TSTP Solution File: ANA018-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA018-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 19:21:33 EDT 2022
% Result : Timeout 300.02s 300.12s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ANA018-1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 05:04:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.44/1.73 ============================== Prover9 ===============================
% 1.44/1.73 Prover9 (32) version 2009-11A, November 2009.
% 1.44/1.73 Process 10411 was started by sandbox on n009.cluster.edu,
% 1.44/1.73 Fri Jul 8 05:04:08 2022
% 1.44/1.73 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10258_n009.cluster.edu".
% 1.44/1.73 ============================== end of head ===========================
% 1.44/1.73
% 1.44/1.73 ============================== INPUT =================================
% 1.44/1.73
% 1.44/1.73 % Reading from file /tmp/Prover9_10258_n009.cluster.edu
% 1.44/1.73
% 1.44/1.73 set(prolog_style_variables).
% 1.44/1.73 set(auto2).
% 1.44/1.73 % set(auto2) -> set(auto).
% 1.44/1.73 % set(auto) -> set(auto_inference).
% 1.44/1.73 % set(auto) -> set(auto_setup).
% 1.44/1.73 % set(auto_setup) -> set(predicate_elim).
% 1.44/1.73 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.44/1.73 % set(auto) -> set(auto_limits).
% 1.44/1.73 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.44/1.73 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.44/1.73 % set(auto) -> set(auto_denials).
% 1.44/1.73 % set(auto) -> set(auto_process).
% 1.44/1.73 % set(auto2) -> assign(new_constants, 1).
% 1.44/1.73 % set(auto2) -> assign(fold_denial_max, 3).
% 1.44/1.73 % set(auto2) -> assign(max_weight, "200.000").
% 1.44/1.73 % set(auto2) -> assign(max_hours, 1).
% 1.44/1.73 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.44/1.73 % set(auto2) -> assign(max_seconds, 0).
% 1.44/1.73 % set(auto2) -> assign(max_minutes, 5).
% 1.44/1.73 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.44/1.73 % set(auto2) -> set(sort_initial_sos).
% 1.44/1.73 % set(auto2) -> assign(sos_limit, -1).
% 1.44/1.73 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.44/1.73 % set(auto2) -> assign(max_megs, 400).
% 1.44/1.73 % set(auto2) -> assign(stats, some).
% 1.44/1.73 % set(auto2) -> clear(echo_input).
% 1.44/1.73 % set(auto2) -> set(quiet).
% 1.44/1.73 % set(auto2) -> clear(print_initial_clauses).
% 1.44/1.73 % set(auto2) -> clear(print_given).
% 1.44/1.73 assign(lrs_ticks,-1).
% 1.44/1.73 assign(sos_limit,10000).
% 1.44/1.73 assign(order,kbo).
% 1.44/1.73 set(lex_order_vars).
% 1.44/1.73 clear(print_given).
% 1.44/1.73
% 1.44/1.73 % formulas(sos). % not echoed (2794 formulas)
% 1.44/1.73
% 1.44/1.73 ============================== end of input ==========================
% 1.44/1.73
% 1.44/1.73 % From the command line: assign(max_seconds, 300).
% 1.44/1.73
% 1.44/1.73 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.44/1.73
% 1.44/1.73 % Formulas that are not ordinary clauses:
% 1.44/1.73
% 1.44/1.73 ============================== end of process non-clausal formulas ===
% 1.44/1.73
% 1.44/1.73 ============================== PROCESS INITIAL CLAUSES ===============
% 1.44/1.73
% 1.44/1.73 ============================== PREDICATE ELIMINATION =================
% 1.44/1.73 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].
% 1.44/1.73 2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom). [assumption].
% 1.44/1.73 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)].
% 1.44/1.73 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].
% 1.44/1.73 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)].
% 1.44/1.73 4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 1.44/1.73 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4,a,1,a)].
% 1.44/1.73 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4,a,3,a)].
% 1.44/1.73 5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 1.44/1.73 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(5,a,1,a)].
% 1.44/1.73 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(5,a,3,a)].
% 1.44/1.73 6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 1.44/1.73 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 1.44/1.73 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 1.44/1.73 7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 1.44/1.75 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(7,b,1,a)].
% 1.44/1.75 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(7,b,3,a)].
% 1.44/1.75 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].
% 1.44/1.75 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)].
% 1.44/1.75 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)].
% 1.44/1.75 9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(9,a,2,a)].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(9,a,4,a)].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(9,a,5,a)].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(9,a,7,b)].
% 1.44/1.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 1.44/1.75 10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 1.44/1.75 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(10,a,2,a)].
% 1.44/1.75 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(10,a,4,a)].
% 1.44/1.75 Derived: class_HOL_Oplus(tc_nat). [resolve(10,a,5,a)].
% 1.44/1.75 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 1.44/1.75 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(10,a,7,b)].
% 1.44/1.75 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 1.44/1.75 11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 1.44/1.75 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 1.44/1.75 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 1.44/1.75 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].
% 1.44/1.75 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)].
% 1.44/1.75 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)].
% 1.44/1.75 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].
% 1.44/1.75 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)].
% 1.44/1.75 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)].
% 1.44/1.75 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].
% 1.44/1.75 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)].
% 1.44/1.75 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)].
% 1.44/1.75 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 1.53/1.77 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 1.53/1.77 19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 1.53/1.77 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(19,b,1,a)].
% 1.53/1.77 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(19,b,3,a)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.53/1.77 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 1.53/1.77 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].
% 1.53/1.77 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)].
% 1.53/1.77 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)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 1.57/1.82 24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 1.57/1.82 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(24,b,1,a)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(24,b,3,a)].
% 1.57/1.82 25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 1.57/1.82 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 1.57/1.82 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 1.57/1.82 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].
% 1.57/1.82 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)].
% 1.57/1.82 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)].
% 1.57/1.82 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 1.57/1.85 37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 1.57/1.85 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 1.57/1.85 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 1.57/1.85 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].
% 1.57/1.85 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)].
% 1.57/1.85 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)].
% 1.57/1.85 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].
% 1.73/1.98 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)].
% 1.73/1.98 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)].
% 1.73/1.98 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].
% 1.73/1.98 42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom). [assumption].
% 1.73/1.98 43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 1.73/1.98 44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 1.73/1.98 45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 1.73/1.98 46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 1.73/1.98 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 1.73/1.98 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 1.73/1.98 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 1.73/1.98 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 1.73/1.98 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 1.73/1.98 47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 1.73/1.98 48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 1.73/1.98 49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 1.73/1.98 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].
% 1.73/1.98 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 1.73/1.98 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 1.73/1.98 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 1.73/1.98 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].
% 1.73/1.98 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].
% 1.73/1.98 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].
% 1.73/1.98 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].
% 1.73/1.98 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].
% 1.73/1.98 56 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 1.73/2.02 57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 1.73/2.02 58 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_14) # label(axiom). [assumption].
% 1.73/2.02 59 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_15) # label(axiom). [assumption].
% 1.73/2.02 60 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) # label(axiom). [assumption].
% 1.73/2.02 61 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 1.73/2.02 62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 1.73/2.02 63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 1.73/2.02 64 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_19) # label(axiom). [assumption].
% 1.73/2.02 65 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) # label(axiom). [assumption].
% 1.73/2.02 66 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_26) # label(axiom). [assumption].
% 1.73/2.02 67 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_25) # label(axiom). [assumption].
% 1.73/2.02 68 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_4) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 1.73/2.02 69 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_19) # label(axiom). [assumption].
% 1.73/2.02 70 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_19) # label(axiom). [assumption].
% 1.73/2.02 71 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 1.73/2.02 72 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_13) # label(axiom). [assumption].
% 1.73/2.02 73 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_15) # label(axiom). [assumption].
% 1.73/2.02 74 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_4) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 1.73/2.02 75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 1.73/2.03 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 1.73/2.03 76 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_4) # label(axiom). [assumption].
% 1.73/2.03 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 1.73/2.03 77 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_9) # label(axiom). [assumption].
% 1.73/2.03 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 1.73/2.03 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 1.73/2.03 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 1.73/2.03 78 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_13) # label(axiom). [assumption].
% 1.73/2.03 79 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(8,b,1,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_OrderedGroup_Oab__group__add(D). [resolve(79,a,42,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(79,a,43,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(79,a,44,a)].
% 1.73/2.03 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 1.73/2.03 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(79,a,46,b)].
% 1.73/2.03 80 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(8,b,3,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_OrderedGroup_Oab__group__add(D). [resolve(80,a,42,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(80,a,43,a)].
% 1.73/2.03 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(80,a,44,a)].
% 1.73/2.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 1.73/2.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(80,a,46,b)].
% 1.73/2.03 81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(81,b,42,a)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(81,b,43,a)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(81,b,44,a)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(81,b,46,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(81,b,54,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(81,b,57,b)].
% 1.73/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(81,b,59,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(81,b,62,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(81,b,66,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(81,b,67,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(81,b,73,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 1.87/2.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 1.87/2.15 82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(82,b,42,a)].
% 1.87/2.15 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(82,b,43,a)].
% 1.87/2.15 Derived: class_HOL_Oplus(tc_nat). [resolve(82,b,44,a)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(82,b,46,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(82,b,54,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(82,b,57,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(82,b,59,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(82,b,62,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(82,b,66,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(82,b,67,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(82,b,73,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 1.87/2.15 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 1.87/2.15 83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom). [assumption].
% 1.87/2.18 84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom). [assumption].
% 1.87/2.18 85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom). [assumption].
% 1.87/2.18 86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom). [assumption].
% 1.87/2.18 87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom). [assumption].
% 1.87/2.18 88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 1.87/2.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(83,a,84,a)].
% 1.87/2.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(83,a,85,a)].
% 1.87/2.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(83,a,86,a)].
% 1.87/2.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(83,a,87,a)].
% 1.87/2.18 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 1.87/2.18 89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom). [assumption].
% 1.87/2.18 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(89,a,84,a)].
% 1.87/2.18 Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(89,a,85,a)].
% 1.87/2.18 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(89,a,86,a)].
% 1.87/2.18 Derived: class_HOL_Otimes(tc_nat). [resolve(89,a,87,a)].
% 1.87/2.18 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 1.87/2.18 90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 1.87/2.18 91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom). [assumption].
% 1.87/2.18 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(91,b,83,a)].
% 1.87/2.18 Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A). [resolve(91,b,89,a)].
% 1.87/2.18 92 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 1.87/2.18 93 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_7) # label(axiom). [assumption].
% 1.87/2.18 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(93,b,83,a)].
% 1.87/2.18 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A). [resolve(93,b,89,a)].
% 1.87/2.18 94 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 1.87/2.18 95 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_1) # label(axiom). [assumption].
% 1.87/2.18 96 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) # label(axiom). [assumption].
% 1.87/2.18 97 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_5) # label(axiom). [assumption].
% 1.87/2.18 98 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) # label(axiom). [assumption].
% 1.87/2.18 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 1.87/2.18 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 1.87/2.18 99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom). [assumption].
% 1.95/2.23 100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 1.95/2.23 101 -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].
% 1.95/2.23 102 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_20) # label(axiom). [assumption].
% 1.95/2.23 103 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 1.95/2.23 104 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 1.95/2.23 105 -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].
% 1.95/2.23 106 -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].
% 1.95/2.23 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(106,b,83,a)].
% 1.95/2.23 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A). [resolve(106,b,89,a)].
% 1.95/2.23 107 -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].
% 1.95/2.23 108 -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].
% 1.95/2.23 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)].
% 1.95/2.23 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)].
% 1.95/2.23 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(108,a,86,a)].
% 1.95/2.23 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(108,a,87,a)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(108,a,88,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(108,a,90,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Power_Orecpower(C). [resolve(108,a,91,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(108,a,92,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(108,a,93,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(108,a,94,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(108,a,95,b)].
% 1.95/2.23 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)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(108,a,97,b)].
% 1.95/2.23 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)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(108,a,99,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(108,a,100,b)].
% 1.95/2.23 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)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(108,a,102,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(108,a,103,b)].
% 1.95/2.23 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(108,a,104,b)].
% 2.03/2.31 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)].
% 2.03/2.31 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(108,a,106,b)].
% 2.03/2.31 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(108,a,107,b)].
% 2.03/2.31 109 -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].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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(109,a,86,a)].
% 2.03/2.31 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(109,a,87,a)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(109,a,101,b)].
% 2.03/2.31 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(109,a,102,b)].
% 2.03/2.31 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(109,a,103,b)].
% 2.03/2.31 Derived: c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(109,a,104,b)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 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)].
% 2.03/2.31 110 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 2.03/2.31 111 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom). [assumption].
% 2.03/2.37 112 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom). [assumption].
% 2.03/2.37 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(110,a,111,a)].
% 2.03/2.37 Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(110,a,112,a)].
% 2.03/2.37 113 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 2.03/2.37 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(113,a,111,a)].
% 2.03/2.37 Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(113,a,112,a)].
% 2.03/2.37 114 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 2.03/2.37 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(114,a,110,a)].
% 2.03/2.37 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(114,a,113,a)].
% 2.03/2.37 115 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 2.03/2.37 Derived: c_times(c_1,A,tc_nat) = A. [resolve(115,a,110,a)].
% 2.03/2.37 Derived: c_times(A,c_1,tc_nat) = A. [resolve(115,a,113,a)].
% 2.03/2.37 116 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.03/2.37 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(116,b,110,a)].
% 2.03/2.37 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(116,b,113,a)].
% 2.03/2.37 117 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 2.03/2.37 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(117,b,110,a)].
% 2.03/2.37 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(117,b,113,a)].
% 2.03/2.37 118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.03/2.37 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(118,a,111,a)].
% 2.03/2.37 Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,112,a)].
% 2.03/2.37 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(118,a,114,a)].
% 2.03/2.37 Derived: class_HOL_Oone(tc_nat). [resolve(118,a,115,a)].
% 2.03/2.37 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(118,a,116,b)].
% 2.03/2.37 Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,117,b)].
% 2.03/2.37 119 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 2.03/2.37 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(119,a,117,b)].
% 2.03/2.37 120 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 2.03/2.37 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(120,a,117,b)].
% 2.03/2.37 121 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 2.03/2.37 Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B. [resolve(121,b,110,a)].
% 2.03/2.37 Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B. [resolve(121,b,113,a)].
% 2.03/2.37 122 -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].
% 2.03/2.37 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B. [resolve(122,b,110,a)].
% 2.03/2.37 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B. [resolve(122,b,113,a)].
% 2.03/2.37 123 -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].
% 2.03/2.37 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(123,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(123,b,113,a)].
% 2.16/2.47 124 -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].
% 2.16/2.47 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(124,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(124,b,113,a)].
% 2.16/2.47 125 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B. [resolve(125,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B. [resolve(125,b,113,a)].
% 2.16/2.47 126 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(126,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(126,b,113,a)].
% 2.16/2.47 127 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B. [resolve(127,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B. [resolve(127,b,113,a)].
% 2.16/2.47 128 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B. [resolve(128,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B. [resolve(128,b,113,a)].
% 2.16/2.47 129 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(129,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(129,b,113,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(129,b,119,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(129,b,120,a)].
% 2.16/2.47 130 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(130,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(130,b,113,a)].
% 2.16/2.47 131 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(131,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(131,b,113,a)].
% 2.16/2.47 132 -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].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(132,b,110,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(132,b,113,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(132,b,118,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(132,b,119,a)].
% 2.16/2.47 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(132,b,120,a)].
% 2.16/2.47 133 -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].
% 2.25/2.54 134 class_Ring__and__Field_Osemiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_17) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.54 135 -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].
% 2.25/2.54 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)].
% 2.25/2.54 136 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.54 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)].
% 2.25/2.54 137 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.54 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)].
% 2.25/2.54 138 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.54 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)].
% 2.25/2.54 139 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.54 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)].
% 2.25/2.54 140 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 2.25/2.54 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)].
% 2.25/2.55 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)].
% 2.25/2.55 141 -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].
% 2.25/2.55 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)].
% 2.25/2.55 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)].
% 2.25/2.55 142 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 2.25/2.55 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)].
% 2.25/2.55 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)].
% 2.25/2.55 143 -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].
% 2.25/2.55 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)].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(143,b,135,b)].
% 2.25/2.55 144 -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].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(144,b,133,b)].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(144,b,135,b)].
% 2.25/2.55 145 -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].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(145,b,133,b)].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(145,b,135,b)].
% 2.25/2.55 146 -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].
% 2.25/2.55 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(146,b,133,b)].
% 2.25/2.56 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)].
% 2.25/2.56 147 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.25/2.56 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)].
% 2.25/2.56 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)].
% 2.25/2.56 148 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.25/2.56 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)].
% 2.25/2.56 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)].
% 2.25/2.56 149 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 2.25/2.56 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)].
% 2.25/2.56 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)].
% 2.25/2.56 150 -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].
% 2.25/2.56 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)].
