)].
% 17.80/17.85 2954 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2377,b,2197,b)].
% 17.80/17.85 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2954,b,2659,a)].
% 17.80/17.85 Derived: -c_less(A,A,tc_nat). [resolve(2954,b,2660,a)].
% 17.80/17.85 2955 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2378,c,2197,b)].
% 17.80/17.85 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2955,c,2659,a)].
% 17.80/17.85 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2955,c,2660,a)].
% 17.80/17.85 2956 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2379,b,2197,b)].
% 17.81/17.86 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2956,b,2659,a)].
% 17.81/17.86 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2956,b,2660,a)].
% 17.81/17.86 2957 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2380,c,2197,b)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2957,c,2659,a)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2957,c,2660,a)].
% 17.81/17.86 2958 -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(2381,c,2197,b)].
% 17.81/17.86 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2958,c,2659,a)].
% 17.81/17.86 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2958,c,2660,a)].
% 17.81/17.86 2959 -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(2382,c,2197,b)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2959,c,2659,a)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2959,c,2660,a)].
% 17.81/17.86 2960 -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(2383,c,2197,b)].
% 17.81/17.86 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2960,c,2659,a)].
% 17.81/17.86 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2960,c,2660,a)].
% 17.81/17.86 2961 -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(2384,c,2197,b)].
% 17.81/17.86 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(2961,c,2659,a)].
% 17.81/17.86 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(2961,c,2660,a)].
% 17.81/17.86 2962 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2385,c,2197,b)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2962,c,2659,a)].
% 17.81/17.86 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2962,c,2660,a)].
% 17.81/17.86 2963 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(2386,b,2197,b)].
% 17.81/17.86 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(2963,b,2659,a)].
% 17.81/17.86 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(2963,b,2660,a)].
% 17.81/17.86 2964 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2387,b,2197,b)].
% 17.81/17.86 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2964,b,2659,a)].
% 17.81/17.86 Derived: c_lessequals(A,A,tc_nat). [resolve(2964,b,2660,a)].
% 17.81/17.87 2965 -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(2388,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2965,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2965,c,2660,a)].
% 17.81/17.87 2966 -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(2389,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2966,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2966,c,2660,a)].
% 17.81/17.87 2967 -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(2390,d,2197,b)].
% 17.81/17.87 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2967,d,2659,a)].
% 17.81/17.87 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2967,d,2660,a)].
% 17.81/17.87 2968 -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(2391,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2968,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2968,c,2660,a)].
% 17.81/17.87 2969 -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(2392,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2969,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2969,c,2660,a)].
% 17.81/17.87 2970 -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(2393,d,2197,b)].
% 17.81/17.87 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(2970,d,2659,a)].
% 17.81/17.87 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(2970,d,2660,a)].
% 17.81/17.87 2971 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2394,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2971,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2971,c,2660,a)].
% 17.81/17.87 2972 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2395,c,2197,b)].
% 17.81/17.87 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2972,c,2659,a)].
% 17.81/17.87 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2972,c,2660,a)].
% 17.81/17.87 2973 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2396,c,2197,b)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2973,c,2659,a)].
% 17.81/17.87 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2973,c,2660,a)].
% 17.81/17.87 2974 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2397,c,2197,b)].
% 17.81/17.88 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2974,c,2659,a)].
% 17.81/17.88 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2974,c,2660,a)].
% 17.81/17.88 2975 -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(2398,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2975,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2975,c,2660,a)].
% 17.81/17.88 2976 -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(2399,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2976,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2976,c,2660,a)].
% 17.81/17.88 2977 -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(2400,d,2197,b)].
% 17.81/17.88 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2977,d,2659,a)].
% 17.81/17.88 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2977,d,2660,a)].
% 17.81/17.88 2978 -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(2401,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2978,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2978,c,2660,a)].
% 17.81/17.88 2979 -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(2402,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2979,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2979,c,2660,a)].
% 17.81/17.88 2980 -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(2403,d,2197,b)].
% 17.81/17.88 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(2980,d,2659,a)].
% 17.81/17.88 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(2980,d,2660,a)].
% 17.81/17.88 2981 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2404,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2981,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2981,c,2660,a)].
% 17.81/17.88 2982 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2405,c,2197,b)].
% 17.81/17.88 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2982,c,2659,a)].
% 17.81/17.88 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2982,c,2660,a)].
% 17.81/17.88 2983 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2406,c,2197,b)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2983,c,2659,a)].
% 17.81/17.88 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2983,c,2660,a)].
% 18.24/18.31 2984 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2407,c,2197,b)].
% 18.24/18.31 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2984,c,2659,a)].
% 18.24/18.31 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2984,c,2660,a)].
% 18.24/18.31 2985 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2421,b,2411,b)].
% 18.24/18.31 2986 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2422,b,2411,b)].
% 18.24/18.31 2987 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2656,b,2511,b)].
% 18.24/18.31 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(2987,b,2659,a)].
% 18.24/18.31 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(2987,b,2660,a)].
% 18.24/18.31 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2987,b,2666,b)].
% 18.24/18.31 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2987,b,2667,b)].
% 18.24/18.31 2988 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2657,b,2511,b)].
% 18.24/18.31 Derived: c_times(A,c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(B,c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2988,b,2659,a)].
% 18.24/18.31 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(2988,b,2660,a)].
% 18.24/18.31 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2988,b,2666,b)].
% 18.24/18.31 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2988,b,2667,b)].
% 18.24/18.31 2989 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_0) # label(axiom). [assumption].
% 18.24/18.31 2990 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 18.24/18.31 2991 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_2) # label(axiom). [assumption].
% 18.24/18.31 2992 -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].
% 18.24/18.31 2993 -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].
% 18.24/18.31 2994 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1311,a,1267,a)].
% 18.24/18.31 2995 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1311,a,1293,b)].
% 18.24/18.31 2996 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1311,a,1294,b)].
% 18.24/18.31 2997 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1620,a)].
% 18.24/18.31 2998 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1621,a)].
% 18.24/18.31 2999 -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(1649,b,1622,a)].
% 18.24/18.31 3000 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1623,a)].
% 18.24/18.31 3001 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1624,a)].
% 18.24/18.31 3002 -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(1649,b,1625,a)].
% 18.24/18.31 3003 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1626,a)].
% 18.60/18.66 3004 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1649,b,1627,a)].
% 18.60/18.66 3005 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1649,b,1628,a)].
% 18.60/18.66 3006 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1649,b,1629,a)].
% 18.60/18.66 3007 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1630,a)].
% 18.60/18.66 3008 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1631,a)].
% 18.60/18.66 3009 -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(1649,b,1632,a)].
% 18.60/18.66 3010 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1633,a)].
% 18.60/18.66 3011 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1634,a)].
% 18.60/18.66 3012 -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(1649,b,1635,a)].
% 18.60/18.66 3013 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1649,b,1636,a)].
% 18.60/18.66 3014 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1649,b,1637,a)].
% 18.60/18.66 3015 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1649,b,1638,a)].
% 18.60/18.66 3016 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1649,b,1639,a)].
% 18.60/18.66 3017 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 18.60/18.66 3018 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 18.60/18.66 3019 -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].
% 18.60/18.66 3020 -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].
% 18.60/18.66 3021 -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].
% 18.60/18.66 3022 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 18.60/18.66 3023 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 18.60/18.66 3024 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom). [assumption].
% 18.60/18.66 3025 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom). [assumption].
% 18.60/18.66 3026 -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].
% 18.60/18.66 3027 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom). [assumption].
% 18.60/18.66 3028 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 18.60/18.66 3029 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom). [assumption].
% 18.64/18.69 3030 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(36,b,1,a)].
% 18.64/18.69 3031 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(36,b,3,a)].
% 18.64/18.69 3032 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 18.64/18.69 3033 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 18.64/18.69 3034 -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(160,b,133,b)].
% 18.64/18.69 3035 -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(160,b,135,b)].
% 18.64/18.69 3036 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(167,a,160,b)].
% 18.64/18.69 3037 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(168,a,160,b)].
% 18.64/18.69 3038 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 18.64/18.69 3039 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 18.64/18.69 3040 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(245,a,232,b)].
% 18.64/18.69 3041 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(246,a,232,b)].
% 18.64/18.69 3042 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,286,a)].
% 18.64/18.69 3043 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,288,a)].
% 18.64/18.69 3044 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(320,a,309,b)].
% 18.64/18.69 3045 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(321,a,309,b)].
% 18.64/18.69 3046 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(323,a,309,b)].
% 18.64/18.69 3047 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,309,b)].
% 18.64/18.69 3048 -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(344,b,327,b)].
% 18.64/18.69 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(3048,a,3019,b)].
% 18.64/18.69 3049 -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(344,b,329,b)].
% 18.64/18.69 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(3049,a,3019,b)].
% 18.64/18.69 3050 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(344,b,330,a)].
% 18.64/18.69 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(3050,a,3019,b)].
% 18.64/18.69 3051 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(344,b,331,a)].
% 18.64/18.69 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(3051,a,3019,b)].
% 18.64/18.69 3052 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(344,b,332,a)].
% 18.79/18.83 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(3052,a,3019,b)].