% 2.25/2.56 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)].
% 2.25/2.56 151 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 2.25/2.56 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)].
% 2.25/2.56 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)].
% 2.25/2.56 152 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 2.25/2.56 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)].
% 2.25/2.58 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)].
% 2.25/2.58 153 -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].
% 2.25/2.58 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)].
% 2.25/2.58 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)].
% 2.25/2.58 154 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 2.25/2.58 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)].
% 2.25/2.58 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)].
% 2.25/2.58 155 -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].
% 2.25/2.58 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)].
% 2.25/2.58 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(155,b,135,b)].
% 2.25/2.58 156 -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].
% 2.25/2.58 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(156,b,133,b)].
% 2.25/2.58 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(156,b,135,b)].
% 2.25/2.58 157 -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].
% 2.25/2.58 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(157,b,133,b)].
% 2.25/2.58 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(157,b,135,b)].
% 2.25/2.58 158 -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].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 159 -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].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 160 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 161 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 162 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 163 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 2.33/2.59 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)].
% 2.33/2.59 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)].
% 2.33/2.59 164 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,134,a)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(164,a,139,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(164,a,140,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(164,a,141,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,142,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,143,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(164,a,144,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,145,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(164,a,147,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(164,a,148,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(164,a,149,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(164,a,150,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(164,a,151,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(164,a,152,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(164,a,154,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(164,a,155,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(164,a,157,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(164,a,158,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,159,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,161,b)].
% 2.33/2.59 165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(165,a,134,a)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,142,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,143,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,145,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,159,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,161,b)].
% 2.33/2.59 166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.33/2.59 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(166,a,134,a)].
% 2.33/2.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,142,b)].
% 2.33/2.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,143,b)].
% 2.33/2.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,145,b)].
% 2.33/2.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,159,b)].
% 2.33/2.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,161,b)].
% 2.33/2.59 167 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(167,a,134,a)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(167,a,140,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(167,a,142,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(167,a,143,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(167,a,144,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(167,a,145,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(167,a,147,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(167,a,148,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(167,a,149,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(167,a,150,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(167,a,151,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(167,a,152,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(167,a,153,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(167,a,155,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(167,a,156,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(167,a,157,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(167,a,159,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(167,a,160,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(167,a,161,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(167,a,162,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(167,a,163,b)].
% 2.33/2.59 168 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.33/2.59 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(168,a,134,a)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(168,a,140,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(168,a,142,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(168,a,143,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(168,a,144,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(168,a,145,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(168,a,147,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(168,a,148,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(168,a,149,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(168,a,150,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(168,a,151,b)].
% 2.33/2.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(168,a,152,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(168,a,153,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(168,a,155,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(168,a,156,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(168,a,157,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(168,a,159,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(168,a,160,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(168,a,161,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(168,a,162,b)].
% 2.46/2.80 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(168,a,163,b)].
% 2.46/2.80 169 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.46/2.80 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)].
% 2.46/2.80 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)].
% 2.46/2.80 170 -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].
% 2.46/2.80 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)].
% 2.46/2.80 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)].
% 2.46/2.80 171 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.46/2.80 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)].
% 2.46/2.80 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)].
% 2.46/2.80 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(171,b,166,a)].
% 2.46/2.80 172 -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].
% 2.46/2.80 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)].
% 2.46/2.80 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)].
% 2.46/2.80 173 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.46/2.80 174 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].
% 2.46/2.80 175 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.63/2.89 176 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.63/2.89 177 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.63/2.89 178 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.63/2.89 179 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_1) # label(axiom). [assumption].
% 2.63/2.89 180 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_6) # label(axiom). [assumption].
% 2.63/2.89 181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.63/2.89 182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.63/2.89 183 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.63/2.89 184 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.63/2.89 185 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_0) # label(axiom). [assumption].
% 2.63/2.89 186 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) # label(axiom). [assumption].
% 2.63/2.89 187 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_4) # label(axiom). [assumption].
% 2.63/2.89 188 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) # label(axiom). [assumption].
% 2.63/2.89 189 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.63/2.89 190 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.63/2.89 191 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) # label(axiom). [assumption].
% 2.63/2.89 192 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_19) # label(axiom). [assumption].
% 2.63/2.89 193 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_16) # label(axiom). [assumption].
% 2.63/2.89 194 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_10) # label(axiom). [assumption].
% 2.63/2.89 195 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) # label(axiom). [assumption].
% 2.63/2.89 196 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_6) # label(axiom). [assumption].
% 2.63/2.89 197 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_1) # label(axiom). [assumption].
% 2.63/2.89 198 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(108,a,94,b)].
% 2.63/2.89 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)].
% 2.63/2.89 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(198,b,175,a)].
% 2.63/2.91 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(198,b,176,a)].
% 2.63/2.91 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(198,b,177,b)].
% 2.63/2.91 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Power_Orecpower(C). [resolve(198,b,178,b)].
% 2.63/2.91 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(198,b,179,b)].
% 2.63/2.91 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(198,b,180,b)].
% 2.63/2.91 199 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 200 -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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 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)].
% 2.63/2.91 201 -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)].
% 2.63/2.91 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)].
% 2.63/2.92 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(201,a,175,a)].
% 2.63/2.92 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(201,a,176,a)].
% 2.63/2.92 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)].
% 2.63/2.92 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)].
% 2.63/2.92 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)].
% 2.63/2.92 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)].
% 2.63/2.92 202 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,142,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(202,b,176,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 2.63/2.92 203 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,142,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(203,b,174,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(203,b,175,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(203,b,176,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(203,b,178,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(203,b,180,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(203,b,186,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(203,b,189,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(203,b,190,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(203,b,191,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(203,b,192,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(203,b,193,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(203,b,195,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(203,b,196,b)].
% 2.63/2.92 204 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,142,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(204,b,174,a)].
% 2.63/2.92 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(204,b,175,a)].
% 2.63/2.92 Derived: class_HOL_Oplus(tc_nat). [resolve(204,b,176,a)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(204,b,178,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(204,b,180,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(204,b,186,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(204,b,189,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(204,b,190,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(204,b,191,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(204,b,192,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(204,b,193,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(204,b,195,b)].
% 2.63/2.92 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(204,b,196,b)].
% 2.63/2.92 205 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(167,a,142,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(205,b,174,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(205,b,175,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(205,b,176,a)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(205,b,177,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(205,b,178,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(205,b,179,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(205,b,180,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(205,b,188,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(205,b,194,b)].
% 2.63/2.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(205,b,196,b)].
% 2.63/2.92 206 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(168,a,142,b)].
% 2.63/2.92 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(206,b,174,a)].
% 2.93/3.19 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(206,b,175,a)].
% 2.93/3.19 Derived: class_HOL_Otimes(tc_nat). [resolve(206,b,176,a)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(206,b,177,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(206,b,178,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(206,b,179,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(206,b,180,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(206,b,188,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(206,b,194,b)].
% 2.93/3.19 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(206,b,196,b)].
% 2.93/3.19 207 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 2.93/3.19 208 class_Ring__and__Field_Osemiring__0(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_19) # label(axiom). [assumption].
% 2.93/3.19 209 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 2.93/3.19 210 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 2.93/3.19 211 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 2.93/3.19 212 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 2.93/3.19 213 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_3) # label(axiom). [assumption].
% 2.93/3.19 214 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_9) # label(axiom). [assumption].
% 2.93/3.19 215 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_10) # label(axiom). [assumption].
% 2.93/3.19 216 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) # label(axiom). [assumption].
% 2.93/3.19 217 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_6) # label(axiom). [assumption].
% 2.93/3.19 218 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) # label(axiom). [assumption].
% 2.93/3.19 219 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 2.93/3.19 220 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 2.93/3.19 221 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Olordered__ring_13) # label(axiom). [assumption].
% 2.93/3.19 222 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) # label(axiom). [assumption].
% 2.93/3.19 223 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_22) # label(axiom). [assumption].
% 2.93/3.19 224 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_19) # label(axiom). [assumption].
% 2.93/3.19 225 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_6) # label(axiom). [assumption].
% 2.93/3.19 226 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_13) # label(axiom). [assumption].
% 2.93/3.20 227 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_0) # label(axiom). [assumption].
% 2.93/3.20 228 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) # label(axiom). [assumption].
% 2.93/3.20 229 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_1) # label(axiom). [assumption].
% 2.93/3.20 230 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_9) # label(axiom). [assumption].
% 2.93/3.20 231 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_3) # label(axiom). [assumption].
% 2.93/3.20 232 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__ring_6) # label(axiom). [assumption].
% 2.93/3.20 233 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__semiring_0) # label(axiom). [assumption].
% 2.93/3.20 234 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 2.93/3.20 235 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring__1_6) # label(axiom). [assumption].
% 2.93/3.20 236 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 2.93/3.20 237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 2.93/3.20 238 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 2.93/3.20 239 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 2.93/3.20 240 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(240,a,208,a)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(240,a,209,a)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(240,a,210,a)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(240,a,212,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(240,a,214,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(240,a,219,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(240,a,223,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(240,a,224,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(240,a,230,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 2.93/3.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 2.93/3.20 241 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 2.93/3.20 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(241,a,208,a)].
% 2.93/3.20 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(241,a,209,a)].
% 2.93/3.20 Derived: class_HOL_Ozero(tc_nat). [resolve(241,a,210,a)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(241,a,212,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(241,a,214,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(241,a,219,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(241,a,223,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(241,a,224,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 2.93/3.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(241,a,230,b)].
% 2.93/3.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 2.93/3.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 2.93/3.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 2.93/3.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 2.93/3.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 2.93/3.25 242 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_0) # label(axiom). [assumption].
% 2.93/3.25 243 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1_3) # label(axiom). [assumption].
% 2.93/3.25 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 2.93/3.25 244 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_2) # label(axiom). [assumption].
% 2.93/3.25 245 -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)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(245,a,215,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(245,a,216,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(245,a,217,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(245,a,218,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(245,a,219,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(245,a,220,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(245,a,221,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(245,a,222,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(245,a,223,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(245,a,224,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(245,a,225,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(245,a,226,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(245,a,227,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(245,a,228,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(245,a,229,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(245,a,230,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(245,a,231,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(245,a,232,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(245,a,233,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(245,a,234,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(245,a,235,b)].
% 2.93/3.25 246 -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)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(246,a,215,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(246,a,216,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(246,a,217,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(246,a,218,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(246,a,219,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(246,a,220,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(246,a,221,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(246,a,222,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(246,a,223,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(246,a,224,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(246,a,225,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(246,a,226,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(246,a,227,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(246,a,228,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(246,a,229,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(246,a,230,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(246,a,231,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(246,a,232,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(246,a,233,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(246,a,234,b)].
% 2.93/3.25 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(246,a,235,b)].
% 3.07/3.41 247 -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].
% 3.07/3.41 248 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].
% 3.07/3.41 249 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.07/3.41 250 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.07/3.41 251 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.07/3.41 252 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.07/3.41 253 -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].
% 3.07/3.41 254 -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].
% 3.07/3.41 255 -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].
% 3.07/3.41 256 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.07/3.41 257 -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].
% 3.07/3.41 258 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.07/3.41 259 -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].
% 3.07/3.41 260 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.07/3.41 261 -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].
% 3.07/3.41 262 -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].
% 3.07/3.41 263 -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].
% 3.07/3.41 264 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.07/3.41 265 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.07/3.41 266 -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].
% 3.07/3.41 267 -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].
% 3.07/3.41 268 -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].
% 3.07/3.41 269 -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].
% 3.07/3.41 270 -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].
% 3.16/3.47 271 -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].
% 3.16/3.47 272 -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].
% 3.16/3.47 273 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(108,a,95,b)].
% 3.16/3.47 274 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)].
% 3.16/3.47 275 -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)].
% 3.16/3.47 276 -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)].
% 3.16/3.47 277 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,143,b)].
% 3.16/3.47 278 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,143,b)].
% 3.16/3.47 279 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,143,b)].
% 3.16/3.47 280 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(167,a,143,b)].
% 3.16/3.47 281 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(168,a,143,b)].
% 3.16/3.47 282 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(282,b,248,a)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(282,b,249,a)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(282,b,250,a)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(282,b,251,b)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(282,b,252,b)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(282,b,253,b)].
% 3.16/3.47 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(282,b,254,b)].
% 3.16/3.47 283 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 3.16/3.47 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(283,b,248,a)].
% 3.16/3.47 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(283,b,249,a)].
% 3.16/3.47 Derived: class_HOL_Ozero(tc_nat). [resolve(283,b,250,a)].
% 3.16/3.47 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(283,b,251,b)].
% 3.16/3.47 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(283,b,252,b)].
% 3.16/3.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(283,b,253,b)].
% 3.16/3.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(283,b,254,b)].
% 3.16/3.47 284 -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)].
% 3.16/3.47 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)].
% 3.16/3.47 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)].
% 3.32/3.57 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)].
% 3.32/3.57 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(284,c,251,b)].
% 3.32/3.57 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(284,c,252,b)].
% 3.32/3.57 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,c,253,b)].
% 3.32/3.57 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(284,c,254,b)].
% 3.32/3.57 285 -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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 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)].
% 3.32/3.57 286 -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].
% 3.32/3.57 287 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].
% 3.32/3.57 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)].
% 3.32/3.57 288 -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].
% 3.32/3.57 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)].
% 3.36/3.62 289 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 3.36/3.62 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(289,a,286,a)].
% 3.36/3.62 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(289,a,288,a)].
% 3.36/3.62 290 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 3.36/3.62 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(290,a,286,a)].
% 3.36/3.62 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(290,a,288,a)].
% 3.36/3.62 291 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 3.36/3.62 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(291,b,286,a)].
% 3.36/3.62 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(291,b,288,a)].
% 3.36/3.62 292 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 3.36/3.62 Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0. [resolve(292,b,286,a)].
% 3.36/3.62 Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0. [resolve(292,b,288,a)].
% 3.36/3.62 293 -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].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,288,a)].
% 3.36/3.62 294 -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].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0. [resolve(294,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0. [resolve(294,b,288,a)].
% 3.36/3.62 295 -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].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,288,a)].
% 3.36/3.62 296 -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].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,288,a)].
% 3.36/3.62 297 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,288,a)].
% 3.36/3.62 298 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 3.36/3.62 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,288,a)].
% 3.36/3.62 299 -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].
% 3.36/3.62 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,286,a)].
% 3.36/3.62 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,288,a)].
% 3.36/3.62 300 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,288,a)].
% 3.38/3.65 301 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,288,a)].
% 3.38/3.65 302 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,288,a)].
% 3.38/3.65 303 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,288,a)].
% 3.38/3.65 304 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,288,a)].
% 3.38/3.65 305 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,288,a)].
% 3.38/3.65 306 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,288,a)].
% 3.38/3.65 307 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,288,a)].
% 3.38/3.65 308 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,288,a)].
% 3.38/3.65 309 -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].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,286,a)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,288,a)].
% 3.38/3.65 310 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 3.38/3.67 Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,286,a)].
% 3.38/3.67 Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,288,a)].
% 3.38/3.67 311 -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].
% 3.38/3.67 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,286,a)].
% 3.38/3.67 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,288,a)].
% 3.38/3.67 312 -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].
% 3.38/3.67 313 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 3.38/3.67 314 -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].
% 3.38/3.67 315 -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].
% 3.38/3.67 316 -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].
% 3.38/3.67 317 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 3.38/3.67 318 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 3.38/3.67 319 -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].
% 3.38/3.67 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(319,b,286,a)].
% 3.38/3.67 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(319,b,288,a)].
% 3.38/3.67 320 -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)].
% 3.38/3.67 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)].
% 3.38/3.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(320,a,292,b)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(320,a,297,b)].
% 3.38/3.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(320,a,298,b)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.67 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(320,a,310,b)].
% 3.38/3.68 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)].
% 3.38/3.68 321 -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)].
% 3.38/3.68 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(321,a,287,a)].
% 3.38/3.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(321,a,292,b)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(321,a,297,b)].
% 3.38/3.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(321,a,298,b)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 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)].
% 3.38/3.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(321,a,310,b)].
% 3.38/3.68 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)].
% 3.38/3.68 322 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 3.38/3.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(322,a,303,b)].
% 3.38/3.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(322,a,309,b)].
% 3.38/3.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(322,a,310,b)].
% 3.38/3.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(322,a,311,b)].
% 3.38/3.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(322,a,319,b)].
% 3.54/3.82 323 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 3.54/3.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(323,a,303,b)].
% 3.54/3.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(323,a,309,b)].
% 3.54/3.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(323,a,311,b)].
% 3.54/3.82 324 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 3.54/3.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,303,b)].
% 3.54/3.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(324,a,307,b)].
% 3.54/3.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,309,b)].
% 3.54/3.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,311,b)].
% 3.54/3.82 325 -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)].
% 3.54/3.82 326 -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)].