% 18.79/18.83 3053 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(350,a,344,b)].
% 18.79/18.83 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3053,b,3019,b)].
% 18.79/18.83 3054 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(351,a,344,b)].
% 18.79/18.83 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3054,b,3019,b)].
% 18.79/18.83 3055 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(362,b,344,b)].
% 18.79/18.83 3056 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(363,b,344,b)].
% 18.79/18.83 3057 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(364,b,344,b)].
% 18.79/18.83 3058 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(365,b,344,b)].
% 18.79/18.83 3059 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,c,344,b)].
% 18.79/18.83 3060 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,c,344,b)].
% 18.79/18.83 3061 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(368,a,344,b)].
% 18.79/18.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3061,b,3019,b)].
% 18.79/18.83 3062 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(369,a,344,b)].
% 18.79/18.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3062,b,3019,b)].
% 18.79/18.83 3063 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(370,c,344,b)].
% 18.79/18.83 3064 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(371,c,344,b)].
% 18.79/18.83 3065 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(804,a,724,a)].
% 18.79/18.83 3066 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(804,a,731,a)].
% 18.79/18.83 3067 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1315,a,1267,a)].
% 18.79/18.83 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(3067,a,3048,a)].
% 18.79/18.83 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(3067,a,3049,a)].
% 18.79/18.83 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(3067,a,3050,a)].
% 18.79/18.83 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(3067,a,3051,a)].
% 18.79/18.83 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(3067,a,3052,a)].
% 18.79/18.83 3068 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1315,a,1293,b)].
% 18.79/18.83 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(3068,a,3048,a)].
% 18.79/18.83 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(3068,a,3049,a)].
% 18.82/18.89 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(3068,a,3050,a)].
% 18.82/18.89 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(3068,a,3051,a)].
% 18.82/18.89 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(3068,a,3052,a)].
% 18.82/18.89 3069 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1315,a,1294,b)].
% 18.82/18.89 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(3069,a,3048,a)].
% 18.82/18.89 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(3069,a,3049,a)].
% 18.82/18.89 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(3069,a,3050,a)].
% 18.82/18.89 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(3069,a,3051,a)].
% 18.82/18.89 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(3069,a,3052,a)].
% 18.82/18.89 3070 -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(1487,b,1462,a)].
% 18.82/18.89 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(3070,a,3019,b)].
% 18.82/18.89 3071 -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(1487,b,1463,a)].
% 18.82/18.89 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(3071,a,3019,b)].
% 18.82/18.89 3072 -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(1487,b,1464,a)].
% 18.82/18.89 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(3072,a,3019,b)].
% 18.82/18.89 3073 -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(1487,b,1465,a)].
% 18.82/18.89 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(3073,a,3019,b)].
% 18.82/18.89 3074 -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(1487,b,1466,a)].
% 18.82/18.89 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(3074,a,3019,b)].
% 18.82/18.89 3075 -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(1487,b,1467,a)].
% 18.82/18.89 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(3075,a,3019,b)].
% 18.82/18.89 3076 -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(1487,b,1468,a)].
% 18.82/18.89 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(3076,a,3019,b)].
% 18.82/18.89 3077 -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(1487,b,1469,a)].
% 18.82/18.89 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(3077,a,3019,b)].
% 18.82/18.89 3078 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1596,b,1566,a)].
% 18.82/18.89 3079 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1567,a)].
% 18.82/18.89 3080 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1568,a)].
% 18.82/18.93 3081 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1569,a)].
% 18.82/18.93 3082 -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(1596,b,1570,a)].
% 18.82/18.93 3083 -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(1596,b,1571,a)].
% 18.82/18.93 3084 -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(1596,b,1572,a)].
% 18.82/18.93 3085 -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(1596,b,1573,a)].
% 18.82/18.93 3086 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1574,a)].
% 18.82/18.93 3087 -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(1596,b,1575,a)].
% 18.82/18.93 3088 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1596,b,1576,a)].
% 18.82/18.93 3089 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1620,a)].
% 18.82/18.93 3090 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1621,a)].
% 18.82/18.93 3091 -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(1659,b,1622,a)].
% 18.82/18.93 3092 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1623,a)].
% 18.82/18.93 3093 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1624,a)].
% 18.82/18.93 3094 -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(1659,b,1625,a)].
% 18.82/18.93 3095 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1626,a)].
% 18.82/18.93 3096 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1627,a)].
% 18.82/18.93 3097 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1628,a)].
% 18.82/18.93 3098 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1629,a)].
% 18.82/18.93 3099 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1630,a)].
% 18.82/18.93 3100 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1631,a)].
% 18.82/18.93 3101 -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(1659,b,1632,a)].
% 18.82/18.93 3102 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1633,a)].
% 18.82/18.93 3103 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1634,a)].
% 18.82/18.93 3104 -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(1659,b,1635,a)].
% 18.82/18.93 3105 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1636,a)].
% 18.82/18.93 3106 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1637,a)].
% 18.95/19.00 3107 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1638,a)].
% 18.95/19.00 3108 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1639,a)].
% 18.95/19.00 3109 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1772,b,1741,a)].
% 18.95/19.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3109,a,3019,b)].
% 18.95/19.00 3110 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1772,b,1748,a)].
% 18.95/19.00 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3110,a,3019,b)].
% 18.95/19.00 3111 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2042,a,2036,b)].
% 18.95/19.00 3112 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2057,a,2036,b)].
% 18.95/19.00 3113 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2058,a,2036,b)].
% 18.95/19.00 3114 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2059,a,2036,b)].
% 18.95/19.00 3115 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2060,a,2036,b)].
% 18.95/19.00 3116 -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(2061,a,2036,b)].
% 18.95/19.00 3117 -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(2062,a,2036,b)].
% 18.95/19.00 3118 -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(2063,a,2036,b)].
% 18.95/19.00 3119 -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(2064,a,2036,b)].
% 18.95/19.00 3120 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2065,a,2036,b)].
% 18.95/19.00 3121 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(2066,a,2036,b)].
% 18.95/19.00 3122 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2067,a,2036,b)].
% 18.95/19.00 3123 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2068,a,2036,b)].
% 18.95/19.00 3124 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2069,a,2036,b)].
% 18.95/19.00 3125 -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(2070,a,2036,b)].
% 18.95/19.00 3126 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2071,a,2036,b)].
% 18.95/19.00 3127 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2072,a,2036,b)].
% 18.95/19.00 3128 -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(2073,a,2036,b)].
% 18.95/19.00 3129 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2074,a,2036,b)].
% 18.95/19.00 3130 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2075,a,2036,b)].
% 18.95/19.00 3131 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2076,a,2036,b)].
% 18.95/19.00 3132 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2036,b)].
% 18.95/19.00 3133 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2078,a,2036,b)].
% 19.20/19.28 3134 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2079,a,2036,b)].
% 19.20/19.28 3135 -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(2080,a,2036,b)].
% 19.20/19.28 3136 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2081,a,2036,b)].
% 19.20/19.28 3137 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2082,a,2036,b)].
% 19.20/19.28 3138 -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(2083,a,2036,b)].
% 19.20/19.28 3139 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2084,a,2036,b)].
% 19.20/19.28 3140 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2085,a,2036,b)].
% 19.20/19.28 3141 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2086,a,2036,b)].
% 19.20/19.28 3142 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2087,a,2036,b)].
% 19.20/19.28 3143 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2157,b,2102,b)].
% 19.20/19.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3143,b,3019,b)].
% 19.20/19.28 3144 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2158,b,2102,b)].
% 19.20/19.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3019,b)].
% 19.20/19.28 3145 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2159,b,2102,b)].
% 19.20/19.28 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3019,b)].
% 19.20/19.28 3146 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2160,b,2102,b)].
% 19.20/19.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3146,b,3019,b)].
% 19.20/19.28 3147 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2161,c,2102,b)].
% 19.20/19.28 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3147,c,3019,b)].
% 19.20/19.28 3148 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2162,c,2102,b)].
% 19.20/19.28 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3148,c,3019,b)].
% 19.20/19.28 3149 -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].
% 19.20/19.28 3150 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 19.20/19.28 3151 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 19.20/19.28 3152 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 19.20/19.28 3153 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom). [assumption].
% 19.37/19.45 3154 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom). [assumption].
% 19.37/19.45 3155 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 19.37/19.45 3156 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom). [assumption].
% 19.37/19.45 3157 -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].
% 19.37/19.45 3158 -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].
% 19.37/19.45 3159 -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].
% 19.37/19.45 3160 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(14,b,1,a)].
% 19.37/19.45 3161 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(14,b,3,a)].
% 19.37/19.45 3162 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 19.37/19.45 3163 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 19.37/19.45 3164 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1076,b,1068,a)].
% 19.37/19.45 3165 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1099,b,1091,a)].
% 19.37/19.45 3166 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1317,a,1267,a)].
% 19.37/19.45 3167 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1317,a,1293,b)].
% 19.37/19.45 3168 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1317,a,1294,b)].
% 19.37/19.45 3169 -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(1473,b,1462,a)].
% 19.37/19.45 3170 -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(1473,b,1463,a)].
% 19.37/19.45 3171 -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(1473,b,1464,a)].
% 19.37/19.45 3172 -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(1473,b,1465,a)].
% 19.37/19.45 3173 -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(1473,b,1466,a)].
% 19.37/19.45 3174 -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(1473,b,1467,a)].
% 19.37/19.45 3175 -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(1473,b,1468,a)].
% 19.37/19.45 3176 -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(1473,b,1469,a)].
% 19.37/19.45 3177 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1488,a,1473,b)].
% 19.37/19.45 3178 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1489,a,1473,b)].
% 19.37/19.45 3179 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1490,b,1473,b)].
% 19.37/19.45 3180 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,b,1473,b)].
% 19.37/19.45 3181 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1533,b,1500,a)].
% 19.37/19.45 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3181,a,3150,a)].
% 19.37/19.45 3182 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1533,b,1501,a)].
% 19.42/19.46 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3182,a,3150,a)].
% 19.42/19.46 3183 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1533,b,1502,a)].
% 19.42/19.46 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3183,a,3150,a)].
% 19.42/19.46 3184 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1533,b,1503,a)].
% 19.42/19.46 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3184,a,3150,a)].
% 19.42/19.46 3185 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1533,b,1504,a)].
% 19.42/19.46 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3185,a,3150,a)].
% 19.42/19.46 3186 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1533,b,1505,a)].
% 19.42/19.46 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3186,a,3150,a)].
% 19.42/19.46 3187 -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(1533,b,1506,a)].
% 19.42/19.46 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(3187,a,3150,a)].
% 19.42/19.46 3188 -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(1533,b,1507,a)].
% 19.42/19.46 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(3188,a,3150,a)].
% 19.42/19.46 3189 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1533,b,1508,a)].
% 19.42/19.46 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3189,a,3150,a)].
% 19.42/19.46 3190 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1533,b,1509,a)].
% 19.42/19.46 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(3190,a,3150,a)].
% 19.42/19.46 3191 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1533,b,1510,a)].
% 19.42/19.46 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(3191,a,3150,a)].
% 19.42/19.46 3192 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1533,b,1511,a)].
% 19.42/19.46 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3192,a,3150,a)].
% 19.42/19.46 3193 -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(1533,b,1512,a)].
% 19.42/19.46 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(3193,a,3150,a)].
% 19.42/19.46 3194 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1533,b,1513,a)].
% 19.42/19.46 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3194,a,3150,a)].
% 19.42/19.46 3195 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1533,b,1514,a)].
% 19.42/19.46 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(3195,a,3150,a)].
% 19.42/19.46 3196 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1533,b,1515,a)].
% 19.42/19.46 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(3196,a,3150,a)].
% 19.42/19.46 3197 -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(1533,b,1516,a)].
% 19.42/19.50 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(3197,a,3150,a)].
% 19.42/19.50 3198 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1533,b,1517,a)].
% 19.42/19.50 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3198,a,3150,a)].
% 19.42/19.50 3199 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1533,b,1518,a)].
% 19.42/19.50 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3199,a,3150,a)].
% 19.42/19.50 3200 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1533,b,1519,a)].
% 19.42/19.50 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3200,a,3150,a)].
% 19.42/19.50 3201 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1533,b,1520,a)].
% 19.42/19.50 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3201,a,3150,a)].
% 19.42/19.50 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3201,a,3157,b)].
% 19.42/19.50 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3201,a,3158,b)].
% 19.42/19.50 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3201,a,3159,b)].
% 19.42/19.50 3202 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1533,b,1521,a)].
% 19.42/19.50 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(3202,a,3150,a)].
% 19.42/19.50 3203 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1581,b,1566,a)].
% 19.42/19.50 3204 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1581,b,1567,a)].
% 19.42/19.50 3205 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1581,b,1568,a)].
% 19.42/19.50 3206 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1581,b,1569,a)].
% 19.42/19.50 3207 -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(1581,b,1570,a)].
% 19.42/19.50 3208 -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(1581,b,1571,a)].
% 19.42/19.50 3209 -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(1581,b,1572,a)].
% 19.42/19.50 3210 -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(1581,b,1573,a)].
% 19.42/19.50 3211 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1581,b,1574,a)].
% 19.42/19.50 3212 -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(1581,b,1575,a)].
% 19.42/19.50 3213 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1581,b,1576,a)].
% 19.42/19.50 3214 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1620,a)].
% 19.42/19.50 3215 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1621,a)].
% 19.42/19.50 3216 -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(1644,b,1622,a)].
% 19.42/19.54 3217 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1623,a)].
% 19.42/19.54 3218 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1624,a)].
% 19.42/19.54 3219 -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(1644,b,1625,a)].
% 19.42/19.54 3220 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1626,a)].
% 19.42/19.54 3221 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1644,b,1627,a)].
% 19.42/19.54 3222 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1644,b,1628,a)].
% 19.42/19.54 3223 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1644,b,1629,a)].
% 19.42/19.54 3224 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1630,a)].
% 19.42/19.54 3225 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1631,a)].
% 19.42/19.54 3226 -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(1644,b,1632,a)].
% 19.42/19.54 3227 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1633,a)].
% 19.42/19.54 3228 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1634,a)].
% 19.42/19.54 3229 -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(1644,b,1635,a)].
% 19.42/19.54 3230 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1644,b,1636,a)].
% 19.42/19.54 3231 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1644,b,1637,a)].
% 19.42/19.54 3232 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1644,b,1638,a)].
% 19.42/19.54 3233 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1644,b,1639,a)].
% 19.42/19.54 3234 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1777,a,1745,b)].
% 19.42/19.54 3235 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1778,a,1745,b)].
% 19.42/19.54 3236 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1779,a,1745,b)].
% 19.42/19.54 3237 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1745,b)].
% 19.42/19.54 3238 -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(1781,a,1745,b)].
% 19.42/19.54 3239 -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(1782,a,1745,b)].
% 19.42/19.54 3240 -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(1783,a,1745,b)].
% 19.42/19.54 3241 -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(1784,a,1745,b)].
% 19.42/19.54 3242 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1785,a,1745,b)].
% 19.42/19.54 3243 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(1786,a,1745,b)].
% 19.81/19.85 3244 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1787,a,1745,b)].
% 19.81/19.85 3245 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1788,a,1745,b)].
% 19.81/19.85 3246 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1789,a,1745,b)].
% 19.81/19.85 3247 -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(1790,a,1745,b)].
% 19.81/19.85 3248 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1791,a,1745,b)].
% 19.81/19.85 3249 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1792,a,1745,b)].
% 19.81/19.85 3250 -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(1793,a,1745,b)].
% 19.81/19.85 3251 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1794,a,1745,b)].
% 19.81/19.85 3252 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1795,a,1745,b)].
% 19.81/19.85 3253 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1796,a,1745,b)].
% 19.81/19.85 3254 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1797,a,1745,b)].
% 19.81/19.85 3255 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1798,a,1745,b)].
% 19.81/19.85 3256 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1799,a,1745,b)].
% 19.81/19.85 3257 -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(1800,a,1745,b)].
% 19.81/19.85 3258 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1801,a,1745,b)].
% 19.81/19.85 3259 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1802,a,1745,b)].
% 19.81/19.85 3260 -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(1803,a,1745,b)].
% 19.81/19.85 3261 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1804,a,1745,b)].
% 19.81/19.85 3262 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1745,b)].
% 19.81/19.85 3263 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1806,a,1745,b)].
% 19.81/19.85 3264 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1807,a,1745,b)].
% 19.81/19.85 3265 -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].
% 19.81/19.85 3266 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 19.81/19.85 3267 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 19.81/19.85 3268 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 19.81/19.85 3269 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom). [assumption].
% 19.92/20.02 3270 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom). [assumption].
% 19.92/20.02 3271 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 19.92/20.02 3272 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom). [assumption].
% 19.92/20.02 3273 -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].
% 19.92/20.02 3274 -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].
% 19.92/20.02 3275 -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].
% 19.92/20.02 3276 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(13,b,1,a)].
% 19.92/20.02 3277 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(13,b,3,a)].
% 19.92/20.02 3278 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 19.92/20.02 3279 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 19.92/20.02 3280 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1075,b,1068,a)].
% 19.92/20.02 3281 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1098,b,1091,a)].
% 19.92/20.02 3282 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1318,a,1267,a)].
% 19.92/20.02 3283 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1318,a,1293,b)].
% 19.92/20.02 3284 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1318,a,1294,b)].
% 19.92/20.02 3285 -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(1472,b,1462,a)].
% 19.92/20.02 3286 -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(1472,b,1463,a)].
% 19.92/20.02 3287 -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(1472,b,1464,a)].
% 19.92/20.02 3288 -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(1472,b,1465,a)].
% 19.92/20.02 3289 -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(1472,b,1466,a)].
% 19.92/20.02 3290 -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(1472,b,1467,a)].
% 19.92/20.02 3291 -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(1472,b,1468,a)].
% 19.92/20.02 3292 -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(1472,b,1469,a)].
% 19.92/20.02 3293 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1488,a,1472,b)].