% 3.54/3.82 327 -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].
% 3.54/3.82 328 class_Ring__and__Field_Oring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_22) # label(axiom). [assumption].
% 3.54/3.82 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)].
% 3.54/3.82 329 -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].
% 3.54/3.82 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)].
% 3.54/3.82 330 -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].
% 3.54/3.82 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)].
% 3.54/3.82 331 -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].
% 3.54/3.82 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)].
% 3.54/3.82 332 -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].
% 3.54/3.82 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)].
% 3.54/3.82 333 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 334 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 335 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 336 -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].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.84 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)].
% 3.54/3.85 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)].
% 3.54/3.85 337 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 338 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 339 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 340 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.54/3.85 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)].
% 3.62/3.87 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)].
% 3.62/3.87 341 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 342 -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].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 343 -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].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 344 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 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)].
% 3.62/3.87 345 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 3.62/3.87 346 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 3.62/3.87 347 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 3.62/3.87 348 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 3.62/3.87 349 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 3.62/3.87 350 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(350,a,328,a)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(350,a,333,a)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(350,a,334,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(350,a,335,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(350,a,336,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(350,a,337,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(350,a,338,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(350,a,339,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(350,a,340,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(350,a,341,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(350,a,342,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(350,a,343,b)].
% 3.62/3.87 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(350,a,344,b)].
% 3.62/3.87 351 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom). [assumption].
% 3.62/3.87 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(351,a,328,a)].
% 3.62/3.87 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(351,a,333,a)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(351,a,334,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(351,a,335,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(351,a,336,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(351,a,337,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(351,a,338,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(351,a,339,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(351,a,340,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(351,a,341,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(351,a,342,b)].
% 3.62/3.87 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(351,a,343,b)].
% 3.64/3.91 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(351,a,344,b)].
% 3.64/3.91 352 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 3.64/3.91 353 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 3.64/3.91 354 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 3.64/3.91 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)].
% 3.64/3.91 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)].
% 3.64/3.91 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)].
% 3.64/3.91 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)].
% 3.64/3.91 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)].
% 3.64/3.91 355 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 3.64/3.91 356 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 3.64/3.91 357 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 3.64/3.91 358 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(358,b,339,b)].
% 3.64/3.91 359 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 3.64/3.91 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(359,b,339,b)].
% 3.64/3.91 360 -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)].
% 3.64/3.91 361 -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)].
% 3.64/3.91 362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(167,a,162,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(362,b,337,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(362,b,338,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,339,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(362,b,340,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(362,b,341,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(362,b,342,b)].
% 3.64/3.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(362,b,344,b)].
% 3.64/3.91 363 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(168,a,162,b)].
% 3.64/3.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(363,b,337,b)].
% 3.64/3.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(363,b,338,b)].
% 3.64/3.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,339,b)].
% 3.64/3.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(363,b,340,b)].
% 3.64/3.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(363,b,341,b)].
% 3.67/3.93 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(363,b,342,b)].
% 3.67/3.93 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(363,b,344,b)].
% 3.67/3.93 364 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(364,b,337,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(364,b,338,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(364,b,339,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(364,b,340,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(364,b,341,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(364,b,342,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(364,b,343,b)].
% 3.67/3.93 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(364,b,344,b)].
% 3.67/3.93 365 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(365,b,337,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(365,b,338,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(365,b,339,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(365,b,340,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(365,b,341,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(365,b,342,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(365,b,343,b)].
% 3.67/3.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(365,b,344,b)].
% 3.67/3.93 366 -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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.93 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)].
% 3.67/3.94 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)].
% 3.67/3.94 367 -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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 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)].
% 3.67/3.94 368 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,286,a)].
% 3.67/3.94 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)].
% 3.67/3.94 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(368,a,333,a)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(368,a,334,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(368,a,335,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(368,a,336,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(368,a,337,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(368,a,338,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(368,a,339,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(368,a,340,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(368,a,341,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(368,a,342,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(368,a,343,b)].
% 3.67/3.94 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(368,a,344,b)].
% 3.67/3.94 369 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,288,a)].
% 3.67/3.94 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)].
% 3.69/3.94 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(369,a,333,a)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(369,a,334,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(369,a,335,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(369,a,336,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(369,a,337,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(369,a,338,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(369,a,339,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(369,a,340,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(369,a,341,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(369,a,342,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(369,a,343,b)].
% 3.69/3.94 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(369,a,344,b)].
% 3.69/3.94 370 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(320,a,310,b)].
% 3.69/3.94 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)].
% 3.69/3.94 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(370,c,333,a)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(370,c,334,b)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(370,c,337,b)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(370,c,338,b)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 371 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(321,a,310,b)].
% 3.69/3.94 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)].
% 3.69/3.94 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(371,c,333,a)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(371,c,334,b)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(371,c,337,b)].
% 3.69/3.94 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(371,c,338,b)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.69/3.94 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)].
% 3.83/4.09 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)].
% 3.83/4.09 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)].
% 3.83/4.09 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)].
% 3.83/4.09 372 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(322,a,310,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(372,b,328,a)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(372,b,333,a)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(372,b,334,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(372,b,335,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(372,b,336,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(372,b,337,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(372,b,338,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(372,b,339,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,b,340,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,b,341,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(372,b,342,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(372,b,343,b)].
% 3.83/4.09 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(372,b,344,b)].
% 3.83/4.09 373 -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].
% 3.83/4.09 374 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].
% 3.83/4.09 375 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 3.83/4.09 376 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 3.83/4.09 377 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 3.83/4.09 378 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 3.83/4.09 379 -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].
% 3.83/4.09 380 -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].
% 3.83/4.09 381 -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].
% 3.83/4.09 382 -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].
% 3.83/4.09 383 -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].
% 3.83/4.09 384 -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].
% 3.83/4.09 385 -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].
% 3.91/4.16 386 -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].
% 3.91/4.16 387 -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].
% 3.91/4.16 388 -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].
% 3.91/4.16 389 -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].
% 3.91/4.16 390 -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].
% 3.91/4.16 391 -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].
% 3.91/4.16 392 -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].
% 3.91/4.16 393 -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].
% 3.91/4.16 394 -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)].
% 3.91/4.16 395 -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)].
% 3.91/4.16 396 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 3.91/4.16 397 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 3.91/4.16 398 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(108,a,96,b)].
% 3.91/4.16 399 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)].
% 3.91/4.16 400 -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)].
% 3.91/4.16 401 -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)].
% 3.91/4.16 402 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(164,a,144,b)].
% 3.91/4.16 403 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(167,a,144,b)].
% 3.91/4.16 404 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(168,a,144,b)].
% 3.91/4.16 405 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(203,b,186,b)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(405,b,374,a)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(405,b,375,a)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(405,b,376,a)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(405,b,377,b)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(405,b,378,b)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(405,b,379,b)].
% 3.91/4.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(405,b,380,b)].
% 4.00/4.31 406 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(204,b,186,b)].
% 4.00/4.31 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(406,b,374,a)].
% 4.00/4.31 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(406,b,375,a)].
% 4.00/4.31 Derived: class_HOL_Oplus(tc_nat). [resolve(406,b,376,a)].
% 4.00/4.31 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(406,b,377,b)].
% 4.00/4.31 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(406,b,378,b)].
% 4.00/4.31 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(406,b,379,b)].
% 4.00/4.31 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(406,b,380,b)].
% 4.00/4.31 407 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 4.00/4.31 408 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 4.00/4.31 409 -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)].
% 4.00/4.31 410 -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)].
% 4.00/4.31 411 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,286,a)].
% 4.00/4.31 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(411,a,376,a)].
% 4.00/4.31 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(411,a,378,b)].
% 4.00/4.31 412 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,288,a)].
% 4.00/4.31 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(412,a,376,a)].
% 4.00/4.31 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(412,a,378,b)].
% 4.00/4.31 413 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)].
% 4.00/4.31 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(413,c,376,a)].
% 4.00/4.31 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(413,c,378,b)].
% 4.00/4.31 414 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)].
% 4.00/4.31 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(414,c,376,a)].
% 4.00/4.31 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(414,c,378,b)].
% 4.00/4.31 415 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom). [assumption].
% 4.00/4.31 416 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].
% 4.00/4.31 417 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 4.00/4.31 418 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 4.00/4.31 419 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 4.00/4.31 420 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 4.00/4.31 421 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom). [assumption].
% 4.00/4.31 422 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 4.00/4.31 423 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 4.00/4.31 424 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 4.00/4.31 425 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 4.08/4.37 426 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 4.08/4.37 427 -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].
% 4.08/4.37 428 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 4.08/4.37 429 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 4.08/4.37 430 -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].
% 4.08/4.37 431 -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].
% 4.08/4.37 432 -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].
% 4.08/4.37 433 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(20,b,1,a)].
% 4.08/4.37 434 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(20,b,3,a)].
% 4.08/4.37 435 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 4.08/4.37 436 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 4.08/4.37 437 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(108,a,92,b)].
% 4.08/4.37 438 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)].
% 4.08/4.37 439 -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)].
% 4.08/4.37 440 -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)].
% 4.08/4.37 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(164,a,140,b)].
% 4.08/4.37 442 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(167,a,140,b)].
% 4.08/4.37 443 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(168,a,140,b)].
% 4.08/4.37 444 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(198,b,179,b)].
% 4.08/4.37 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)].
% 4.08/4.37 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(444,b,417,a)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(444,b,418,b)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(444,b,428,b)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(444,b,429,b)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(444,b,430,b)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(444,b,431,b)].
% 4.08/4.37 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(444,b,432,b)].
% 4.08/4.37 445 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)].
% 4.08/4.37 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)].
% 4.08/4.37 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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.39 446 -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)].
% 4.14/4.39 447 -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)].
% 4.14/4.39 448 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 4.14/4.39 449 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 4.14/4.39 450 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 4.14/4.39 451 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(205,b,179,b)].
% 4.14/4.39 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(451,b,416,a)].
% 4.14/4.39 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(451,b,417,a)].
% 4.14/4.39 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(451,b,418,b)].
% 4.14/4.39 452 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(206,b,179,b)].
% 4.14/4.39 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(452,b,416,a)].
% 4.14/4.39 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(452,b,417,a)].
% 4.14/4.39 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(452,b,418,b)].
% 4.14/4.39 453 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 4.14/4.39 454 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 4.14/4.39 455 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(282,b,253,b)].
% 4.14/4.39 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(455,b,416,a)].
% 4.14/4.39 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(455,b,417,a)].
% 4.14/4.39 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(455,b,418,b)].
% 4.14/4.39 456 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(283,b,253,b)].
% 4.14/4.39 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(456,b,416,a)].
% 4.14/4.39 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(456,b,417,a)].
% 4.14/4.39 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(456,b,418,b)].
% 4.14/4.39 457 -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)].
% 4.14/4.39 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)].
% 4.14/4.39 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)].
% 4.14/4.40 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)].
% 4.14/4.40 458 -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)].
% 4.14/4.40 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)].
% 4.14/4.40 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)].
% 4.14/4.40 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_Numeral_Onumber__ring(A). [resolve(458,c,418,b)].
% 4.14/4.40 459 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,286,a)].
% 4.14/4.40 460 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,288,a)].
% 4.14/4.40 461 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(320,a,293,b)].
% 4.14/4.40 462 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(321,a,293,b)].
% 4.14/4.40 463 -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)].
% 4.14/4.40 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)].
% 4.14/4.40 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)].
% 4.14/4.40 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)].
% 4.14/4.40 464 -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)].
% 4.14/4.40 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)].
% 4.14/4.40 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)].
% 4.14/4.41 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)].
% 4.14/4.41 465 -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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 466 -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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 467 -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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 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)].
% 4.14/4.41 468 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(350,a,335,b)].
% 4.14/4.41 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(468,b,416,a)].
% 4.14/4.41 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(468,b,417,a)].
% 4.14/4.41 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(468,b,418,b)].
% 4.14/4.41 469 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(351,a,335,b)].
% 4.14/4.41 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(469,b,416,a)].
% 4.14/4.41 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(469,b,417,a)].
% 4.14/4.41 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(469,b,418,b)].
% 4.14/4.41 470 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(368,a,335,b)].
% 4.14/4.41 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)].
% 4.14/4.41 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(470,b,417,a)].
% 4.14/4.41 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(470,b,418,b)].
% 4.14/4.41 471 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(369,a,335,b)].
% 4.14/4.41 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)].
% 4.14/4.41 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(471,b,417,a)].
% 4.14/4.41 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(471,b,418,b)].
% 4.14/4.41 472 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(370,c,335,b)].
% 4.14/4.41 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(472,c,416,a)].
% 4.14/4.41 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(472,c,417,a)].
% 4.14/4.41 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(472,c,418,b)].
% 4.14/4.41 473 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(371,c,335,b)].
% 4.14/4.41 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(473,c,416,a)].
% 4.30/4.54 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(473,c,417,a)].
% 4.30/4.54 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(473,c,418,b)].
% 4.30/4.54 474 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(372,b,335,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(474,b,416,a)].
% 4.30/4.54 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(474,b,417,a)].
% 4.30/4.54 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(474,b,418,b)].
% 4.30/4.54 475 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(405,b,379,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(475,b,416,a)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(475,b,417,a)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(475,b,418,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(475,b,428,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(475,b,429,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(475,b,430,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(475,b,431,b)].
% 4.30/4.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(475,b,432,b)].
% 4.30/4.54 476 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(406,b,379,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(476,b,416,a)].
% 4.30/4.54 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(476,b,417,a)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(476,b,418,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(476,b,428,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(476,b,429,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(476,b,430,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(476,b,431,b)].
% 4.30/4.54 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(476,b,432,b)].
% 4.30/4.54 477 -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].
% 4.30/4.54 478 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].
% 4.30/4.54 Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(477,a,478,a)].
% 4.30/4.54 479 -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].
% 4.30/4.54 Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(479,a,478,a)].
% 4.30/4.54 480 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 4.30/4.54 Derived: c_0 != c_1. [resolve(480,a,477,a)].
% 4.30/4.54 Derived: c_1 != c_0. [resolve(480,a,479,a)].
% 4.30/4.54 481 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 4.30/4.54 482 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 4.30/4.54 483 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 4.30/4.54 484 -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].
% 4.30/4.54 485 -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].
% 4.55/4.79 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(485,a,478,a)].
% 4.55/4.79 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(485,a,483,b)].
% 4.55/4.79 486 -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].
% 4.55/4.79 487 -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].
% 4.55/4.79 488 -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].
% 4.55/4.79 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(488,b,485,a)].
% 4.55/4.79 489 -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].
% 4.55/4.79 490 -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].
% 4.55/4.79 491 -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].
% 4.55/4.79 492 -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].
% 4.55/4.79 493 -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].
% 4.55/4.79 494 -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].
% 4.55/4.79 495 -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].
% 4.55/4.79 496 -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].
% 4.55/4.79 497 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 4.55/4.79 498 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].
% 4.55/4.79 499 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 4.55/4.79 500 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 4.55/4.79 501 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 4.55/4.79 502 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 4.55/4.79 503 -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].
% 4.55/4.79 504 -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].
% 4.55/4.79 505 -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].
% 4.55/4.79 506 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 4.55/4.79 507 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 4.55/4.79 508 -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].
% 4.55/4.81 509 -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].
% 4.55/4.81 510 -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].
% 4.55/4.81 511 -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].
% 4.55/4.81 512 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom). [assumption].
% 4.55/4.81 513 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(513,a,503,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(513,a,504,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(513,a,506,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(513,a,507,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(513,a,508,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(513,a,509,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(513,a,510,b)].
% 4.55/4.81 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(513,a,511,b)].
% 4.55/4.81 514 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 4.55/4.81 515 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 4.55/4.81 516 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 4.55/4.81 517 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 4.55/4.81 518 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 4.55/4.81 519 -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].
% 4.55/4.81 520 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(131,b,110,a)].
% 4.55/4.81 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(520,a,498,a)].
% 4.55/4.81 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(520,a,499,a)].
% 4.55/4.81 Derived: c_times(c_1,A,tc_nat) = A. [resolve(520,a,500,a)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(520,a,501,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(520,a,502,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(520,a,503,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(520,a,504,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(520,a,505,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(520,a,506,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(520,a,507,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(520,a,508,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(520,a,509,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(520,a,510,b)].
% 4.55/4.81 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(520,a,511,b)].
% 4.55/4.81 521 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(131,b,113,a)].
% 4.74/4.99 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(521,a,498,a)].
% 4.74/4.99 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(521,a,499,a)].
% 4.74/4.99 Derived: c_times(A,c_1,tc_nat) = A. [resolve(521,a,500,a)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(521,a,501,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(521,a,502,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(521,a,503,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(521,a,504,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(521,a,505,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(521,a,506,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(521,a,507,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(521,a,508,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(521,a,509,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(521,a,510,b)].
% 4.74/4.99 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(521,a,511,b)].