% 19.92/20.02 3294 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1489,a,1472,b)].
% 19.92/20.02 3295 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1490,b,1472,b)].
% 19.92/20.02 3296 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,b,1472,b)].
% 19.92/20.02 3297 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1532,b,1500,a)].
% 19.92/20.02 3298 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1532,b,1501,a)].
% 19.92/20.04 3299 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1532,b,1502,a)].
% 19.92/20.04 3300 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1532,b,1503,a)].
% 19.92/20.04 3301 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1532,b,1504,a)].
% 19.92/20.04 3302 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1532,b,1505,a)].
% 19.92/20.04 3303 -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(1532,b,1506,a)].
% 19.92/20.04 3304 -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(1532,b,1507,a)].
% 19.92/20.04 3305 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1532,b,1508,a)].
% 19.92/20.04 3306 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1532,b,1509,a)].
% 19.92/20.04 3307 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1532,b,1510,a)].
% 19.92/20.04 3308 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1532,b,1511,a)].
% 19.92/20.04 3309 -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(1532,b,1512,a)].
% 19.92/20.04 3310 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1532,b,1513,a)].
% 19.92/20.04 3311 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1532,b,1514,a)].
% 19.92/20.04 3312 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1532,b,1515,a)].
% 19.92/20.04 3313 -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(1532,b,1516,a)].
% 19.92/20.04 3314 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1532,b,1517,a)].
% 19.92/20.04 3315 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1532,b,1518,a)].
% 19.92/20.04 3316 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1532,b,1519,a)].
% 19.92/20.04 3317 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1532,b,1520,a)].
% 19.92/20.04 3318 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1532,b,1521,a)].
% 19.92/20.04 3319 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1580,b,1566,a)].
% 19.92/20.04 3320 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1580,b,1567,a)].
% 19.92/20.04 3321 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1580,b,1568,a)].
% 19.92/20.04 3322 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1580,b,1569,a)].
% 19.92/20.04 3323 -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(1580,b,1570,a)].
% 19.92/20.04 3324 -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(1580,b,1571,a)].
% 19.92/20.04 3325 -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(1580,b,1572,a)].
% 19.92/20.04 3326 -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(1580,b,1573,a)].
% 20.01/20.09 3327 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1580,b,1574,a)].
% 20.01/20.09 3328 -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(1580,b,1575,a)].
% 20.01/20.09 3329 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1580,b,1576,a)].
% 20.01/20.09 3330 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1620,a)].
% 20.01/20.09 3331 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1643,b,1621,a)].
% 20.01/20.09 3332 -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(1643,b,1622,a)].
% 20.01/20.09 3333 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1623,a)].
% 20.01/20.09 3334 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1643,b,1624,a)].
% 20.01/20.09 3335 -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(1643,b,1625,a)].
% 20.01/20.09 3336 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1643,b,1626,a)].
% 20.01/20.09 3337 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1643,b,1627,a)].
% 20.01/20.09 3338 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1643,b,1628,a)].
% 20.01/20.09 3339 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1643,b,1629,a)].
% 20.01/20.09 3340 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1643,b,1630,a)].
% 20.01/20.09 3341 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1643,b,1631,a)].
% 20.01/20.09 3342 -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(1643,b,1632,a)].
% 20.01/20.09 3343 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1643,b,1633,a)].
% 20.01/20.09 3344 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1643,b,1634,a)].
% 20.01/20.09 3345 -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(1643,b,1635,a)].
% 20.01/20.09 3346 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1643,b,1636,a)].
% 20.01/20.09 3347 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1643,b,1637,a)].
% 20.01/20.09 3348 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1643,b,1638,a)].
% 20.01/20.09 3349 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1643,b,1639,a)].
% 20.01/20.09 3350 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1777,a,1744,b)].
% 20.01/20.09 3351 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1778,a,1744,b)].
% 20.01/20.09 3352 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1779,a,1744,b)].
% 20.01/20.09 3353 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1744,b)].
% 20.08/20.11 3354 -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(1781,a,1744,b)].
% 20.08/20.11 3355 -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(1782,a,1744,b)].
% 20.08/20.11 3356 -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(1783,a,1744,b)].
% 20.08/20.11 3357 -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(1784,a,1744,b)].
% 20.08/20.11 3358 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1785,a,1744,b)].
% 20.08/20.11 3359 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(1786,a,1744,b)].
% 20.08/20.11 3360 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1787,a,1744,b)].
% 20.08/20.11 3361 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1788,a,1744,b)].
% 20.08/20.11 3362 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1789,a,1744,b)].
% 20.08/20.11 3363 -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(1790,a,1744,b)].
% 20.08/20.11 3364 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1791,a,1744,b)].
% 20.08/20.11 3365 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1792,a,1744,b)].
% 20.08/20.11 3366 -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(1793,a,1744,b)].
% 20.08/20.11 3367 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1794,a,1744,b)].
% 20.08/20.11 3368 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1795,a,1744,b)].
% 20.08/20.11 3369 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1796,a,1744,b)].
% 20.08/20.11 3370 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1797,a,1744,b)].
% 20.08/20.11 3371 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1798,a,1744,b)].
% 20.08/20.11 3372 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1799,a,1744,b)].
% 20.08/20.11 3373 -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(1800,a,1744,b)].
% 20.08/20.11 3374 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1801,a,1744,b)].
% 20.08/20.11 3375 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1802,a,1744,b)].
% 20.08/20.11 3376 -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(1803,a,1744,b)].
% 20.08/20.11 3377 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1804,a,1744,b)].
% 20.08/20.11 3378 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1744,b)].
% 20.08/20.11 3379 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1806,a,1744,b)].
% 20.37/20.41 3380 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1807,a,1744,b)].
% 20.37/20.41 3381 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 20.37/20.41 3382 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 20.37/20.41 3383 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom). [assumption].
% 20.37/20.41 3384 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 20.37/20.41 3385 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom). [assumption].
% 20.37/20.41 3386 -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].
% 20.37/20.41 3387 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 20.37/20.41 3388 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom). [assumption].
% 20.37/20.41 3389 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 20.37/20.41 3390 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom). [assumption].
% 20.37/20.41 3391 -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].
% 20.37/20.41 3392 -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].
% 20.37/20.41 3393 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(26,b,1,a)].
% 20.37/20.41 3394 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(26,b,3,a)].
% 20.37/20.41 3395 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 20.37/20.41 3396 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 20.37/20.41 3397 -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(149,b,133,b)].
% 20.37/20.41 3398 -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(149,b,135,b)].
% 20.37/20.41 3399 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(167,a,149,b)].
% 20.37/20.41 3400 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(168,a,149,b)].
% 20.37/20.41 3401 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 20.37/20.41 3402 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 20.37/20.41 3403 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(245,a,221,b)].
% 20.37/20.41 3404 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(246,a,221,b)].
% 20.37/20.41 3405 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,286,a)].
% 20.51/20.55 3406 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,288,a)].
% 20.51/20.55 3407 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(320,a,299,b)].
% 20.51/20.55 3408 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(321,a,299,b)].
% 20.51/20.55 3409 -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(339,b,327,b)].
% 20.51/20.55 3410 -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(339,b,329,b)].
% 20.51/20.55 3411 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(339,b,330,a)].
% 20.51/20.55 3412 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,331,a)].
% 20.51/20.55 3413 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,332,a)].
% 20.51/20.55 3414 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(350,a,339,b)].
% 20.51/20.55 3415 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(351,a,339,b)].
% 20.51/20.55 3416 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(358,b,339,b)].
% 20.51/20.55 3417 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(359,b,339,b)].
% 20.51/20.55 3418 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,339,b)].
% 20.51/20.55 3419 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,339,b)].
% 20.51/20.55 3420 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(364,b,339,b)].
% 20.51/20.55 3421 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(365,b,339,b)].
% 20.51/20.55 3422 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,c,339,b)].
% 20.51/20.55 3423 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,c,339,b)].
% 20.51/20.55 3424 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(368,a,339,b)].
% 20.51/20.55 3425 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(369,a,339,b)].
% 20.51/20.55 3426 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(370,c,339,b)].
% 20.51/20.55 3427 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(371,c,339,b)].
% 20.51/20.55 3428 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(799,a,724,a)].
% 20.51/20.55 3429 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(799,a,731,a)].
% 20.51/20.55 3430 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1078,b,1068,a)].
% 20.51/20.55 3431 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1091,a)].
% 20.51/20.55 3432 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1314,a,1267,a)].
% 20.51/20.55 3433 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1314,a,1293,b)].
% 20.51/20.55 3434 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1314,a,1294,b)].
% 20.51/20.55 3435 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1449,b,1420,a)].
% 20.51/20.55 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3435,a,3382,a)].
% 20.51/20.55 3436 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1449,b,1421,a)].
% 20.51/20.55 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3436,a,3382,a)].
% 20.51/20.57 3437 -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(1449,b,1422,a)].
% 20.51/20.57 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(3437,a,3382,a)].
% 20.51/20.57 3438 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1449,b,1423,a)].
% 20.51/20.57 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3438,a,3382,a)].
% 20.51/20.57 3439 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1449,b,1424,a)].
% 20.51/20.57 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3439,a,3382,a)].
% 20.51/20.57 3440 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1449,b,1425,a)].
% 20.51/20.57 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3440,a,3382,a)].
% 20.51/20.57 3441 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1449,b,1426,a)].
% 20.51/20.57 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3441,a,3382,a)].
% 20.51/20.57 3442 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1449,b,1427,a)].
% 20.51/20.57 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3442,a,3382,a)].
% 20.51/20.57 3443 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1449,b,1428,a)].
% 20.51/20.57 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3443,a,3382,a)].
% 20.51/20.57 3444 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1449,b,1429,a)].
% 20.51/20.57 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3444,a,3382,a)].
% 20.51/20.57 3445 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1449,b,1430,a)].
% 20.51/20.57 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3445,a,3382,a)].
% 20.51/20.57 3446 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1449,b,1431,a)].
% 20.51/20.57 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3446,a,3382,a)].
% 20.51/20.57 3447 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1449,b,1432,a)].
% 20.51/20.57 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3447,a,3382,a)].
% 20.51/20.57 3448 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1449,b,1433,a)].
% 20.51/20.57 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3448,a,3382,a)].
% 20.51/20.57 3449 -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1449,b,1434,a)].
% 20.51/20.57 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3449,a,3382,a)].
% 20.51/20.57 3450 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1449,b,1436,a)].
% 20.51/20.57 3451 -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(1482,b,1462,a)].
% 20.51/20.57 3452 -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(1482,b,1463,a)].
% 20.51/20.57 3453 -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(1482,b,1464,a)].
% 20.51/20.57 3454 -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(1482,b,1465,a)].
% 20.51/20.57 3455 -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(1482,b,1466,a)].
% 20.51/20.57 3456 -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(1482,b,1467,a)].
% 20.51/20.57 3457 -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(1482,b,1468,a)].
% 20.51/20.60 3458 -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(1482,b,1469,a)].
% 20.51/20.60 3459 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1534,b,1500,a)].
% 20.51/20.60 3460 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1534,b,1501,a)].
% 20.51/20.60 3461 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1534,b,1502,a)].
% 20.51/20.60 3462 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1534,b,1503,a)].
% 20.51/20.60 3463 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1534,b,1504,a)].
% 20.51/20.60 3464 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1534,b,1505,a)].
% 20.51/20.60 3465 -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(1534,b,1506,a)].
% 20.51/20.60 3466 -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(1534,b,1507,a)].
% 20.51/20.60 3467 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1534,b,1508,a)].
% 20.51/20.60 3468 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1534,b,1509,a)].
% 20.51/20.60 3469 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1534,b,1510,a)].
% 20.51/20.60 3470 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1534,b,1511,a)].
% 20.51/20.60 3471 -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(1534,b,1512,a)].
% 20.51/20.60 3472 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1534,b,1513,a)].
% 20.51/20.60 3473 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1534,b,1514,a)].
% 20.51/20.60 3474 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1534,b,1515,a)].
% 20.51/20.60 3475 -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(1534,b,1516,a)].
% 20.51/20.60 3476 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1534,b,1517,a)].
% 20.51/20.60 3477 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1534,b,1518,a)].
% 20.51/20.60 3478 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1534,b,1519,a)].
% 20.51/20.60 3479 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1561,c,1534,b)].
% 20.51/20.60 3480 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1562,c,1534,b)].
% 20.51/20.60 3481 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1563,b,1534,b)].
% 20.51/20.60 3482 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1564,b,1534,b)].
% 20.51/20.60 3483 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1587,b,1566,a)].
% 20.51/20.60 3484 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1587,b,1567,a)].
% 20.51/20.60 3485 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1587,b,1568,a)].
% 20.51/20.60 3486 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1587,b,1569,a)].
% 20.51/20.60 3487 -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(1587,b,1570,a)].
% 20.62/20.67 3488 -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(1587,b,1571,a)].
% 20.62/20.67 3489 -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(1587,b,1572,a)].
% 20.62/20.67 3490 -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(1587,b,1573,a)].
% 20.62/20.67 3491 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1587,b,1574,a)].
% 20.62/20.67 3492 -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(1587,b,1575,a)].
% 20.62/20.67 3493 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1587,b,1576,a)].
% 20.62/20.67 3494 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1620,a)].
% 20.62/20.67 3495 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1621,a)].
% 20.62/20.67 3496 -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(1650,b,1622,a)].
% 20.62/20.67 3497 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1623,a)].
% 20.62/20.67 3498 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1624,a)].
% 20.62/20.67 3499 -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(1650,b,1625,a)].
% 20.62/20.67 3500 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1626,a)].
% 20.62/20.67 3501 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1650,b,1627,a)].
% 20.62/20.67 3502 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1650,b,1628,a)].
% 20.62/20.67 3503 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1650,b,1629,a)].
% 20.62/20.67 3504 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1630,a)].
% 20.62/20.67 3505 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1631,a)].
% 20.62/20.67 3506 -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(1650,b,1632,a)].
% 20.62/20.67 3507 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1633,a)].
% 20.62/20.67 3508 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1634,a)].
% 20.62/20.67 3509 -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(1650,b,1635,a)].
% 20.62/20.67 3510 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1650,b,1636,a)].
% 20.62/20.67 3511 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1650,b,1637,a)].
% 20.62/20.67 3512 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1650,b,1638,a)].
% 20.62/20.67 3513 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1650,b,1639,a)].
% 20.62/20.67 3514 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2042,a,2027,b)].
% 20.62/20.68 3515 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2057,a,2027,b)].
% 20.62/20.68 3516 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2058,a,2027,b)].
% 20.62/20.68 3517 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2059,a,2027,b)].
% 20.62/20.68 3518 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2060,a,2027,b)].
% 20.62/20.68 3519 -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(2061,a,2027,b)].
% 20.62/20.68 3520 -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(2062,a,2027,b)].
% 20.62/20.68 3521 -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(2063,a,2027,b)].
% 20.62/20.68 3522 -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(2064,a,2027,b)].
% 20.62/20.68 3523 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2065,a,2027,b)].
% 20.62/20.68 3524 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(2066,a,2027,b)].
% 20.62/20.68 3525 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2067,a,2027,b)].
% 20.62/20.68 3526 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2068,a,2027,b)].
% 20.62/20.68 3527 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2069,a,2027,b)].
% 20.62/20.68 3528 -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(2070,a,2027,b)].
% 20.62/20.68 3529 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2071,a,2027,b)].
% 20.62/20.68 3530 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2072,a,2027,b)].
% 20.62/20.68 3531 -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(2073,a,2027,b)].
% 20.62/20.68 3532 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2074,a,2027,b)].
% 20.62/20.68 3533 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2075,a,2027,b)].
% 20.62/20.68 3534 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2076,a,2027,b)].
% 20.62/20.68 3535 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2027,b)].
% 20.62/20.68 3536 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2078,a,2027,b)].
% 20.62/20.68 3537 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2079,a,2027,b)].
% 20.62/20.68 3538 -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(2080,a,2027,b)].
% 20.62/20.68 3539 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2081,a,2027,b)].
% 20.62/20.68 3540 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2082,a,2027,b)].
% 20.62/20.68 3541 -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(2083,a,2027,b)].
% 20.62/20.68 3542 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2084,a,2027,b)].
% 20.62/20.70 3543 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2085,a,2027,b)].
% 20.62/20.70 3544 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2086,a,2027,b)].
% 20.62/20.70 3545 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2087,a,2027,b)].
% 20.62/20.70 3546 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(D,A,C),c_times(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2156,d,2091,b)].
% 20.62/20.70 3547 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2157,b,2091,b)].
% 20.62/20.70 3548 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2158,b,2091,b)].
% 20.62/20.70 3549 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2159,b,2091,b)].
% 20.62/20.70 3550 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2160,b,2091,b)].
% 20.62/20.70 3551 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2161,c,2091,b)].
% 20.62/20.70 3552 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2162,c,2091,b)].
% 20.62/20.70 3553 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2163,b,2091,b)].
% 20.62/20.70 3554 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2164,c,2091,b)].
% 20.62/20.70 3555 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2165,b,2091,b)].
% 20.62/20.70 3556 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2166,c,2091,b)].
% 20.62/20.70 3557 -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(2167,c,2091,b)].
% 20.62/20.70 3558 -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(2168,c,2091,b)].
% 20.62/20.70 3559 -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(2169,c,2091,b)].
% 20.62/20.70 3560 -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(2170,c,2091,b)].
% 20.62/20.70 3561 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2171,c,2091,b)].
% 20.62/20.70 3562 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(2172,b,2091,b)].
% 20.62/20.70 3563 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2173,b,2091,b)].
% 20.62/20.70 3564 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2174,c,2091,b)].
% 20.62/20.70 3565 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2175,c,2091,b)].
% 20.62/20.70 3566 -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(2176,d,2091,b)].
% 20.62/20.70 3567 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2177,c,2091,b)].
% 20.62/20.70 3568 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2178,c,2091,b)].
% 20.62/20.70 3569 -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(2179,d,2091,b)].
% 20.76/20.81 3570 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2180,c,2091,b)].