% 4.74/4.99 522 -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)].
% 4.74/4.99 523 -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)].
% 4.74/4.99 524 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(171,b,166,a)].
% 4.74/4.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(524,a,504,b)].
% 4.74/4.99 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(524,a,519,b)].
% 4.74/4.99 525 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 4.74/4.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(525,a,504,b)].
% 4.74/4.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(525,a,505,b)].
% 4.74/4.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(525,a,510,b)].
% 4.74/4.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(525,a,511,b)].
% 4.74/4.99 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(525,a,519,b)].
% 4.74/4.99 526 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 4.74/4.99 527 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].
% 4.74/4.99 528 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 4.74/4.99 529 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 4.74/4.99 530 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 4.74/4.99 531 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 4.74/4.99 532 -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].
% 4.74/4.99 533 -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].
% 4.74/4.99 534 -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].
% 4.74/4.99 535 -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].
% 4.74/5.05 536 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_13) # label(axiom). [assumption].
% 4.74/5.05 537 -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].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(537,a,527,a)].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(537,a,528,a)].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(537,a,529,a)].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(537,a,530,b)].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(537,a,531,b)].
% 4.74/5.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(537,a,532,b)].
% 4.74/5.05 538 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 4.74/5.05 539 -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].
% 4.74/5.05 540 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 4.74/5.05 541 -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].
% 4.74/5.05 542 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 4.74/5.05 543 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 4.74/5.05 544 -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].
% 4.74/5.05 545 -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].
% 4.74/5.05 546 -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].
% 4.74/5.05 547 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(108,a,97,b)].
% 4.74/5.05 548 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)].
% 4.74/5.05 549 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(123,b,110,a)].
% 4.74/5.05 550 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(123,b,113,a)].
% 4.74/5.05 551 -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)].
% 4.74/5.05 552 -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)].
% 4.74/5.05 553 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,145,b)].
% 4.74/5.05 554 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,145,b)].
% 4.74/5.05 555 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,145,b)].
% 4.74/5.05 556 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(167,a,145,b)].
% 4.74/5.05 557 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(168,a,145,b)].
% 4.86/5.11 558 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 4.86/5.11 559 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 4.86/5.11 560 -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)].
% 4.86/5.11 561 -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)].
% 4.86/5.11 562 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(513,a,504,b)].
% 4.86/5.11 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(562,b,527,a)].
% 4.86/5.11 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(562,b,528,a)].
% 4.86/5.11 Derived: class_HOL_Oone(tc_nat). [resolve(562,b,529,a)].
% 4.86/5.11 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(562,b,530,b)].
% 4.86/5.11 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(562,b,531,b)].
% 4.86/5.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(562,b,532,b)].
% 4.86/5.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(562,b,541,b)].
% 4.86/5.11 563 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(520,a,504,b)].
% 4.86/5.11 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(563,b,527,a)].
% 4.86/5.11 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(563,b,528,a)].
% 4.86/5.11 Derived: c_times(c_1,A,tc_nat) = A. [resolve(563,b,529,a)].
% 4.86/5.11 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(563,b,530,b)].
% 4.86/5.11 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(563,b,531,b)].
% 4.86/5.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(563,b,532,b)].
% 4.86/5.11 564 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(521,a,504,b)].
% 4.86/5.11 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(564,b,527,a)].
% 4.86/5.11 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(564,b,528,a)].
% 4.86/5.11 Derived: c_times(A,c_1,tc_nat) = A. [resolve(564,b,529,a)].
% 4.86/5.11 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(564,b,530,b)].
% 4.86/5.11 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(564,b,531,b)].
% 4.86/5.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(564,b,532,b)].
% 4.86/5.11 565 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(524,a,504,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(565,b,527,a)].
% 4.86/5.11 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(565,b,528,a)].
% 4.86/5.11 Derived: class_HOL_Oplus(tc_nat). [resolve(565,b,529,a)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(565,b,530,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(565,b,531,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(565,b,532,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(565,b,541,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(565,b,542,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(565,b,543,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(565,b,544,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(565,b,545,b)].
% 4.86/5.11 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(565,b,546,b)].
% 4.86/5.11 566 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(525,a,504,b)].
% 4.86/5.11 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(566,b,527,a)].
% 4.99/5.25 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(566,b,528,a)].
% 4.99/5.25 Derived: class_HOL_Ozero(tc_nat). [resolve(566,b,529,a)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(566,b,530,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(566,b,531,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(566,b,532,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(566,b,542,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(566,b,543,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(566,b,544,b)].
% 4.99/5.25 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(566,b,545,b)].
% 4.99/5.25 567 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 4.99/5.25 568 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].
% 4.99/5.25 569 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 4.99/5.25 570 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 4.99/5.25 571 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 4.99/5.25 572 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 4.99/5.25 573 -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].
% 4.99/5.25 574 -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].
% 4.99/5.25 575 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 4.99/5.25 576 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 4.99/5.25 577 -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].
% 4.99/5.25 578 -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].
% 4.99/5.25 579 -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].
% 4.99/5.25 580 -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].
% 4.99/5.25 581 -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].
% 4.99/5.25 582 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 4.99/5.25 583 -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].
% 4.99/5.25 584 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 4.99/5.25 585 -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].
% 4.99/5.25 586 -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].
% 4.99/5.25 587 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_8) # label(axiom). [assumption].
% 5.19/5.47 588 -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)].
% 5.19/5.47 589 -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)].
% 5.19/5.47 590 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 5.19/5.47 591 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 5.19/5.47 592 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(132,b,110,a)].
% 5.19/5.47 593 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(132,b,113,a)].
% 5.19/5.47 594 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(132,b,118,a)].
% 5.19/5.47 595 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(132,b,119,a)].
% 5.19/5.47 596 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(132,b,120,a)].
% 5.19/5.47 597 -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)].
% 5.19/5.47 598 -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)].
% 5.19/5.47 599 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(319,b,286,a)].
% 5.19/5.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,574,b)].
% 5.19/5.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,579,b)].
% 5.19/5.47 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,580,b)].
% 5.19/5.47 600 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(319,b,288,a)].
% 5.19/5.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(600,a,574,b)].
% 5.19/5.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(600,a,579,b)].
% 5.19/5.47 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(600,a,580,b)].
% 5.19/5.47 601 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(322,a,319,b)].
% 5.19/5.47 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(601,b,570,a)].
% 5.19/5.47 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(601,b,572,b)].
% 5.19/5.47 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(601,b,574,b)].
% 5.19/5.47 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(601,b,579,b)].
% 5.19/5.47 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(601,b,580,b)].
% 5.19/5.47 602 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(524,a,519,b)].
% 5.19/5.47 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(602,b,580,b)].
% 5.19/5.47 603 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(525,a,519,b)].
% 5.19/5.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(603,b,574,b)].
% 5.19/5.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(603,b,579,b)].
% 5.19/5.47 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(603,b,580,b)].
% 5.19/5.47 604 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 5.19/5.47 605 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].
% 5.19/5.47 606 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 5.19/5.52 607 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 5.19/5.52 608 -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].
% 5.19/5.52 609 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 5.19/5.52 610 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 5.19/5.52 611 -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].
% 5.19/5.52 612 -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].
% 5.19/5.52 613 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 5.19/5.52 614 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 5.19/5.52 615 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 5.19/5.52 616 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom). [assumption].
% 5.19/5.52 617 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 5.19/5.52 618 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 5.19/5.52 619 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom). [assumption].
% 5.19/5.52 620 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 5.19/5.52 621 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 5.19/5.52 622 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(38,b,1,a)].
% 5.19/5.52 623 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(38,b,3,a)].
% 5.19/5.52 624 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 5.19/5.52 625 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 5.19/5.52 626 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 5.19/5.52 627 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(130,b,110,a)].
% 5.19/5.52 628 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(130,b,113,a)].
% 5.19/5.52 629 -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)].
% 5.19/5.52 630 -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)].
% 5.19/5.52 631 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(167,a,163,b)].
% 5.19/5.52 632 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(168,a,163,b)].
% 5.19/5.52 633 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 5.19/5.52 634 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 5.19/5.52 635 -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)].
% 5.19/5.52 636 -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)].
% 5.29/5.54 637 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,286,a)].
% 5.29/5.54 638 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,288,a)].
% 5.29/5.54 639 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(320,a,311,b)].
% 5.29/5.54 640 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(321,a,311,b)].
% 5.29/5.54 641 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(322,a,311,b)].
% 5.29/5.54 642 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(323,a,311,b)].
% 5.29/5.54 643 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,311,b)].
% 5.29/5.54 644 -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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 645 -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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 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)].
% 5.29/5.54 646 -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)].
% 5.29/5.54 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 647 -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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 648 -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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 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)].
% 5.29/5.57 649 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(513,a,511,b)].
% 5.29/5.57 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(649,b,609,b)].
% 5.29/5.57 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(649,b,610,b)].
% 5.29/5.57 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(649,b,611,b)].
% 5.29/5.57 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(649,b,612,b)].
% 5.29/5.57 650 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(520,a,511,b)].
% 5.29/5.57 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(650,b,609,b)].
% 5.29/5.57 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(650,b,610,b)].
% 5.29/5.57 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(650,b,611,b)].
% 5.29/5.57 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(650,b,612,b)].
% 5.29/5.57 651 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(521,a,511,b)].
% 5.29/5.57 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(651,b,609,b)].
% 5.29/5.57 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(651,b,610,b)].
% 5.29/5.57 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(651,b,611,b)].
% 5.29/5.57 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(651,b,612,b)].
% 5.29/5.57 652 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(525,a,511,b)].
% 5.29/5.57 653 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,580,b)].
% 5.29/5.57 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)].
% 5.29/5.57 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(653,b,606,a)].
% 5.29/5.57 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(653,b,607,b)].
% 5.29/5.57 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(653,b,608,b)].
% 5.37/5.63 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(653,b,609,b)].
% 5.37/5.63 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(653,b,610,b)].
% 5.37/5.63 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(653,b,611,b)].
% 5.37/5.63 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(653,b,612,b)].
% 5.37/5.63 654 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(600,a,580,b)].
% 5.37/5.63 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)].
% 5.37/5.63 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(654,b,606,a)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(654,b,607,b)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(654,b,608,b)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(654,b,609,b)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(654,b,610,b)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(654,b,611,b)].
% 5.37/5.63 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(654,b,612,b)].
% 5.37/5.63 655 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(601,b,580,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(655,b,605,a)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(655,b,606,a)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(655,b,607,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(655,b,608,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(655,b,609,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(655,b,610,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(655,b,611,b)].
% 5.37/5.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(655,b,612,b)].
% 5.37/5.63 656 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(602,b,580,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(656,b,605,a)].
% 5.37/5.63 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(656,b,606,a)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(656,b,607,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(656,b,608,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(656,b,609,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(656,b,610,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(656,b,611,b)].
% 5.37/5.63 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(656,b,612,b)].
% 5.37/5.63 657 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(603,b,580,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(657,b,605,a)].
% 5.37/5.63 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(657,b,606,a)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(657,b,607,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(657,b,608,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(657,b,609,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(657,b,610,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(657,b,611,b)].
% 5.37/5.63 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(657,b,612,b)].
% 5.37/5.63 658 -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].
% 5.37/5.67 659 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].
% 5.37/5.67 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)].
% 5.37/5.67 660 -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].
% 5.37/5.67 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)].
% 5.37/5.67 661 -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].
% 5.37/5.67 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)].
% 5.37/5.67 662 -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].
% 5.37/5.67 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)].
% 5.37/5.67 663 -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].
% 5.37/5.67 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)].
% 5.37/5.67 664 -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].
% 5.37/5.67 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)].
% 5.37/5.67 665 -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].
% 5.37/5.67 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)].
% 5.37/5.67 666 -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].
% 5.37/5.67 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)].
% 5.37/5.67 667 -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].
% 5.37/5.67 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)].
% 5.37/5.67 668 -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].
% 5.37/5.67 Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(668,a,659,a)].
% 5.37/5.67 669 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 5.37/5.67 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,658,a)].
% 5.37/5.67 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,660,a)].
% 5.37/5.67 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)].
% 5.37/5.67 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)].
% 5.44/5.69 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(669,a,663,a)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(669,a,665,a)].
% 5.44/5.69 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)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(669,a,668,a)].
% 5.44/5.69 670 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 5.44/5.69 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(670,a,658,a)].
% 5.44/5.69 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(670,a,660,a)].
% 5.44/5.69 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)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(670,a,663,a)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(670,a,665,a)].
% 5.44/5.69 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)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(670,a,668,a)].
% 5.44/5.69 671 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 5.44/5.69 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(671,b,658,a)].
% 5.44/5.69 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(671,b,660,a)].
% 5.44/5.69 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)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(671,b,663,a)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(671,b,665,a)].
% 5.44/5.69 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)].
% 5.44/5.69 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)].
% 5.44/5.69 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(671,b,668,a)].
% 5.44/5.69 672 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 5.44/5.69 Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(672,b,658,a)].
% 5.44/5.69 Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(672,b,660,a)].
% 5.44/5.69 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)].
% 5.46/5.70 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)].
% 5.46/5.70 Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(672,b,663,a)].
% 5.46/5.70 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)].
% 5.46/5.70 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(672,b,665,a)].
% 5.46/5.70 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)].
% 5.46/5.70 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)].
% 5.46/5.70 Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A). [resolve(672,b,668,a)].
% 5.46/5.70 673 -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].
% 5.46/5.70 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(673,b,658,a)].
% 5.46/5.70 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(673,b,660,a)].
% 5.46/5.70 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)].
% 5.46/5.70 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)].
% 5.46/5.70 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)].
% 5.46/5.70 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)].
% 5.46/5.70 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(673,b,665,a)].
% 5.46/5.70 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)].
% 5.46/5.70 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)].
% 5.46/5.70 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A). [resolve(673,b,668,a)].
% 5.46/5.70 674 -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].
% 5.46/5.70 675 -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].
% 5.46/5.70 676 -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].
% 5.46/5.70 677 -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].
% 5.46/5.70 678 -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].
% 5.46/5.70 679 -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].
% 5.46/5.70 680 -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].
% 5.46/5.70 681 -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].
% 5.46/5.70 682 -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].
% 5.46/5.71 683 -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].
% 5.46/5.71 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(683,b,658,a)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(683,b,660,a)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(683,b,663,a)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(683,b,665,a)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A). [resolve(683,b,668,a)].
% 5.46/5.71 684 -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].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(684,b,658,a)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(684,b,660,a)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(684,b,663,a)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(684,b,665,a)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(684,b,668,a)].
% 5.46/5.71 685 -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].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(685,b,658,a)].
% 5.46/5.71 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(685,b,660,a)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.46/5.71 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(685,b,665,a)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A). [resolve(685,b,668,a)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(685,b,681,a)].
% 5.49/5.73 686 -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].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(686,b,658,a)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(686,b,660,a)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(686,b,665,a)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(686,b,668,a)].
% 5.49/5.73 687 -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].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(687,b,658,a)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(687,b,660,a)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(687,b,665,a)].
% 5.49/5.73 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)].
% 5.49/5.73 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)].
% 5.49/5.73 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(687,b,668,a)].
% 5.49/5.73 688 -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)].
% 5.49/5.80 689 -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)].
% 5.49/5.80 690 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 5.49/5.80 691 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 5.49/5.80 692 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 5.49/5.80 693 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 5.49/5.80 694 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 5.49/5.80 695 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(108,a,98,b)].
% 5.49/5.80 696 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)].
% 5.49/5.80 697 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(124,b,110,a)].
% 5.49/5.81 698 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(124,b,113,a)].
% 5.49/5.81 699 -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)].
% 5.49/5.81 700 -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)].
% 5.49/5.81 701 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 5.49/5.81 702 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 5.49/5.81 703 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 5.49/5.81 704 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(205,b,188,b)].
% 5.49/5.81 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(704,b,670,a)].
% 5.49/5.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(704,b,672,b)].
% 5.49/5.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(704,b,673,b)].
% 5.49/5.81 705 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(206,b,188,b)].
% 5.49/5.81 Derived: class_HOL_Otimes(tc_nat). [resolve(705,b,670,a)].
% 5.49/5.81 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(705,b,672,b)].
% 5.49/5.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(705,b,673,b)].
% 5.49/5.81 706 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 5.49/5.81 707 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 5.49/5.81 708 -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)].
% 5.49/5.81 709 -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)].
% 5.49/5.81 710 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,286,a)].
% 5.49/5.81 711 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,288,a)].
% 5.49/5.81 712 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)].
% 5.49/5.81 713 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)].
% 5.49/5.81 714 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(488,b,485,a)].
% 5.66/5.93 715 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(520,a,505,b)].
% 5.66/5.93 716 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(521,a,505,b)].
% 5.66/5.93 717 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(525,a,505,b)].
% 5.66/5.93 718 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(562,b,541,b)].