% 20.76/20.81 3571 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2181,c,2091,b)].
% 20.76/20.81 3572 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2182,c,2091,b)].
% 20.76/20.81 3573 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2183,c,2091,b)].
% 20.76/20.81 3574 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2184,c,2091,b)].
% 20.76/20.81 3575 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2185,c,2091,b)].
% 20.76/20.81 3576 -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(2186,d,2091,b)].
% 20.76/20.82 3577 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2187,c,2091,b)].
% 20.76/20.82 3578 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2188,c,2091,b)].
% 20.76/20.82 3579 -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(2189,d,2091,b)].
% 20.76/20.82 3580 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2190,c,2091,b)].
% 20.76/20.82 3581 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2191,c,2091,b)].
% 20.76/20.82 3582 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2192,c,2091,b)].
% 20.76/20.82 3583 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2193,c,2091,b)].
% 20.76/20.82 3584 -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(3048,a,3019,b)].
% 20.76/20.82 3585 -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(3049,a,3019,b)].
% 20.76/20.82 3586 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3050,a,3019,b)].
% 20.76/20.82 3587 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3051,a,3019,b)].
% 20.76/20.82 3588 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3052,a,3019,b)].
% 20.76/20.82 3589 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3053,b,3019,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3589,b,3391,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3589,b,3392,b)].
% 20.76/20.82 3590 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3054,b,3019,b)].
% 20.76/20.82 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(3590,b,3382,a)].
% 20.76/20.82 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3590,b,3391,b)].
% 20.76/20.82 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3590,b,3392,b)].
% 20.76/20.82 3591 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3061,b,3019,b)].
% 20.76/20.82 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3591,b,3382,a)].
% 20.76/20.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3591,b,3391,b)].
% 20.76/20.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3591,b,3392,b)].
% 20.76/20.82 3592 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3062,b,3019,b)].
% 20.76/20.82 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3592,b,3382,a)].
% 20.76/20.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3592,b,3391,b)].
% 20.76/20.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3592,b,3392,b)].
% 20.76/20.82 3593 -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(3070,a,3019,b)].
% 20.76/20.82 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(3593,c,3382,a)].
% 20.76/20.82 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(3593,c,3391,b)].
% 20.76/20.82 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(3593,c,3392,b)].
% 20.76/20.82 3594 -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(3071,a,3019,b)].
% 20.76/20.82 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(3594,c,3382,a)].
% 20.76/20.82 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(3594,c,3391,b)].
% 20.76/20.82 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(3594,c,3392,b)].
% 20.76/20.82 3595 -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(3072,a,3019,b)].
% 20.76/20.82 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(3595,c,3382,a)].
% 20.76/20.82 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(3595,c,3391,b)].
% 20.76/20.82 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(3595,c,3392,b)].
% 20.76/20.82 3596 -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(3073,a,3019,b)].
% 20.76/20.82 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(3596,c,3382,a)].
% 20.76/20.82 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(3596,c,3391,b)].
% 20.76/20.82 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(3596,c,3392,b)].
% 20.76/20.82 3597 -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(3074,a,3019,b)].
% 20.76/20.82 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(3597,c,3382,a)].
% 20.76/20.82 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(3597,c,3391,b)].
% 20.76/20.82 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(3597,c,3392,b)].
% 20.76/20.82 3598 -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(3075,a,3019,b)].
% 20.76/20.82 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(3598,c,3382,a)].
% 20.76/20.82 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(3598,c,3391,b)].
% 20.76/20.82 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(3598,c,3392,b)].
% 20.76/20.82 3599 -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(3076,a,3019,b)].
% 20.76/20.82 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(3599,c,3382,a)].
% 20.76/20.82 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(3599,c,3391,b)].
% 20.76/20.82 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(3599,c,3392,b)].
% 20.76/20.82 3600 -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(3077,a,3019,b)].
% 20.76/20.82 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(3600,c,3382,a)].
% 20.76/20.82 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(3600,c,3391,b)].
% 20.76/20.82 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(3600,c,3392,b)].
% 20.76/20.82 3601 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3109,a,3019,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3601,b,3382,a)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3601,b,3391,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3601,b,3392,b)].
% 20.76/20.82 3602 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3110,a,3019,b)].
% 20.76/20.82 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3602,b,3382,a)].
% 20.76/20.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3602,b,3391,b)].
% 20.76/20.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3602,b,3392,b)].
% 20.76/20.82 3603 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3143,b,3019,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3603,b,3382,a)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3603,b,3391,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3603,b,3392,b)].
% 20.76/20.82 3604 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3019,b)].
% 20.76/20.82 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3604,b,3382,a)].
% 20.76/20.82 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3604,b,3391,b)].
% 20.76/20.82 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3604,b,3392,b)].
% 20.76/20.82 3605 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3019,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3605,b,3382,a)].
% 20.76/20.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3605,b,3391,b)].
% 20.76/20.82 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3605,b,3392,b)].
% 20.76/20.82 3606 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3146,b,3019,b)].
% 20.76/20.82 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3606,b,3382,a)].
% 20.76/20.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3606,b,3391,b)].
% 20.76/20.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3606,b,3392,b)].
% 20.76/20.82 3607 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3147,c,3019,b)].
% 20.76/20.82 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(3607,c,3382,a)].
% 20.76/20.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3607,c,3391,b)].
% 21.36/21.43 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3607,c,3392,b)].
% 21.36/21.43 3608 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3148,c,3019,b)].
% 21.36/21.43 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(3608,c,3382,a)].
% 21.36/21.43 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3608,c,3391,b)].
% 21.36/21.43 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3608,c,3392,b)].
% 21.36/21.43 3609 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3201,a,3157,b)].
% 21.36/21.43 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3609,b,3382,a)].
% 21.36/21.43 3610 -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].
% 21.36/21.43 3611 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom). [assumption].
% 21.36/21.43 3612 -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].
% 21.36/21.43 3613 -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].
% 21.36/21.43 3614 -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].
% 21.36/21.43 3615 -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].
% 21.36/21.43 3616 -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].
% 21.36/21.43 3617 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1319,a,1267,a)].
% 21.36/21.43 3618 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1319,a,1293,b)].
% 21.36/21.43 3619 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1319,a,1294,b)].
% 21.36/21.43 3620 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 21.36/21.43 3621 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 21.36/21.43 3622 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 21.36/21.43 Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A). [resolve(3620,a,3622,b)].
% 21.36/21.43 3623 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 21.36/21.43 3624 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 21.36/21.43 3625 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom). [assumption].
% 21.43/21.45 3626 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 21.43/21.45 3627 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom). [assumption].
% 21.43/21.45 3628 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 21.43/21.45 3629 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom). [assumption].
% 21.43/21.45 3630 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 21.43/21.45 3631 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom). [assumption].
% 21.43/21.45 3632 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 21.43/21.45 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3632,a,3622,b)].
% 21.43/21.45 3633 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 21.43/21.45 3634 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 21.43/21.45 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A). [resolve(3634,b,3620,a)].
% 21.43/21.45 3635 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 21.43/21.45 3636 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 21.43/21.45 3637 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 21.43/21.45 3638 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 21.43/21.45 3639 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(108,a,100,b)].
% 21.43/21.45 3640 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(109,a,100,b)].
% 21.43/21.45 3641 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(126,b,110,a)].
% 21.43/21.45 3642 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(126,b,113,a)].
% 21.43/21.45 3643 -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(148,b,133,b)].
% 21.43/21.45 3644 -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(148,b,135,b)].
% 21.43/21.45 3645 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(167,a,148,b)].
% 21.43/21.45 3646 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(168,a,148,b)].
% 21.43/21.45 3647 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(203,b,190,b)].
% 21.43/21.45 3648 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(204,b,190,b)].
% 21.43/21.45 3649 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 21.43/21.45 3650 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 21.43/21.45 3651 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(245,a,220,b)].
% 21.43/21.45 3652 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(246,a,220,b)].
% 21.43/21.45 3653 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,286,a)].
% 21.43/21.45 3654 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,288,a)].
% 21.43/21.46 3655 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(320,a,298,b)].
% 21.43/21.46 3656 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(321,a,298,b)].
% 21.43/21.46 3657 -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(338,b,327,b)].
% 21.43/21.46 3658 -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(338,b,329,b)].
% 21.43/21.46 3659 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,330,a)].
% 21.43/21.46 3660 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,331,a)].
% 21.43/21.46 3661 -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,332,a)].
% 21.43/21.46 3662 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(350,a,338,b)].
% 21.43/21.46 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3662,b,3622,b)].
% 21.43/21.46 3663 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(351,a,338,b)].
% 21.43/21.46 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3663,b,3622,b)].
% 21.43/21.46 3664 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(362,b,338,b)].
% 21.43/21.46 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3664,b,3622,b)].
% 21.43/21.46 3665 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(363,b,338,b)].
% 21.43/21.46 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(3665,b,3622,b)].
% 21.43/21.46 3666 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(364,b,338,b)].
% 21.43/21.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3666,b,3622,b)].
% 21.43/21.46 3667 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(365,b,338,b)].
% 21.43/21.46 3668 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(366,c,338,b)].