% 5.66/5.93 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(718,b,659,a)].
% 5.66/5.93 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(718,b,669,a)].
% 5.66/5.93 Derived: class_HOL_Oone(tc_nat). [resolve(718,b,670,a)].
% 5.66/5.93 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(718,b,671,b)].
% 5.66/5.93 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(718,b,672,b)].
% 5.66/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(718,b,673,b)].
% 5.66/5.93 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(718,b,687,b)].
% 5.66/5.93 719 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(565,b,541,b)].
% 5.66/5.93 Derived: class_HOL_Oplus(tc_nat). [resolve(719,b,670,a)].
% 5.66/5.93 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(719,b,672,b)].
% 5.66/5.93 720 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,574,b)].
% 5.66/5.93 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(720,b,670,a)].
% 5.66/5.93 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(720,b,672,b)].
% 5.66/5.93 721 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(600,a,574,b)].
% 5.66/5.93 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(721,b,670,a)].
% 5.66/5.93 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(721,b,672,b)].
% 5.66/5.93 722 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(601,b,574,b)].
% 5.66/5.93 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(722,b,670,a)].
% 5.66/5.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(722,b,672,b)].
% 5.66/5.93 723 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(603,b,574,b)].
% 5.66/5.93 Derived: class_HOL_Ozero(tc_nat). [resolve(723,b,670,a)].
% 5.66/5.93 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(723,b,672,b)].
% 5.66/5.93 724 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom). [assumption].
% 5.66/5.93 725 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom). [assumption].
% 5.66/5.93 726 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom). [assumption].
% 5.66/5.93 727 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom). [assumption].
% 5.66/5.93 728 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom). [assumption].
% 5.66/5.93 729 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 5.66/5.93 730 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom). [assumption].
% 5.66/5.93 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(724,a,725,a)].
% 5.66/5.93 Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(724,a,726,a)].
% 5.66/5.93 731 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom). [assumption].
% 5.66/5.93 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(731,a,725,a)].
% 5.66/5.93 Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(731,a,726,a)].
% 5.66/5.93 732 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 5.66/5.96 733 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 5.66/5.96 734 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 5.66/5.96 735 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 5.66/5.96 736 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 5.66/5.96 737 -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].
% 5.66/5.96 738 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom). [assumption].
% 5.66/5.96 739 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 5.66/5.96 740 -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].
% 5.66/5.96 741 -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].
% 5.66/5.96 742 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom). [assumption].
% 5.66/5.96 743 -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].
% 5.66/5.96 744 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom). [assumption].
% 5.66/5.96 745 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 5.66/5.96 746 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 5.66/5.96 747 -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].
% 5.66/5.96 748 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_27) # label(axiom). [assumption].
% 5.66/5.96 749 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 5.66/5.96 750 -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].
% 5.66/5.96 751 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 5.66/5.96 752 -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].
% 5.66/5.96 753 -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].
% 5.66/5.96 754 -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].
% 5.75/5.98 755 -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].
% 5.75/5.98 756 -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].
% 5.75/5.98 757 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 5.75/5.98 758 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 5.75/5.98 759 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 5.75/5.98 760 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 5.75/5.98 761 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 5.75/5.98 762 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 5.75/5.98 763 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 5.75/5.98 764 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 5.75/5.98 765 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 5.75/5.98 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(765,b,724,a)].
% 5.75/5.98 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(765,b,731,a)].
% 5.75/5.98 766 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 5.75/5.98 767 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 5.75/5.98 768 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 5.75/5.98 769 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,134,a)].
% 5.75/5.98 770 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(164,a,139,b)].
% 5.75/5.98 771 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(164,a,141,b)].
% 5.75/5.98 772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(164,a,147,b)].
% 5.75/5.98 773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(164,a,148,b)].
% 5.75/5.98 774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(164,a,149,b)].
% 5.75/5.98 775 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(164,a,150,b)].
% 5.75/5.98 776 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(164,a,151,b)].
% 5.75/5.98 777 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(164,a,152,b)].
% 5.75/5.98 778 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(164,a,154,b)].
% 5.75/5.98 779 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(164,a,155,b)].
% 5.75/5.98 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(779,a,724,a)].
% 5.75/5.98 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(779,a,731,a)].
% 5.75/5.98 780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(164,a,157,b)].
% 5.75/5.98 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(780,a,724,a)].
% 5.75/5.98 781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(164,a,158,b)].
% 5.79/6.04 782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,159,b)].
% 5.79/6.04 783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,161,b)].
% 5.79/6.04 784 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 5.79/6.04 785 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 5.79/6.04 786 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(202,b,176,a)].
% 5.79/6.04 787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 5.79/6.04 788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 5.79/6.04 789 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 5.79/6.04 790 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 5.79/6.04 791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(322,a,303,b)].
% 5.79/6.04 792 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(322,a,309,b)].
% 5.79/6.04 793 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(372,b,328,a)].
% 5.79/6.04 794 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(372,b,333,a)].
% 5.79/6.04 795 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(372,b,334,b)].
% 5.79/6.04 796 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(372,b,336,b)].
% 5.79/6.04 797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(372,b,337,b)].
% 5.79/6.04 798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(372,b,338,b)].
% 5.79/6.04 799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(372,b,339,b)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(799,a,724,a)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(799,a,731,a)].
% 5.79/6.04 800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,b,340,b)].
% 5.79/6.04 801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,b,341,b)].
% 5.79/6.04 802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(372,b,342,b)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(802,a,724,a)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(802,a,731,a)].
% 5.79/6.04 803 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(372,b,343,b)].
% 5.79/6.04 804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(372,b,344,b)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(804,a,724,a)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(804,a,731,a)].
% 5.79/6.04 805 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(474,b,416,a)].
% 5.79/6.04 806 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(474,b,417,a)].
% 5.79/6.04 807 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(474,b,418,b)].
% 5.79/6.04 808 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(601,b,570,a)].
% 5.79/6.04 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(808,a,724,a)].
% 5.79/6.04 809 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(601,b,572,b)].
% 5.79/6.04 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,724,a)].
% 5.79/6.04 810 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(601,b,579,b)].
% 5.79/6.04 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(810,a,724,a)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(810,a,731,a)].
% 5.89/6.15 811 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(655,b,605,a)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)). [resolve(811,a,724,a)].
% 5.89/6.15 812 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(655,b,606,a)].
% 5.89/6.15 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(812,a,724,a)].
% 5.89/6.15 813 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(655,b,607,b)].
% 5.89/6.15 Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(813,a,724,a)].
% 5.89/6.15 814 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(655,b,608,b)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,724,a)].
% 5.89/6.15 815 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(655,b,609,b)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(815,a,724,a)].
% 5.89/6.15 816 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(655,b,610,b)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(816,a,724,a)].
% 5.89/6.15 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(655,b,611,b)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(817,a,724,a)].
% 5.89/6.15 818 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(655,b,612,b)].
% 5.89/6.15 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(818,a,724,a)].
% 5.89/6.15 819 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(722,b,670,a)].
% 5.89/6.15 Derived: class_HOL_Oplus(tc_nat). [resolve(819,a,731,a)].
% 5.89/6.15 820 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(722,b,672,b)].
% 5.89/6.15 Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A). [resolve(820,a,731,a)].
% 5.89/6.15 821 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 5.89/6.15 822 -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].
% 5.89/6.15 823 -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].
% 5.89/6.15 824 -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].
% 5.89/6.15 825 -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].
% 5.89/6.15 826 -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].
% 5.89/6.15 827 -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].
% 5.89/6.15 828 -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].
% 5.89/6.15 829 -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].
% 5.89/6.15 830 -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].
% 5.89/6.15 831 -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].
% 5.89/6.15 832 -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].
% 5.89/6.15 833 -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].
% 5.89/6.15 834 -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].
% 5.89/6.15 835 -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].
% 5.89/6.15 836 -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].
% 5.89/6.15 837 -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].
% 5.89/6.15 838 -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].
% 5.89/6.15 839 -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].
% 5.89/6.15 840 -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].
% 5.89/6.15 841 -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].
% 5.89/6.15 842 -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].
% 5.89/6.15 843 -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].
% 5.89/6.15 844 -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].
% 5.89/6.15 845 -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].
% 5.89/6.15 846 -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].
% 5.89/6.15 847 -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].
% 5.89/6.15 848 -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].
% 5.89/6.15 849 -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].
% 5.89/6.15 850 -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].
% 5.89/6.15 851 -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].
% 5.89/6.15 852 -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].
% 5.89/6.15 853 -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].
% 5.89/6.15 854 -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].
% 5.89/6.15 855 -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].
% 5.89/6.15 856 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 5.89/6.15 857 -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].
% 5.89/6.15 858 -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].
% 5.89/6.15 859 -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].
% 5.89/6.15 860 -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].
% 5.89/6.15 861 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 5.89/6.15 862 -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].
% 5.89/6.15 863 -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].
% 5.89/6.15 864 -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].
% 5.89/6.15 865 -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].
% 5.89/6.15 866 -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].
% 5.89/6.15 867 -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].
% 5.89/6.16 868 -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].
% 5.89/6.16 869 -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].
% 5.89/6.16 870 -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].
% 5.89/6.16 871 -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].
% 5.89/6.16 872 -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].
% 5.89/6.16 873 -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].
% 5.89/6.16 874 -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].
% 5.89/6.16 875 -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].
% 5.89/6.16 876 -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].
% 5.89/6.16 877 -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].
% 5.89/6.16 878 -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].
% 5.89/6.16 879 -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].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,831,a)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(821,a,841,a)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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)].
% 5.89/6.16 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(821,a,845,b)].
% 5.89/6.16 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(821,a,846,b)].
% 5.89/6.16 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(821,a,856,a)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(821,a,861,a)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(821,a,867,a)].
% 5.89/6.17 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(821,a,868,a)].
% 5.89/6.17 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(821,a,869,a)].
% 5.89/6.17 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(821,a,870,a)].
% 5.89/6.17 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(821,a,871,a)].
% 5.89/6.17 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(821,a,872,a)].
% 5.89/6.17 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(821,a,873,a)].
% 5.89/6.17 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(821,a,874,a)].
% 5.89/6.17 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(821,a,875,a)].
% 5.89/6.17 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)].
% 5.89/6.17 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(821,a,877,a)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 880 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(880,a,831,a)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.17 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)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(880,a,841,a)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(880,a,847,a)].
% 5.89/6.18 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(880,a,848,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(880,a,850,a)].
% 5.89/6.18 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(880,a,851,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(880,a,853,a)].
% 5.89/6.18 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(880,a,854,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(880,a,856,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(880,a,858,a)].
% 5.89/6.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(880,a,859,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(880,a,861,a)].
% 5.89/6.18 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)].
% 5.89/6.18 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(880,a,863,a)].
% 5.89/6.18 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(880,a,864,a)].
% 5.89/6.18 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(880,a,865,a)].
% 5.89/6.18 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(880,a,866,a)].
% 5.89/6.18 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(880,a,867,a)].
% 5.89/6.18 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(880,a,868,a)].
% 5.89/6.19 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(880,a,869,a)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(880,a,877,a)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 881 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.19 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(881,b,856,a)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(881,b,861,a)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.89/6.20 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 882 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 5.99/6.21 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(882,a,821,a)].
% 5.99/6.21 Derived: class_LOrder_Olorder(tc_nat). [resolve(882,a,880,a)].
% 5.99/6.21 Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(882,a,881,b)].
% 5.99/6.21 883 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 5.99/6.21 Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(883,a,821,a)].
% 5.99/6.21 Derived: class_LOrder_Ojoin__semilorder(tc_nat). [resolve(883,a,880,a)].
% 5.99/6.21 Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(883,a,881,b)].
% 5.99/6.21 884 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 5.99/6.21 Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(884,a,821,a)].
% 5.99/6.21 Derived: class_LOrder_Omeet__semilorder(tc_nat). [resolve(884,a,880,a)].
% 5.99/6.21 Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(884,a,881,b)].
% 5.99/6.21 885 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 5.99/6.21 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(885,a,821,a)].
% 5.99/6.21 Derived: class_Orderings_Oord(tc_nat). [resolve(885,a,880,a)].
% 5.99/6.21 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(885,a,881,b)].
% 5.99/6.21 886 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 5.99/6.21 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(886,a,821,a)].
% 5.99/6.21 Derived: class_Orderings_Oorder(tc_nat). [resolve(886,a,880,a)].
% 5.99/6.21 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(886,a,881,b)].
% 5.99/6.21 887 -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].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.21 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(887,b,856,a)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(887,b,861,a)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.22 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 888 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.23 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B. [resolve(888,b,856,a)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B. [resolve(888,b,861,a)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 889 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.24 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(889,b,856,a)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.25 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)].
% 5.99/6.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(889,b,861,a)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 890 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.26 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(890,b,856,a)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(890,b,861,a)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 891 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.27 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.28 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,856,a)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,861,a)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 5.99/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 892 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.29 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(892,b,856,a)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.30 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)].
% 6.07/6.31 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)].
% 6.07/6.31 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(892,b,861,a)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 893 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,831,a)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 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)].
% 6.07/6.31 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,841,a)].
% 6.07/6.31 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(893,b,856,a)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(893,b,861,a)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 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)].
% 6.07/6.32 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(893,b,867,a)].
% 6.07/6.32 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(893,b,868,a)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(893,b,869,a)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(893,b,877,a)].
% 6.29/6.59 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)].
% 6.29/6.59 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)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(893,b,882,a)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(893,b,883,a)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(893,b,884,a)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(893,b,885,a)].
% 6.29/6.59 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(893,b,886,a)].
% 6.29/6.59 894 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 6.29/6.59 895 -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].
% 6.29/6.59 896 -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].
% 6.29/6.59 897 -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].
% 6.29/6.59 898 -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].
% 6.29/6.59 899 -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].
% 6.29/6.59 900 -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].
% 6.29/6.59 901 -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].
% 6.29/6.59 902 -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].
% 6.29/6.59 903 -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].
% 6.29/6.59 904 -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].
% 6.29/6.59 905 -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].
% 6.29/6.59 906 -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].
% 6.29/6.59 907 -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].
% 6.29/6.59 908 -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].
% 6.29/6.59 909 -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].
% 6.29/6.59 910 -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].
% 6.29/6.59 911 -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].
% 6.29/6.59 912 -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].
% 6.29/6.59 913 -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].
% 6.29/6.59 914 -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].
% 6.29/6.59 915 -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].
% 6.29/6.59 916 -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].
% 6.29/6.59 917 -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].
% 6.29/6.59 918 -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].
% 6.29/6.59 919 -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].
% 6.29/6.59 920 -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].
% 6.29/6.59 921 -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].
% 6.29/6.59 922 -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].
% 6.29/6.59 923 -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].
% 6.29/6.59 924 -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].
% 6.29/6.59 925 -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].
% 6.29/6.59 926 -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].
% 6.29/6.59 927 -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].
% 6.29/6.59 928 -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].
% 6.29/6.59 929 -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].
% 6.29/6.59 930 -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].
% 6.29/6.59 931 -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].
% 6.29/6.59 932 -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].
% 6.29/6.59 933 -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].
% 6.29/6.59 934 -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].
% 6.29/6.59 935 -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].
% 6.29/6.59 936 -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].
% 6.29/6.59 937 -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].
% 6.29/6.59 938 -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].
% 6.29/6.59 939 -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].
% 6.29/6.59 940 -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].
% 6.29/6.59 941 -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].
% 6.29/6.59 942 -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].
% 6.29/6.59 943 -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].
% 6.29/6.59 944 -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].
% 6.29/6.59 945 -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].
% 6.29/6.59 946 -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].
% 6.29/6.59 947 -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].
% 6.29/6.59 948 -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].
% 6.29/6.59 949 -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].
% 6.29/6.59 950 -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].
% 6.29/6.59 951 -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].
% 6.29/6.59 952 -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].
% 6.29/6.59 953 -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].
% 6.29/6.59 954 -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].
% 6.29/6.59 955 -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].
% 6.29/6.59 956 -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].
% 6.29/6.59 957 -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].
% 6.29/6.59 958 -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].
% 6.29/6.59 959 -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].
% 6.37/6.59 960 -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].
% 6.37/6.59 961 -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].
% 6.37/6.59 962 -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].
% 6.37/6.59 963 -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].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.59 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(894,a,936,a)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(894,a,948,a)].
% 6.37/6.60 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(894,a,949,a)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.60 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)].
% 6.37/6.64 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)].
% 6.37/6.64 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)].
% 6.37/6.64 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)].
% 6.37/6.64 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)].
% 6.37/6.64 Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0. [resolve(894,a,960,a)].
% 6.37/6.64 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)].
% 6.37/6.64 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)].
% 6.37/6.64 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)].
% 6.37/6.64 964 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom). [assumption].
% 6.37/6.64 965 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom). [assumption].
% 6.37/6.64 966 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom). [assumption].