% 21.43/21.46 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3668,c,3622,b)].
% 21.43/21.46 3669 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(367,c,338,b)].
% 21.43/21.46 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3669,c,3622,b)].
% 21.43/21.46 3670 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(368,a,338,b)].
% 21.43/21.46 3671 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(369,a,338,b)].
% 21.43/21.46 3672 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(370,c,338,b)].
% 21.43/21.46 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3672,c,3622,b)].
% 21.43/21.46 3673 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(371,c,338,b)].
% 21.43/21.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3673,c,3622,b)].
% 21.43/21.46 3674 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(444,b,429,b)].
% 21.43/21.46 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(3674,b,3622,b)].
% 21.43/21.46 3675 c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(445,b,429,b)].
% 21.46/21.49 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(3675,b,3622,b)].
% 21.46/21.49 3676 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(475,b,429,b)].
% 21.46/21.49 3677 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(476,b,429,b)].
% 21.46/21.49 3678 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(513,a,507,b)].
% 21.46/21.49 3679 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(520,a,507,b)].
% 21.46/21.49 3680 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(521,a,507,b)].
% 21.46/21.49 3681 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(565,b,543,b)].
% 21.46/21.49 3682 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(566,b,543,b)].
% 21.46/21.49 3683 -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(644,a,610,b)].
% 21.46/21.49 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(3683,c,3622,b)].
% 21.46/21.49 3684 -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(645,a,610,b)].
% 21.46/21.49 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(3684,c,3622,b)].
% 21.46/21.49 3685 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(646,a,610,b)].
% 21.46/21.49 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3685,b,3622,b)].
% 21.46/21.49 3686 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(647,a,610,b)].
% 21.46/21.49 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3686,b,3622,b)].
% 21.46/21.49 3687 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(648,a,610,b)].
% 21.46/21.49 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3687,b,3622,b)].
% 21.46/21.49 3688 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(649,b,610,b)].
% 21.46/21.49 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(3688,b,3622,b)].
% 21.46/21.49 3689 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(650,b,610,b)].
% 21.46/21.49 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3689,b,3622,b)].
% 21.46/21.49 3690 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(651,b,610,b)].
% 21.46/21.49 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3690,b,3622,b)].
% 21.46/21.49 3691 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(653,b,610,b)].
% 21.46/21.49 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3691,b,3622,b)].
% 21.46/21.49 3692 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(654,b,610,b)].
% 21.46/21.49 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3692,b,3622,b)].
% 21.46/21.49 3693 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(656,b,610,b)].
% 21.46/21.49 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3693,b,3622,b)].
% 21.46/21.49 3694 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(657,b,610,b)].
% 21.46/21.49 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(3694,b,3622,b)].
% 21.46/21.49 3695 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(684,b,658,a)].
% 21.46/21.49 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3695,a,3622,b)].
% 21.46/21.49 3696 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(684,b,660,a)].
% 21.46/21.49 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3696,a,3622,b)].
% 23.34/23.37 3697 -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(684,b,661,a)].
% 23.34/23.37 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(3697,a,3622,b)].
% 23.34/23.37 3698 -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(684,b,662,a)].
% 23.34/23.37 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(3698,a,3622,b)].
% 23.34/23.37 3699 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(684,b,663,a)].
% 23.34/23.37 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3699,a,3622,b)].
% 23.34/23.37 3700 -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(684,b,664,a)].
% 23.34/23.37 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(3700,a,3622,b)].
% 23.34/23.37 3701 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(684,b,665,a)].
% 23.34/23.37 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3701,a,3622,b)].
% 23.34/23.37 3702 -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(684,b,666,a)].
% 23.34/23.37 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(3702,a,3622,b)].
% 23.34/23.37 3703 -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(684,b,667,a)].
% 23.34/23.37 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(3703,a,3622,b)].
% 23.34/23.37 3704 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(684,b,668,a)].
% 23.34/23.37 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3704,a,3622,b)].
% 23.34/23.37 3705 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(816,a,724,a)].
% 23.34/23.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3705,a,3622,b)].
% 23.34/23.37 3706 -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(893,b,822,a)].
% 23.34/23.37 3707 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 23.34/23.37 3708 -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(893,b,823,a)].
% 23.34/23.37 3709 -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(893,b,824,a)].
% 23.34/23.37 3710 -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(893,b,825,a)].
% 23.34/23.37 3711 -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(893,b,826,a)].
% 23.34/23.37 3712 -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(893,b,827,a)].
% 23.34/23.37 3713 -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(893,b,828,a)].
% 23.34/23.37 3714 -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(893,b,829,a)].
% 23.34/23.37 3715 -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(893,b,830,a)].
% 23.34/23.37 3716 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,831,a)].
% 23.34/23.37 3717 -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(893,b,832,a)].
% 23.34/23.37 3718 -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(893,b,833,a)].
% 23.34/23.37 3719 -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(893,b,834,a)].
% 23.34/23.37 3720 -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(893,b,835,a)].
% 23.34/23.37 3721 -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(893,b,836,a)].
% 23.34/23.37 3722 -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(893,b,837,a)].
% 23.34/23.37 3723 -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(893,b,838,a)].
% 23.34/23.37 3724 -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(893,b,839,a)].
% 23.34/23.37 3725 -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(893,b,840,a)].
% 23.34/23.37 3726 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,841,a)].
% 23.34/23.37 3727 -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(893,b,842,a)].
% 23.34/23.37 3728 -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(893,b,843,a)].
% 23.34/23.37 3729 -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(893,b,844,a)].
% 23.34/23.37 3730 -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(893,b,845,b)].
% 23.34/23.37 3731 -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(893,b,846,b)].
% 23.34/23.37 3732 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(893,b,847,a)].
% 23.34/23.37 3733 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(893,b,848,a)].
% 23.34/23.37 3734 -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(893,b,849,a)].
% 23.34/23.37 3735 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(893,b,850,a)].
% 23.34/23.38 3736 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(893,b,851,a)].
% 23.34/23.38 3737 -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(893,b,852,a)].
% 23.34/23.38 3738 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(893,b,853,a)].
% 23.34/23.38 3739 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(893,b,854,a)].
% 23.34/23.38 3740 -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(893,b,855,a)].
% 23.34/23.38 3741 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(893,b,856,a)].
% 23.34/23.38 3742 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(893,b,857,a)].
% 23.34/23.38 3743 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(893,b,858,a)].
% 23.34/23.38 3744 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(893,b,859,a)].
% 23.34/23.38 3745 -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(893,b,860,a)].
% 23.34/23.38 3746 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(893,b,861,a)].
% 23.34/23.38 3747 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(893,b,862,a)].
% 23.34/23.38 3748 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(893,b,863,a)].
% 23.34/23.38 3749 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(893,b,864,a)].
% 23.34/23.38 3750 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(893,b,865,a)].
% 23.34/23.38 3751 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(893,b,866,a)].
% 23.34/23.38 3752 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(893,b,867,a)].
% 23.34/23.38 3753 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(893,b,868,a)].
% 23.34/23.38 3754 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(893,b,869,a)].
% 23.34/23.38 3755 -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(893,b,870,a)].
% 23.34/23.38 3756 -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(893,b,871,a)].
% 23.34/23.38 3757 -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(893,b,872,a)].
% 23.34/23.38 3758 -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(893,b,873,a)].
% 23.34/23.38 3759 -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(893,b,874,a)].
% 23.34/23.38 3760 -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(893,b,875,a)].
% 23.34/23.38 3761 -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(893,b,876,a)].
% 23.43/23.49 3762 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(893,b,877,a)].
% 23.43/23.49 3763 -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(893,b,878,a)].
% 23.43/23.49 3764 -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(893,b,879,a)].
% 23.43/23.49 3765 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1068,a)].
% 23.43/23.49 3766 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1091,a)].
% 23.43/23.49 3767 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1598,b,1566,a)].
% 23.43/23.49 3768 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1567,a)].
% 23.43/23.49 3769 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1568,a)].
% 23.43/23.49 3770 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1569,a)].
% 23.43/23.49 3771 -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(1598,b,1570,a)].
% 23.43/23.49 3772 -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(1598,b,1571,a)].
% 23.43/23.49 3773 -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(1598,b,1572,a)].
% 23.43/23.49 3774 -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(1598,b,1573,a)].
% 23.43/23.49 3775 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1574,a)].
% 23.43/23.49 3776 -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(1598,b,1575,a)].
% 23.43/23.49 3777 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1598,b,1576,a)].
% 23.43/23.49 3778 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1620,a)].
% 23.43/23.49 3779 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1621,a)].
% 23.43/23.49 3780 -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(1661,b,1622,a)].
% 23.43/23.49 3781 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1623,a)].
% 23.43/23.49 3782 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1624,a)].
% 23.43/23.49 3783 -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(1661,b,1625,a)].
% 23.43/23.49 3784 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1626,a)].
% 23.43/23.49 3785 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1627,a)].
% 23.43/23.49 3786 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1628,a)].
% 23.43/23.49 3787 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1629,a)].
% 23.43/23.49 3788 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1630,a)].
% 25.35/25.40 3789 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1631,a)].
% 25.35/25.40 3790 -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(1661,b,1632,a)].
% 25.35/25.40 3791 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1633,a)].
% 25.35/25.40 3792 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1634,a)].
% 25.35/25.40 3793 -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(1661,b,1635,a)].
% 25.35/25.40 3794 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1636,a)].
% 25.35/25.40 3795 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1637,a)].
% 25.35/25.40 3796 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1638,a)].
% 25.35/25.40 3797 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1639,a)].
% 25.35/25.40
% 25.35/25.40 ============================== end predicate elimination =============
% 25.35/25.40
% 25.35/25.40 Auto_denials: (non-Horn, no changes).
% 25.35/25.40
% 25.35/25.40 Term ordering decisions:
% 25.35/25.40 Function symbol KB weights: tc_IntDef_Oint=1. tc_nat=1. c_0=1. c_emptyset=1. c_1=1. c_Finite__Set_OFinites=1. c_List_Olist_ONil=1. c_IntDef_ONats=1. c_Numeral_OPls=1. c_Numeral_Obit_OB1=1. c_Numeral_Obit_OB0=1. c_UNIV=1. c_Numeral_OMin=1. tc_List_Onibble=1. c_Relation_OId=1. c_IntDef_OInts=1. c_IntDef_Ointrel=1. c_Datatype_Ooption_ONone=1. t_b=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. tc_List_Ochar=1. tc_bool=1. v_c=1. c_Numeral_Onumber__of=1. c_uminus=1. tc_fun=1. c_NatArith_Oof__nat=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. c_SetInterval_OlessThan=1. tc_prod=1. c_Finite__Set_OMax=1. c_Finite__Set_OMin=1. c_SetInterval_OgreaterThan=1. c_Numeral_OBit=1. tc_Datatype__Universe_Onode=1. c_HOL_Oabs=1. c_Nat_Osize=1. c_Numeral_Obin__add=1. c_List_Oset=1. c_HOL_Oinverse=1. c_IntDef_Oof__int=1. c_List_Orev=1. c_OrderedGroup_Onprt=1. c_OrderedGroup_Opprt=1. c_Union=1. c_List_Olists=1. c_Transitive__Closure_Ortrancl=1. c_Finite__Set_Ocard=1. c_Inter=1. c_List_Oremdups=1. c_List_Oupt=1. c_List_Olast=1. c_List_Oconcat=1. c_List_Olistrel=1. c_List_Olex=1. c_Pow=1. c_Datatype_Ooption_OSome=1. c_Numeral_Obin__mult=1. c_Relation_Odiag=1. tc_sum=1. c_Binomial_Obinomial=1. c_List_Olexord=1. c_List_Orotate1=1. c_List_Obutlast=1. c_List_Ohd=1. c_List_Otl=1. c_Transitive__Closure_Otrancl=1. c_Datatype_Oo2s=1. c_List_Ochar_OChar=1. c_IntDiv_Oadjust=1. c_List_Olistset=1. c_Main_OIdE__1=1. c_Main_OInter__UNIV__conv__1__1=1. c_Main_OInter__UNIV__conv__2__1=1. c_Main_ONil__eq__concat__conv__1=1. c_Main_OUnion__empty__conv__1=1. c_Main_Oconcat__eq__Nil__conv__1=1. c_Main_Oempty__Union__conv__1=1. c_Main_Ofinite__Union__1=1. c_Datatype_Othe=1. c_Fun_Oid=1. c_List_Olenlex=1. c_Main_Oall__not__in__conv__1=1. c_Main_Olexord__Nil__left__1=1. c_Main_Olexord__Nil__left__2=1. c_Main_Omod__eq__0D__dest__1=1. c_Main_Onot__None__eq__1=1. c_Main_Onot__Some__eq__1=1. c_Main_Ozmod__eq__0D__dest__1=1. c_Set_Ocontents=1. tc_set=1. tc_List_Olist=1. c_Suc=1. c_Numeral_Obin__minus=1. c_IntDef_Oint=1. c_IntDef_Onat=1. c_GCD_Ogcd=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Numeral_Obin__pred=1. c_IntDiv_OnegateSnd=1. c_Numeral_Obin__succ=1. c_IntDef_OAbs__Integ=1. tc_Datatype_Ooption=1. c_IntDef_ORep__Integ=1. v_b=1. v_g=1. v_f=1. v_x=1. c_times=1. c_plus=1. c_SetInterval_OatLeastLessThan=1. c_minus=1. c_insert=1. c_divide=1. c_Orderings_Omin=1. c_Orderings_Omax=1. c_Nat_Opower=1. c_SetInterval_OatLeastAtMost=1. c_List_Olist_OCons=1. c_SetInterval_OgreaterThanAtMost=1. c_Divides_Oop_Amod=1. c_append=1. c_SetInterval_OgreaterThanLessThan=1. c_div=1. c_inter=1. c_union=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=1. c_Main_OMax__le__iff__1=1. c_Main_OMax__less__iff__1=1. c_Main_OMin__ge__iff__1=1. c_Main_OMin__gr__iff__1=1. c_List_Onth=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_Datatype__Universe_OIn0=1. c_Datatype__Universe_OIn1=1. c_Relation_ODomain=1. c_Relation_Oconverse=1. c_List_Orotate=1. c_Relation_ORange=1. c_fst=1. c_snd=1. c_List_Oremove1=1. c_List_Osublist=1. c_SetsAndFunctions_Oelt__set__plus=1. c_SetsAndFunctions_Oelt__set__times=1. c_Sum__Type_OInl=1. c_Sum__Type_OInr=1. c_List_Olist__inter=1. c_Datatype__Universe_OAtom=1. c_Datatype__Universe_OLeaf=1. c_Datatype__Universe_ONumb=1. c_Equiv__Relations_Oquotient=1. c_List_Oitrev=1. c_Main_OdiagE__1=1. c_Main_OInterI__1=1. c_Main_OInter__iff__1=1. c_Main_OUnionE__1=1. c_Main_OUnion__iff__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Datatype_Ounit_Ounit__case=1. c_Datatype_Ounit_Ounit__rec=1. c_List_Olexn=1. c_List_Oset__Cons=1. c_Main_Osurj__pair__1=1. c_Main_Osurj__pair__2=1. c_Pair=1. c_Relation_OImage=1. c_Datatype__Universe_Ontrunc=1. c_Datatype__Universe_OScons=1. c_List_Ozip=1. c_List_Olist__update=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Datatype__Universe_Odprod=1. c_Datatype__Universe_Ouprod=1. c_Main_OPlusE__1=1. c_Main_OPlusE__2=1. c_Main_OdsumE__1=1. c_Main_OdsumE__2=1. c_Main_OdsumE__3=1. c_Main_OdsumE__4=1. c_Main_OusumE__1=1. c_Main_OusumE__2=1. c_Extraction_Osumbool_Osumbool__case=1. c_Extraction_Osumbool_Osumbool__rec=1. c_Main_OconverseE__1=1. c_Main_OconverseE__2=1. c_Numeral_Obit_Obit__case=1. c_Numeral_Obit_Obit__rec=1. c_Wellfounded__Relations_Olex__prod=1. c_Main_ODomainE__1=1. c_Main_ORangeE__1=1. c_Map_Omap__of=1. c_Relation_Orel__comp=1. c_Main_OImageE__1=1. c_Main_OdprodE__1=1. c_Main_OdprodE__2=1. c_Main_OdprodE__3=1. c_Main_OdprodE__4=1. c_Main_Olistrel__Cons1__1=1. c_Main_Olistrel__Cons1__2=1. c_Main_Olistrel__Cons2__1=1. c_Main_Olistrel__Cons2__2=1. c_Main_OuprodE__1=1. c_Main_OuprodE__2=1. c_Main_Orel__compE__1=1. c_Main_Orel__compE__2=1. c_Main_Orel__compE__3=1. c_List_Onibble_Onibble__case=1. c_List_Onibble_Onibble__rec=1.
% 26.64/26.64
% 26.64/26.64 ============================== end of process initial clauses ========
% 26.64/26.64
% 26.64/26.64 ============================== CLAUSES FOR SEARCH ====================
% 26.64/26.64
% 26.64/26.64 ============================== end of clauses for search =============
% 26.64/26.64
% 26.64/26.64 ============================== SEARCH ================================
% 26.64/26.64
% 26.64/26.64 % Starting search at 23.74 seconds.
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=41.000, iters=3446
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=39.000, iters=3352
% 26.64/26.64
% 26.64/26.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 24.19 sec).
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=37.000, iters=3388
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=36.000, iters=3355
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=35.000, iters=3375
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=34.000, iters=3347
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=33.000, iters=3360
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=32.000, iters=3343
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=31.000, iters=3370
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=30.000, iters=3427
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=29.000, iters=3393
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=28.000, iters=3366
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=27.000, iters=3340
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=26.000, iters=3340
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=25.000, iters=3352
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=24.000, iters=3343
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=23.000, iters=3361
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=22.000, iters=3359
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=21.000, iters=3334
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=20.000, iters=3337
% 26.64/26.64
% 26.64/26.64 Low Water (keep): wt=19Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------