% 6.37/6.64 967 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 6.37/6.64 968 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 6.37/6.64 969 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 6.37/6.64 970 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 6.37/6.64 Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(970,a,894,a)].
% 6.37/6.64 971 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom). [assumption].
% 6.37/6.64 972 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom). [assumption].
% 6.37/6.64 Derived: class_Numeral_Onumber(tc_IntDef_Oint). [resolve(972,a,894,a)].
% 6.37/6.64 973 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 6.37/6.64 974 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom). [assumption].
% 6.37/6.64 975 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 6.37/6.64 976 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 6.37/6.64 977 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 6.37/6.64 978 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 6.37/6.64 979 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 6.37/6.64 980 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 6.37/6.64 981 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 6.37/6.64 982 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 6.37/6.68 983 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 6.37/6.68 984 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 6.37/6.68 985 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 6.37/6.68 986 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(108,a,88,b)].
% 6.37/6.68 987 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)].
% 6.37/6.68 988 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(116,b,110,a)].
% 6.37/6.68 989 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(116,b,113,a)].
% 6.37/6.68 990 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(118,a,116,b)].
% 6.37/6.68 991 -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)].
% 6.37/6.68 992 -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)].
% 6.37/6.68 993 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(198,b,177,b)].
% 6.37/6.68 994 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)].
% 6.37/6.68 995 -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)].
% 6.37/6.68 996 -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)].
% 6.37/6.68 997 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 6.37/6.68 998 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 6.37/6.68 999 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(205,b,177,b)].
% 6.37/6.68 1000 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(206,b,177,b)].
% 6.37/6.68 1001 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 6.37/6.68 1002 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 6.37/6.68 1003 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(282,b,251,b)].
% 6.37/6.68 1004 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(283,b,251,b)].
% 6.37/6.68 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)].
% 6.37/6.68 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)].
% 6.37/6.68 1007 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(291,b,286,a)].
% 6.37/6.68 1008 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(291,b,288,a)].
% 6.37/6.68 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)].
% 6.37/6.68 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)].
% 6.37/6.68 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)].
% 6.37/6.68 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)].
% 6.37/6.68 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)].
% 6.47/6.70 1014 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(350,a,334,b)].
% 6.47/6.70 1015 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(351,a,334,b)].
% 6.47/6.70 1016 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(368,a,334,b)].
% 6.47/6.70 1017 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(369,a,334,b)].
% 6.47/6.70 1018 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(370,c,334,b)].
% 6.47/6.70 1019 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(371,c,334,b)].
% 6.47/6.70 1020 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(405,b,377,b)].
% 6.47/6.70 1021 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(406,b,377,b)].
% 6.47/6.70 1022 c_times(A,B,C) = c_times(B,A,C) | -class_Numeral_Onumber__ring(C). [resolve(444,b,418,b)].
% 6.47/6.70 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(1022,b,894,a)].
% 6.47/6.70 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)].
% 6.47/6.70 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)].
% 6.47/6.70 1024 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(451,b,418,b)].
% 6.47/6.70 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1024,b,894,a)].
% 6.47/6.70 1025 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(452,b,418,b)].
% 6.47/6.70 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1025,b,894,a)].
% 6.47/6.70 1026 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(455,b,418,b)].
% 6.47/6.70 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1026,b,894,a)].
% 6.47/6.70 1027 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(456,b,418,b)].
% 6.47/6.70 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)].
% 6.47/6.70 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)].
% 6.47/6.70 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)].
% 6.47/6.70 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(1029,c,894,a)].
% 6.47/6.70 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)].
% 6.47/6.70 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(1030,c,894,a)].
% 6.47/6.70 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)].
% 6.47/6.70 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(1031,c,894,a)].
% 6.49/6.72 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)].
% 6.49/6.72 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(1032,b,894,a)].
% 6.49/6.72 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)].
% 6.49/6.72 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(1033,b,894,a)].
% 6.49/6.72 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)].
% 6.49/6.72 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(1034,b,894,a)].
% 6.49/6.72 1035 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(468,b,418,b)].
% 6.49/6.72 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1035,b,894,a)].
% 6.49/6.72 1036 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(469,b,418,b)].
% 6.49/6.72 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1036,b,894,a)].
% 6.49/6.72 1037 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(470,b,418,b)].
% 6.49/6.72 1038 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(471,b,418,b)].
% 6.49/6.72 1039 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(472,c,418,b)].
% 6.49/6.72 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1039,c,894,a)].
% 6.49/6.72 1040 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(473,c,418,b)].
% 6.49/6.72 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1040,c,894,a)].
% 6.49/6.72 1041 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(475,b,418,b)].
% 6.49/6.72 1042 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(476,b,418,b)].
% 6.49/6.72 1043 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(520,a,501,b)].
% 6.49/6.72 1044 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(521,a,501,b)].
% 6.49/6.72 1045 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(537,a,530,b)].
% 6.49/6.72 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(1045,b,894,a)].
% 6.49/6.72 1046 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(562,b,530,b)].
% 6.49/6.72 1047 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(563,b,530,b)].
% 6.49/6.72 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1047,b,894,a)].
% 6.49/6.72 1048 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(564,b,530,b)].
% 6.49/6.72 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1048,b,894,a)].
% 6.49/6.72 1049 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(565,b,530,b)].
% 6.49/6.72 1050 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(566,b,530,b)].
% 6.49/6.72 1051 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(653,b,607,b)].
% 6.49/6.72 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1051,b,894,a)].
% 6.49/6.72 1052 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(654,b,607,b)].
% 6.49/6.72 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1052,b,894,a)].
% 6.49/6.72 1053 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(656,b,607,b)].
% 6.49/6.72 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1053,b,894,a)].
% 6.49/6.72 1054 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(657,b,607,b)].
% 6.49/6.72 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1054,b,894,a)].
% 6.49/6.72 1055 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(671,b,658,a)].
% 6.49/6.72 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1055,a,894,a)].
% 6.49/6.72 1056 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(671,b,660,a)].
% 6.49/6.72 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1056,a,894,a)].
% 6.49/6.72 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)].
% 6.49/6.72 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)].
% 6.67/6.92 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)].
% 6.67/6.92 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)].
% 6.67/6.92 1059 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(671,b,663,a)].
% 6.67/6.92 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1059,a,894,a)].
% 6.67/6.92 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)].
% 6.67/6.92 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)].
% 6.67/6.92 1061 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(671,b,665,a)].
% 6.67/6.92 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1061,a,894,a)].
% 6.67/6.92 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)].
% 6.67/6.92 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)].
% 6.67/6.92 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)].
% 6.67/6.92 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)].
% 6.67/6.92 1064 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(671,b,668,a)].
% 6.67/6.92 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1064,a,894,a)].
% 6.67/6.92 1065 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(718,b,671,b)].
% 6.67/6.92 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(1065,b,894,a)].
% 6.67/6.92 1066 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(813,a,724,a)].
% 6.67/6.92 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1066,a,894,a)].
% 6.67/6.92 1067 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 6.67/6.92 1068 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 6.67/6.92 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1067,a,1068,a)].
% 6.67/6.92 1069 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 6.67/6.92 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1069,a,1068,a)].
% 6.67/6.92 1070 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 6.67/6.92 1071 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 6.67/6.92 1072 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 6.67/6.92 Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1072,b,1068,a)].
% 6.67/6.92 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1072,b,1070,a)].
% 6.67/6.92 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1072,b,1071,a)].
% 6.67/6.92 1073 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 6.67/6.92 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1073,b,1068,a)].
% 6.67/6.92 1074 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 6.67/6.92 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1074,b,1068,a)].
% 6.91/7.19 1075 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1075,b,1068,a)].
% 6.91/7.19 1076 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1076,b,1068,a)].
% 6.91/7.19 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].
% 6.91/7.19 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1077,b,1068,a)].
% 6.91/7.19 1078 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1078,b,1068,a)].
% 6.91/7.19 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1078,b,1070,a)].
% 6.91/7.19 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1078,b,1071,a)].
% 6.91/7.19 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].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1079,b,1068,a)].
% 6.91/7.19 1080 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1068,a)].
% 6.91/7.19 1081 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1068,a)].
% 6.91/7.19 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].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1068,a)].
% 6.91/7.19 1083 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1068,a)].
% 6.91/7.19 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].
% 6.91/7.19 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1068,a)].
% 6.91/7.19 1085 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 6.91/7.19 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1068,a)].
% 6.91/7.19 1086 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(883,a,821,a)].
% 6.91/7.19 1087 class_LOrder_Ojoin__semilorder(tc_nat). [resolve(883,a,880,a)].
% 6.91/7.19 1088 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(883,a,881,b)].
% 6.91/7.19 1089 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(893,b,883,a)].
% 6.91/7.19 1090 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 6.91/7.19 1091 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 6.98/7.21 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1090,a,1091,a)].
% 6.98/7.21 1092 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 6.98/7.21 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1092,a,1091,a)].
% 6.98/7.21 1093 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1093,b,1091,a)].
% 6.98/7.21 1094 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 6.98/7.21 1095 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 6.98/7.21 1096 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1096,b,1091,a)].
% 6.98/7.21 1097 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1097,b,1091,a)].
% 6.98/7.21 1098 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1098,b,1091,a)].
% 6.98/7.21 1099 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1099,b,1091,a)].
% 6.98/7.21 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].
% 6.98/7.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1100,b,1091,a)].
% 6.98/7.21 1101 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1091,a)].
% 6.98/7.21 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].
% 6.98/7.21 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1102,b,1091,a)].
% 6.98/7.21 1103 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1103,b,1091,a)].
% 6.98/7.21 1104 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1091,a)].
% 6.98/7.21 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].
% 6.98/7.21 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1091,a)].
% 6.98/7.21 1106 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 6.98/7.21 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1091,a)].
% 6.98/7.21 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].
% 7.21/7.47 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1091,a)].
% 7.21/7.47 1108 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 7.21/7.47 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1091,a)].
% 7.21/7.47 1109 class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(884,a,821,a)].
% 7.21/7.47 1110 class_LOrder_Omeet__semilorder(tc_nat). [resolve(884,a,880,a)].
% 7.21/7.47 1111 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(884,a,881,b)].
% 7.21/7.47 1112 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(893,b,884,a)].
% 7.21/7.47 1113 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 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].
% 7.21/7.47 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(1113,a,1114,a)].
% 7.21/7.47 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(1113,a,1115,a)].
% 7.21/7.47 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1113,a,1116,a)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1113,a,1119,a)].
% 7.21/7.47 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(1113,a,1120,a)].
% 7.21/7.47 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(1113,a,1121,a)].
% 7.21/7.47 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1113,a,1122,a)].
% 7.21/7.47 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1113,a,1123,a)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1113,a,1126,a)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.21/7.47 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)].
% 7.27/7.49 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)].
% 7.27/7.49 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(1113,a,1134,a)].
% 7.27/7.49 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(1113,a,1135,a)].
% 7.27/7.49 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(1113,a,1136,a)].
% 7.27/7.49 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(1113,a,1137,a)].
% 7.27/7.49 1138 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 7.27/7.49 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(1138,a,1114,a)].
% 7.27/7.49 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(1138,a,1115,a)].
% 7.27/7.49 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1138,a,1116,a)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(1138,a,1119,a)].
% 7.27/7.49 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(1138,a,1120,a)].
% 7.27/7.49 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(1138,a,1121,a)].
% 7.27/7.49 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(1138,a,1122,a)].
% 7.27/7.49 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(1138,a,1123,a)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat). [resolve(1138,a,1126,a)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 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)].
% 7.27/7.49 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(1138,a,1134,a)].
% 7.27/7.49 Derived: -c_less(c_1,c_0,tc_nat). [resolve(1138,a,1135,a)].
% 7.27/7.49 Derived: c_less(c_0,c_1,tc_nat). [resolve(1138,a,1136,a)].
% 7.27/7.49 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(1138,a,1137,a)].
% 7.27/7.49 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].
% 7.27/7.49 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1139,b,1114,a)].
% 7.27/7.49 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1139,b,1115,a)].
% 7.27/7.49 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1139,b,1116,a)].
% 7.27/7.49 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)].
% 7.27/7.50 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)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1139,b,1119,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1139,b,1120,a)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1139,b,1126,a)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A). [resolve(1139,b,1134,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A). [resolve(1139,b,1135,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A). [resolve(1139,b,1136,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A). [resolve(1139,b,1137,a)].
% 7.27/7.50 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].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1140,b,1114,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1140,b,1115,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1140,b,1116,a)].
% 7.27/7.50 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)].
% 7.27/7.50 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)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1140,b,1119,a)].
% 7.27/7.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1140,b,1120,a)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1140,b,1126,a)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 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)].
% 7.27/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A). [resolve(1140,b,1134,a)].
% 7.27/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A). [resolve(1140,b,1135,a)].
% 7.27/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A). [resolve(1140,b,1136,a)].
% 7.27/7.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A). [resolve(1140,b,1137,a)].
% 7.27/7.51 1141 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 7.27/7.51 1142 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom). [assumption].
% 7.27/7.51 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].
% 7.27/7.51 1144 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom). [assumption].
% 7.27/7.51 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].
% 7.27/7.51 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1145,a,1140,b)].
% 7.27/7.51 1146 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 7.27/7.51 1147 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom). [assumption].
% 7.27/7.51 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].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1148,a,1113,a)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1148,a,1138,a)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1148,a,1139,b)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1148,a,1140,b)].
% 7.27/7.52 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].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1149,a,1113,a)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1149,a,1138,a)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1149,a,1139,b)].
% 7.27/7.52 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1149,a,1140,b)].
% 7.27/7.52 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].
% 7.27/7.52 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1150,a,1113,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1150,a,1138,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1150,a,1139,b)].
% 7.27/7.52 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1150,a,1140,b)].
% 7.27/7.52 1151 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 7.27/7.52 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1151,a,1139,b)].
% 7.27/7.52 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1151,a,1140,b)].
% 7.27/7.52 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].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1152,a,1113,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1152,a,1138,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1152,a,1139,b)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1152,a,1140,b)].
% 7.27/7.52 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].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1153,a,1113,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1153,a,1138,a)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1153,a,1139,b)].
% 7.27/7.52 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1140,b)].
% 7.27/7.52 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].
% 7.27/7.52 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1154,a,1113,a)].
% 7.27/7.52 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1154,a,1138,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1154,a,1139,b)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1154,a,1140,b)].
% 7.27/7.54 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].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1155,a,1113,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1155,a,1138,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1155,a,1139,b)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1155,a,1140,b)].
% 7.27/7.54 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].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1156,a,1113,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1156,a,1138,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1139,b)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1140,b)].
% 7.27/7.54 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].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1157,a,1113,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1157,a,1138,a)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1139,b)].
% 7.27/7.54 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1140,b)].
% 7.27/7.54 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].
% 7.27/7.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1113,a)].
% 7.27/7.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1158,a,1138,a)].
% 7.27/7.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1139,b)].
% 7.27/7.54 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1140,b)].
% 7.27/7.54 1159 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 7.27/7.54 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1139,b)].
% 7.27/7.54 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1140,b)].
% 7.27/7.54 1160 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 7.27/7.54 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1139,b)].
% 7.27/7.54 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1140,b)].
% 7.27/7.54 1161 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 7.27/7.54 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)].
% 7.27/7.54 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)].
% 7.27/7.54 1164 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 7.36/7.60 1165 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 7.36/7.60 1166 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(108,a,104,b)].
% 7.36/7.60 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)].
% 7.36/7.60 1168 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(129,b,110,a)].
% 7.36/7.60 1169 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(129,b,113,a)].
% 7.36/7.60 1170 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(129,b,119,a)].
% 7.36/7.60 1171 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(129,b,120,a)].
% 7.36/7.60 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)].
% 7.36/7.60 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)].
% 7.36/7.60 1174 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 7.36/7.60 1175 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 7.36/7.60 1176 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(205,b,194,b)].
% 7.36/7.60 1177 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(206,b,194,b)].
% 7.36/7.60 1178 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 7.36/7.60 1179 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 7.36/7.60 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)].
% 7.36/7.60 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)].
% 7.36/7.60 1182 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,286,a)].
% 7.36/7.60 1183 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,288,a)].
% 7.36/7.60 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)].
% 7.36/7.60 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)].
% 7.36/7.60 1186 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(513,a,510,b)].
% 7.36/7.60 1187 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(520,a,510,b)].
% 7.36/7.60 1188 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(521,a,510,b)].
% 7.36/7.60 1189 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(525,a,510,b)].
% 7.36/7.60 1190 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(565,b,546,b)].
% 7.36/7.60 1191 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,579,b)].
% 7.36/7.60 1192 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(600,a,579,b)].
% 7.36/7.60 1193 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(603,b,579,b)].
% 7.36/7.60 1194 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(687,b,658,a)].
% 7.36/7.60 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(1194,a,1138,a)].
% 7.36/7.60 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1194,a,1139,b)].
% 7.36/7.60 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1194,a,1140,b)].
% 7.36/7.60 1195 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(687,b,660,a)].
% 7.36/7.60 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(1195,a,1138,a)].
% 7.36/7.60 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1195,a,1139,b)].
% 7.36/7.60 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1195,a,1140,b)].
% 7.36/7.60 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)].
% 7.36/7.60 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)].
% 7.36/7.60 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1196,a,1139,b)].
% 7.36/7.60 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1196,a,1140,b)].
% 7.36/7.60 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1198,a,1138,a)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 1200 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(687,b,665,a)].
% 7.36/7.61 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(1200,a,1138,a)].
% 7.36/7.61 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1200,a,1139,b)].
% 7.36/7.61 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1200,a,1140,b)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.36/7.61 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 1203 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(687,b,668,a)].
% 7.43/7.66 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(1203,a,1138,a)].
% 7.43/7.66 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1203,a,1139,b)].
% 7.43/7.66 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1203,a,1140,b)].
% 7.43/7.66 1204 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(718,b,687,b)].
% 7.43/7.66 Derived: class_HOL_Oone(tc_nat). [resolve(1204,b,1138,a)].
% 7.43/7.66 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1204,b,1139,b)].
% 7.43/7.66 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1204,b,1140,b)].
% 7.43/7.66 1205 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(810,a,724,a)].
% 7.43/7.66 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1205,a,1138,a)].
% 7.43/7.66 1206 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(810,a,731,a)].
% 7.43/7.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1206,a,1139,b)].
% 7.43/7.66 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1206,a,1140,b)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1216,a,1113,a)].
% 7.43/7.66 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1216,a,1138,a)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.66 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1226,a,1113,a)].
% 7.43/7.67 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1226,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1232,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1233,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1235,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1236,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1238,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1239,a,1138,a)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.67 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 1241 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,856,a)].
% 7.43/7.68 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1241,a,1113,a)].
% 7.43/7.68 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1241,a,1138,a)].
% 7.43/7.68 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1241,a,1139,b)].
% 7.43/7.68 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1241,a,1140,b)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1243,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1244,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 1246 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,861,a)].
% 7.43/7.68 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1246,a,1113,a)].
% 7.43/7.68 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1246,a,1138,a)].
% 7.43/7.68 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1246,a,1139,b)].
% 7.43/7.68 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1246,a,1140,b)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1248,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1249,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1250,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1251,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1252,a,1113,a)].
% 7.43/7.68 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1252,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1253,a,1113,a)].
% 7.43/7.68 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1253,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1254,a,1113,a)].
% 7.43/7.68 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1254,a,1138,a)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.68 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1262,a,1113,a)].
% 7.43/7.71 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1262,a,1138,a)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 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)].
% 7.43/7.71 1265 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1068,a)].
% 7.43/7.71 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1265,a,1113,a)].
% 7.65/7.87 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1265,a,1138,a)].
% 7.65/7.87 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1265,a,1139,b)].
% 7.65/7.87 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1265,a,1140,b)].
% 7.65/7.87 1266 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1091,a)].
% 7.65/7.87 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1266,a,1113,a)].
% 7.65/7.87 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1266,a,1138,a)].
% 7.65/7.87 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1266,a,1139,b)].
% 7.65/7.87 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1266,a,1140,b)].
% 7.65/7.87 1267 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.87 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.65/7.88 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(1267,a,1292,a)].
% 7.68/7.89 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].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.89 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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)].
% 7.68/7.90 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].
% 7.68/7.90 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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)].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.91 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 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].
% 7.68/7.92 Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1311,a,1267,a)].
% 7.68/7.92 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1311,a,1293,b)].
% 7.68/7.92 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1311,a,1294,b)].
% 7.68/7.92 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].
% 7.68/7.92 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1312,a,1267,a)].
% 7.68/7.92 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1312,a,1293,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1312,a,1294,b)].
% 7.68/7.92 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].
% 7.68/7.92 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1313,a,1267,a)].
% 7.68/7.92 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1313,a,1293,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1313,a,1294,b)].
% 7.68/7.92 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].
% 7.68/7.92 Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1314,a,1267,a)].
% 7.68/7.92 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1314,a,1293,b)].
% 7.68/7.92 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1314,a,1294,b)].
% 7.68/7.92 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].
% 7.68/7.92 Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1315,a,1267,a)].
% 7.68/7.92 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1315,a,1293,b)].
% 7.68/7.92 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1315,a,1294,b)].
% 7.68/7.92 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].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1316,a,1267,a)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1316,a,1293,b)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1316,a,1294,b)].
% 7.74/7.96 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].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1317,a,1267,a)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1317,a,1293,b)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1317,a,1294,b)].
% 7.74/7.96 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].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1318,a,1267,a)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1318,a,1293,b)].
% 7.74/7.96 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1318,a,1294,b)].
% 7.74/7.96 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].
% 7.74/7.96 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1319,a,1267,a)].
% 7.74/7.96 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1319,a,1293,b)].
% 7.74/7.96 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1319,a,1294,b)].
% 7.74/7.96 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].
% 7.74/7.96 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].
% 7.74/7.96 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)].
% 7.74/7.96 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)].
% 7.74/7.96 1324 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 7.74/7.96 1325 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 7.74/7.96 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)].
% 7.74/7.96 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)].
% 7.74/7.96 1328 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(167,a,153,b)].
% 7.74/7.96 1329 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(168,a,153,b)].
% 7.74/7.96 1330 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 7.74/7.96 1331 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 7.74/7.96 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)].
% 7.74/7.97 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)].
% 7.74/7.97 1334 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,286,a)].
% 7.74/7.97 1335 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,288,a)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.74/7.97 1338 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(323,a,303,b)].
% 7.74/7.97 1339 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,303,b)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.74/7.97 1345 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(350,a,342,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1345,b,1293,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1345,b,1294,b)].
% 7.74/7.97 1346 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(351,a,342,b)].
% 7.74/7.97 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1346,b,1293,b)].
% 7.74/7.97 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1346,b,1294,b)].
% 7.74/7.97 1347 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(362,b,342,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1347,b,1293,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1347,b,1294,b)].
% 7.74/7.97 1348 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(363,b,342,b)].
% 7.74/7.97 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1348,b,1293,b)].
% 7.74/7.97 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1348,b,1294,b)].
% 7.74/7.97 1349 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(364,b,342,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1349,b,1293,b)].
% 7.74/7.97 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1349,b,1294,b)].
% 7.74/7.97 1350 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(365,b,342,b)].
% 7.74/7.97 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)].
% 7.74/7.97 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 1353 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(368,a,342,b)].
% 7.81/8.05 1354 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(369,a,342,b)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 1357 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(802,a,724,a)].
% 7.81/8.05 1358 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(802,a,731,a)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.05 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.81/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 1393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(890,b,856,a)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 1398 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(890,b,861,a)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 7.86/8.06 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)].
% 8.04/8.26 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)].
% 8.04/8.26 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)].
% 8.04/8.26 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)].
% 8.04/8.26 1417 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1068,a)].
% 8.04/8.26 1418 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1091,a)].
% 8.04/8.26 1419 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 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].
% 8.04/8.26 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1420,a)].
% 8.04/8.26 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(1419,a,1421,a)].
% 8.04/8.26 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)].
% 8.04/8.26 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1419,a,1423,a)].
% 8.04/8.26 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(1419,a,1424,a)].
% 8.04/8.28 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1419,a,1425,a)].
% 8.04/8.28 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)].
% 8.04/8.28 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1427,a)].
% 8.04/8.28 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1419,a,1428,a)].
% 8.04/8.28 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)].
% 8.04/8.28 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1419,a,1430,a)].
% 8.04/8.28 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(1419,a,1431,a)].
% 8.04/8.28 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)].
% 8.04/8.28 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1419,a,1433,a)].
% 8.04/8.28 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(1419,a,1434,a)].
% 8.04/8.28 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].
% 8.04/8.28 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].
% 8.04/8.28 1437 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 8.04/8.28 1438 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom). [assumption].
% 8.04/8.28 1439 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 8.04/8.28 1440 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 8.04/8.28 1441 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 8.04/8.28 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].
% 8.04/8.28 1443 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom). [assumption].
% 8.04/8.28 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].
% 8.04/8.28 1445 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom). [assumption].
% 8.04/8.28 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].
% 8.04/8.28 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].
% 8.04/8.28 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].
% 8.04/8.28 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].
% 8.04/8.28 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1449,b,1420,a)].
% 8.04/8.28 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1449,b,1421,a)].
% 8.04/8.28 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1449,b,1423,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1449,b,1424,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1449,b,1425,a)].
% 8.04/8.29 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)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1449,b,1428,a)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1449,b,1430,a)].
% 8.04/8.29 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)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1449,b,1433,a)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1449,b,1436,a)].
% 8.04/8.29 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].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1450,b,1420,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1450,b,1421,a)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1450,b,1423,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1450,b,1424,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1450,b,1425,a)].
% 8.04/8.29 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)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1450,b,1428,a)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1450,b,1430,a)].
% 8.04/8.29 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)].
% 8.04/8.29 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)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1450,b,1433,a)].
% 8.04/8.29 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)].
% 8.04/8.29 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].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1451,b,1420,a)].
% 8.04/8.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1451,b,1421,a)].
% 8.30/8.50 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)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1451,b,1423,a)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1451,b,1424,a)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1451,b,1425,a)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1451,b,1428,a)].
% 8.30/8.50 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)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1451,b,1430,a)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1451,b,1433,a)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 1454 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 8.30/8.50 1455 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 8.30/8.50 1456 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1074,b,1068,a)].
% 8.30/8.50 1457 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1097,b,1091,a)].
% 8.30/8.50 1458 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1316,a,1267,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1458,a,1435,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1458,a,1436,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1458,a,1437,a)].
% 8.30/8.50 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1458,a,1438,a)].
% 8.30/8.50 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1458,a,1439,a)].
% 8.30/8.50 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1458,a,1440,a)].
% 8.30/8.50 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1458,a,1441,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1458,a,1442,a)].
% 8.30/8.50 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1458,a,1443,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1458,a,1444,a)].
% 8.30/8.50 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1458,a,1445,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1458,a,1446,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1447,a)].
% 8.30/8.50 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1448,a)].
% 8.30/8.50 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1458,a,1452,a)].
% 8.30/8.50 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1458,a,1453,a)].
% 8.30/8.50 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1458,a,1456,a)].
% 8.30/8.50 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1458,a,1457,a)].
% 8.30/8.50 1459 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1316,a,1293,b)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1459,a,1435,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1459,a,1436,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1459,a,1437,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1459,a,1438,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1459,a,1439,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1459,a,1440,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1459,a,1441,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A). [resolve(1459,a,1445,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1459,a,1446,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1459,a,1447,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1459,a,1448,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1459,a,1456,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1459,a,1457,a)].
% 8.33/8.61 1460 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1316,a,1294,b)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1460,a,1435,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1460,a,1436,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1460,a,1437,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1460,a,1438,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1460,a,1439,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1460,a,1440,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1460,a,1441,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(1460,a,1445,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1460,a,1446,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1460,a,1447,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1460,a,1448,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1460,a,1456,a)].
% 8.33/8.61 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1460,a,1457,a)].
% 8.33/8.61 1461 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 8.33/8.61 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].
% 8.33/8.61 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].
% 8.33/8.61 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].
% 8.33/8.61 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].
% 8.33/8.62 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].
% 8.33/8.62 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].
% 8.33/8.62 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].
% 8.33/8.62 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].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 1470 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 8.33/8.62 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1470,a,1462,a)].
% 8.33/8.62 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1470,a,1463,a)].
% 8.33/8.62 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1470,a,1464,a)].
% 8.33/8.62 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1470,a,1465,a)].
% 8.33/8.62 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1470,a,1466,a)].
% 8.33/8.62 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1470,a,1467,a)].
% 8.33/8.62 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1470,a,1468,a)].
% 8.33/8.62 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1470,a,1469,a)].
% 8.33/8.62 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].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.33/8.62 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.63 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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)].
% 8.42/8.64 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].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1476,a,1471,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1476,a,1472,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1476,a,1473,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1476,a,1474,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1476,a,1475,b)].
% 8.42/8.64 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].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1477,a,1471,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1477,a,1472,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1477,a,1473,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1477,a,1474,b)].
% 8.42/8.64 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1477,a,1475,b)].
% 8.42/8.64 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].
% 8.42/8.65 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1478,a,1471,b)].
% 8.42/8.65 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1478,a,1472,b)].
% 8.42/8.65 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1478,a,1473,b)].
% 8.42/8.65 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1478,a,1475,b)].
% 8.42/8.65 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].
% 8.42/8.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1479,a,1471,b)].
% 8.42/8.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1479,a,1472,b)].
% 8.42/8.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1479,a,1473,b)].
% 8.42/8.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1479,a,1475,b)].
% 8.42/8.65 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].
% 8.42/8.65 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].
% 8.42/8.65 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].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.65 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.66 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1487,b,1477,a)].
% 8.42/8.68 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1487,b,1478,a)].
% 8.42/8.68 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1487,b,1479,a)].
% 8.42/8.68 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)].
% 8.42/8.68 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1488,a,1471,b)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1489,a,1471,b)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 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)].
% 8.42/8.68 1490 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 8.42/8.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1490,b,1471,b)].
% 8.42/8.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1490,b,1472,b)].
% 8.42/8.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1490,b,1473,b)].
% 8.72/9.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1490,b,1474,b)].
% 8.72/9.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1490,b,1475,b)].
% 8.72/9.00 1491 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 8.72/9.00 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,b,1471,b)].
% 8.72/9.00 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,b,1472,b)].
% 8.72/9.00 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,b,1473,b)].
% 8.72/9.00 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,b,1474,b)].
% 8.72/9.00 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,b,1475,b)].
% 8.72/9.00 1492 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1152,a,1113,a)].
% 8.72/9.00 1493 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1152,a,1138,a)].
% 8.72/9.00 Derived: class_Orderings_Oorder(tc_nat). [resolve(1493,a,1478,a)].
% 8.72/9.00 Derived: class_Orderings_Oord(tc_nat). [resolve(1493,a,1479,a)].
% 8.72/9.00 Derived: class_HOL_Oplus(tc_nat). [resolve(1493,a,1481,a)].
% 8.72/9.00 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1493,a,1488,a)].
% 8.72/9.00 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1493,a,1489,a)].
% 8.72/9.00 1494 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1152,a,1139,b)].
% 8.72/9.00 1495 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1152,a,1140,b)].
% 8.72/9.00 1496 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1458,a,1446,a)].
% 8.72/9.00 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1496,a,1478,a)].
% 8.72/9.00 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1496,a,1479,a)].
% 8.72/9.00 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1496,a,1480,a)].
% 8.72/9.00 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1496,a,1481,a)].
% 8.72/9.00 1497 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1459,a,1446,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1497,b,1478,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1497,b,1479,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1497,b,1480,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1497,b,1481,a)].
% 8.72/9.00 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)].
% 8.72/9.00 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)].
% 8.72/9.00 1498 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1460,a,1446,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1498,b,1478,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1498,b,1479,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1498,b,1480,a)].
% 8.72/9.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1498,b,1481,a)].
% 8.72/9.00 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)].
% 8.72/9.00 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)].
% 8.72/9.00 1499 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 1508 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 1513 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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].
% 8.72/9.00 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)].
% 8.72/9.00 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)].
% 8.72/9.00 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1499,a,1502,a)].
% 8.72/9.00 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1499,a,1503,a)].
% 8.80/9.01 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1499,a,1504,a)].
% 8.80/9.01 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1499,a,1505,a)].
% 8.80/9.01 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)].
% 8.80/9.01 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)].
% 8.80/9.01 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1499,a,1508,a)].
% 8.80/9.01 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(1499,a,1509,a)].
% 8.80/9.01 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(1499,a,1510,a)].
% 8.80/9.01 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1499,a,1511,a)].
% 8.80/9.01 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)].
% 8.80/9.01 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1499,a,1513,a)].
% 8.80/9.01 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(1499,a,1514,a)].
% 8.80/9.01 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(1499,a,1515,a)].
% 8.80/9.01 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)].
% 8.80/9.01 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)].
% 8.80/9.01 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)].
% 8.80/9.01 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1499,a,1519,a)].
% 8.80/9.01 1520 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 8.80/9.01 1521 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 8.80/9.01 1522 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 8.80/9.01 1523 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom). [assumption].
% 8.80/9.01 1524 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 8.80/9.01 1525 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom). [assumption].
% 8.80/9.01 1526 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 8.80/9.01 1527 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom). [assumption].
% 8.80/9.01 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].
% 8.80/9.01 1529 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 8.80/9.01 1530 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 8.80/9.01 1531 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 8.80/9.02 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].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1532,b,1508,a)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1532,b,1511,a)].
% 8.80/9.02 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)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1532,b,1513,a)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1532,b,1519,a)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1532,b,1520,a)].
% 8.80/9.02 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1532,b,1521,a)].
% 8.80/9.02 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].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.02 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1533,b,1508,a)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1533,b,1511,a)].
% 8.80/9.04 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)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1533,b,1513,a)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1533,b,1519,a)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1533,b,1520,a)].
% 8.80/9.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1533,b,1521,a)].
% 8.80/9.04 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].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 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)].
% 8.80/9.04 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1534,b,1508,a)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1534,b,1511,a)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1534,b,1513,a)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1534,b,1519,a)].
% 8.80/9.05 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].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1535,b,1508,a)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1535,b,1511,a)].
% 8.80/9.05 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)].
% 8.80/9.05 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1535,b,1513,a)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.80/9.05 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1535,b,1519,a)].
% 8.92/9.20 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].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1536,b,1508,a)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1536,b,1511,a)].
% 8.92/9.20 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)].
% 8.92/9.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1536,b,1513,a)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 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)].
% 8.92/9.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1536,b,1519,a)].
% 8.92/9.20 1537 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 8.92/9.20 1538 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 8.92/9.20 1539 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 8.92/9.20 1540 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 8.92/9.20 1541 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1073,b,1068,a)].
% 8.92/9.20 1542 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1096,b,1091,a)].
% 9.10/9.31 1543 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1312,a,1267,a)].
% 9.10/9.31 1544 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1312,a,1293,b)].
% 9.10/9.31 1545 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1312,a,1294,b)].
% 9.10/9.31 1546 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1458,a,1435,a)].
% 9.10/9.31 1547 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1459,a,1435,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1521,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A). [resolve(1547,b,1525,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1547,b,1526,a)].
% 9.10/9.31 1548 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1460,a,1435,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1521,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A). [resolve(1548,b,1525,a)].
% 9.10/9.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1548,b,1526,a)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 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)].
% 9.10/9.31 1557 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1476,a,1471,b)].
% 9.10/9.31 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1557,b,1499,a)].
% 9.10/9.31 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1557,b,1534,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1557,b,1535,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1557,b,1536,b)].
% 9.22/9.44 1558 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1477,a,1471,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1558,b,1499,a)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1558,b,1534,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1558,b,1535,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1558,b,1536,b)].
% 9.22/9.44 1559 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1478,a,1471,b)].
% 9.22/9.44 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1559,b,1534,b)].
% 9.22/9.44 1560 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1479,a,1471,b)].
% 9.22/9.44 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1560,b,1534,b)].
% 9.22/9.44 1561 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1488,a,1471,b)].
% 9.22/9.44 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1561,c,1499,a)].
% 9.22/9.44 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)].
% 9.22/9.44 1562 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1489,a,1471,b)].
% 9.22/9.44 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1562,c,1499,a)].
% 9.22/9.44 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)].
% 9.22/9.44 1563 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1490,b,1471,b)].
% 9.22/9.44 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1563,b,1534,b)].
% 9.22/9.44 1564 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,b,1471,b)].
% 9.22/9.44 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1564,b,1534,b)].
% 9.22/9.44 1565 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 9.22/9.44 1566 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.44 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].
% 9.22/9.45 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].
% 9.22/9.45 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].
% 9.22/9.45 1576 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 9.22/9.45 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1565,a,1566,a)].
% 9.22/9.45 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1567,a)].
% 9.22/9.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1565,a,1568,a)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1569,a)].
% 9.22/9.45 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1565,a,1570,a)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1565,a,1571,a)].
% 9.22/9.45 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1565,a,1572,a)].
% 9.22/9.45 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)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1565,a,1574,a)].
% 9.22/9.45 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)].
% 9.22/9.45 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1565,a,1576,a)].
% 9.22/9.45 1577 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 9.22/9.45 Derived: -c_less(A,A,tc_nat). [resolve(1577,a,1566,a)].
% 9.22/9.45 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1567,a)].
% 9.22/9.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1577,a,1568,a)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1569,a)].
% 9.22/9.45 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1577,a,1570,a)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1577,a,1571,a)].
% 9.22/9.45 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1577,a,1572,a)].
% 9.22/9.45 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)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1577,a,1574,a)].
% 9.22/9.45 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)].
% 9.22/9.45 Derived: c_lessequals(A,A,tc_nat). [resolve(1577,a,1576,a)].
% 9.22/9.45 1578 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 9.22/9.45 Derived: -c_less(A,A,tc_set(B)). [resolve(1578,a,1566,a)].
% 9.22/9.45 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1567,a)].
% 9.22/9.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(1578,a,1568,a)].
% 9.22/9.45 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1569,a)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1578,a,1574,a)].
% 9.22/9.46 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)].
% 9.22/9.46 Derived: c_lessequals(A,A,tc_set(B)). [resolve(1578,a,1576,a)].
% 9.22/9.46 1579 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1579,b,1566,a)].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1567,a)].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1579,b,1568,a)].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1579,b,1569,a)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1574,a)].
% 9.22/9.46 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)].
% 9.22/9.46 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1579,b,1576,a)].
% 9.22/9.46 1580 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 9.22/9.46 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1580,b,1566,a)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.46 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1580,b,1576,a)].
% 9.22/9.47 1581 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 9.22/9.47 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1581,b,1566,a)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1581,b,1576,a)].
% 9.22/9.47 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].
% 9.22/9.47 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1582,b,1566,a)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.47 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1582,b,1576,a)].
% 9.22/9.48 1583 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 9.22/9.48 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A). [resolve(1583,b,1566,a)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(1583,b,1576,a)].
% 9.22/9.48 1584 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 9.22/9.48 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1584,b,1566,a)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.48 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1584,b,1576,a)].
% 9.22/9.49 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].
% 9.22/9.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1585,b,1566,a)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1585,b,1576,a)].
% 9.22/9.49 1586 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 9.22/9.49 Derived: class_Orderings_Oord(tc_set(A)). [resolve(1586,a,1578,a)].
% 9.22/9.49 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1586,a,1584,b)].
% 9.22/9.49 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1586,a,1585,b)].
% 9.22/9.49 1587 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 9.22/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1587,b,1566,a)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.49 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1587,b,1576,a)].
% 9.22/9.50 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].
% 9.22/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1588,b,1566,a)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1588,b,1576,a)].
% 9.22/9.50 1589 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 9.22/9.50 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A). [resolve(1589,b,1566,a)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.50 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(1589,b,1576,a)].
% 9.22/9.51 1590 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 9.22/9.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A). [resolve(1590,b,1566,a)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(1590,b,1576,a)].
% 9.22/9.51 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].
% 9.22/9.51 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1591,b,1566,a)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.51 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1591,b,1576,a)].
% 9.22/9.52 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].
% 9.22/9.52 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1592,b,1566,a)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1592,b,1576,a)].
% 9.22/9.52 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].
% 9.22/9.52 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1593,b,1566,a)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.22/9.52 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1593,b,1576,a)].
% 9.34/9.53 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].
% 9.34/9.53 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A). [resolve(1594,b,1566,a)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(1594,b,1576,a)].
% 9.34/9.53 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].
% 9.34/9.53 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1595,b,1566,a)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.53 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)].
% 9.34/9.54 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)].
% 9.34/9.54 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1595,b,1576,a)].
% 9.34/9.54 1596 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 9.34/9.54 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1596,b,1566,a)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1596,b,1576,a)].
% 9.34/9.54 1597 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 9.34/9.54 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1597,b,1566,a)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.54 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)].
% 9.34/9.55 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1597,b,1576,a)].
% 9.34/9.55 1598 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1598,b,1566,a)].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1567,a)].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1568,a)].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1569,a)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1574,a)].
% 9.34/9.55 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)].
% 9.34/9.55 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1598,b,1576,a)].
% 9.34/9.55 1599 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_lessequals(D,C,A) # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 9.34/9.55 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1599,a,1565,a)].
% 9.34/9.55 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1599,a,1577,a)].
% 9.34/9.55 Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_lessequals(D,B,tc_set(C)). [resolve(1599,a,1578,a)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1599,a,1579,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1599,a,1580,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1599,a,1581,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1599,a,1582,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1599,a,1583,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1599,a,1584,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1599,a,1585,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1599,a,1587,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1599,a,1588,b)].
% 9.34/9.55 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1599,a,1589,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1599,a,1590,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1599,a,1591,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1599,a,1592,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1599,a,1593,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1599,a,1594,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1599,a,1595,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1599,a,1596,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1599,a,1597,b)].
% 9.34/9.56 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1599,a,1598,b)].
% 9.34/9.56 1600 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_lessequals(B,C,A) # label(cls_Orderings_Oorder__less__imp__le_0) # label(axiom). [assumption].
% 9.34/9.56 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1600,a,1565,a)].
% 9.34/9.56 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1600,a,1577,a)].
% 9.34/9.56 Derived: -c_less(A,B,tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1600,a,1578,a)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_LOrder_Olorder(C). [resolve(1600,a,1579,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1600,a,1580,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1600,a,1581,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1600,a,1582,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1600,a,1583,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1600,a,1584,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1600,a,1585,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1600,a,1587,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1600,a,1588,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1600,a,1589,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1600,a,1590,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1600,a,1591,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1600,a,1592,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1600,a,1593,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1600,a,1594,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1600,a,1595,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1600,a,1596,b)].
% 9.34/9.56 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1600,a,1597,b)].
% 9.72/9.97 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1600,a,1598,b)].
% 9.72/9.97 1601 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(886,a,821,a)].
% 9.72/9.97 1602 class_Orderings_Oorder(tc_nat). [resolve(886,a,880,a)].
% 9.72/9.97 1603 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(886,a,881,b)].
% 9.72/9.97 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1603,a,1586,a)].
% 9.72/9.97 1604 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(893,b,886,a)].
% 9.72/9.97 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1604,b,1586,a)].
% 9.72/9.97 1605 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1072,b,1071,a)].
% 9.72/9.97 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1605,b,1586,a)].
% 9.72/9.97 1606 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1078,b,1071,a)].
% 9.72/9.97 1607 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1139,b)].
% 9.72/9.97 1608 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1140,b)].
% 9.72/9.97 1609 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1458,a,1440,a)].
% 9.72/9.97 1610 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1459,a,1440,a)].
% 9.72/9.97 1611 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1460,a,1440,a)].
% 9.72/9.97 1612 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1478,a,1472,b)].
% 9.72/9.97 1613 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1478,a,1473,b)].
% 9.72/9.97 1614 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1478,a,1475,b)].
% 9.72/9.97 1615 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1487,b,1478,a)].
% 9.72/9.97 1616 class_Orderings_Oorder(tc_nat). [resolve(1493,a,1478,a)].
% 9.72/9.97 1617 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1496,a,1478,a)].
% 9.72/9.97 1618 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1497,b,1478,a)].
% 9.72/9.97 1619 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1498,b,1478,a)].
% 9.72/9.97 1620 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1559,b,1534,b)].
% 9.72/9.97 1621 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 9.72/9.97 1622 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastAtMost__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1623 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OatLeastAtMost__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1624 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A) # label(cls_SetInterval_OatLeastAtMost__iff_2) # label(axiom). [assumption].
% 9.72/9.97 1625 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastLessThan__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1626 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OatLeastLessThan__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1627 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A) # label(cls_SetInterval_OatLeastLessThan__iff_2) # label(axiom). [assumption].
% 9.72/9.97 1628 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1629 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A) # label(cls_SetInterval_OatLeast__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1630 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1631 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A) # label(cls_SetInterval_OatMost__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1632 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1633 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1634 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A) # label(cls_SetInterval_OgreaterThanAtMost__iff_2) # label(axiom). [assumption].
% 9.72/9.97 1635 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1636 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1637 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A) # label(cls_SetInterval_OgreaterThanLessThan__iff_2) # label(axiom). [assumption].
% 9.72/9.97 1638 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThan__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1639 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A) # label(cls_SetInterval_OgreaterThan__iff_1) # label(axiom). [assumption].
% 9.72/9.97 1640 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A) # label(cls_SetInterval_OlessThan__iff_0) # label(axiom). [assumption].
% 9.72/9.97 1641 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A) # label(cls_SetInterval_OlessThan__iff_1) # label(axiom). [assumption].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1621,a,1622,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1621,a,1623,a)].
% 9.72/9.97 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(1621,a,1624,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1621,a,1625,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1621,a,1626,a)].
% 9.72/9.97 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(1621,a,1627,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1621,a,1628,a)].
% 9.72/9.97 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1621,a,1629,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1621,a,1630,a)].
% 9.72/9.97 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1621,a,1631,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1621,a,1632,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1621,a,1633,a)].
% 9.72/9.97 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(1621,a,1634,a)].
% 9.72/9.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1621,a,1635,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1621,a,1636,a)].
% 9.72/9.99 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(1621,a,1637,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1621,a,1638,a)].
% 9.72/9.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1621,a,1639,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1621,a,1640,a)].
% 9.72/9.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1621,a,1641,a)].
% 9.72/9.99 1642 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1642,a,1622,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1642,a,1623,a)].
% 9.72/9.99 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(1642,a,1624,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1642,a,1625,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1642,a,1626,a)].
% 9.72/9.99 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(1642,a,1627,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1642,a,1628,a)].
% 9.72/9.99 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1642,a,1629,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1642,a,1630,a)].
% 9.72/9.99 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1642,a,1631,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1642,a,1632,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1642,a,1633,a)].
% 9.72/9.99 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(1642,a,1634,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1642,a,1635,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1642,a,1636,a)].
% 9.72/9.99 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(1642,a,1637,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1642,a,1638,a)].
% 9.72/9.99 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1642,a,1639,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1642,a,1640,a)].
% 9.72/9.99 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1642,a,1641,a)].
% 9.72/9.99 1643 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1643,a,1622,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1643,a,1623,a)].
% 9.72/9.99 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(1643,a,1624,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1643,a,1625,a)].
% 9.72/9.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1643,a,1626,a)].
% 9.81/10.00 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(1643,a,1627,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1643,a,1628,a)].
% 9.81/10.00 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1643,a,1629,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1643,a,1630,a)].
% 9.81/10.00 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1643,a,1631,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1643,a,1632,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1643,a,1633,a)].
% 9.81/10.00 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(1643,a,1634,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1643,a,1635,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1643,a,1636,a)].
% 9.81/10.00 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(1643,a,1637,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1643,a,1638,a)].
% 9.81/10.00 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1643,a,1639,a)].
% 9.81/10.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1643,a,1640,a)].
% 9.81/10.00 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1643,a,1641,a)].
% 9.81/10.00 1644 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1622,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1623,a)].
% 9.81/10.00 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(1644,b,1624,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1625,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1626,a)].
% 9.81/10.00 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(1644,b,1627,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1628,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1644,b,1629,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1644,b,1630,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1644,b,1631,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1632,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1633,a)].
% 9.81/10.00 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(1644,b,1634,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1635,a)].
% 9.81/10.00 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1636,a)].
% 9.81/10.01 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(1644,b,1637,a)].
% 9.81/10.01 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1644,b,1638,a)].
% 9.81/10.01 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1644,b,1639,a)].
% 9.81/10.01 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1644,b,1640,a)].
% 9.81/10.01 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1644,b,1641,a)].
% 9.81/10.01 1645 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1622,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1623,a)].
% 9.81/10.01 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(1645,b,1624,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1625,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1626,a)].
% 9.81/10.01 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(1645,b,1627,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1628,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1645,b,1629,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1645,b,1630,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1645,b,1631,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1632,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1633,a)].
% 9.81/10.01 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(1645,b,1634,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1635,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1636,a)].
% 9.81/10.01 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(1645,b,1637,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1645,b,1638,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1645,b,1639,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1645,b,1640,a)].
% 9.81/10.01 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1645,b,1641,a)].
% 9.81/10.01 1646 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1622,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1623,a)].
% 9.81/10.02 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(1646,b,1624,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1625,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1626,a)].
% 9.81/10.02 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(1646,b,1627,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1628,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1646,b,1629,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1646,b,1630,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1646,b,1631,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1632,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1633,a)].
% 9.81/10.02 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(1646,b,1634,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1635,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1636,a)].
% 9.81/10.02 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(1646,b,1637,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1646,b,1638,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1646,b,1639,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1646,b,1640,a)].
% 9.81/10.02 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1646,b,1641,a)].
% 9.81/10.02 1647 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 9.81/10.02 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(1647,b,1622,a)].
% 9.81/10.02 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(1647,b,1623,a)].
% 9.81/10.02 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(1647,b,1624,a)].
% 9.81/10.02 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(1647,b,1625,a)].
% 9.81/10.03 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(1647,b,1626,a)].
% 9.81/10.03 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(1647,b,1627,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1628,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1647,b,1629,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1647,b,1630,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1647,b,1631,a)].
% 9.81/10.03 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(1647,b,1632,a)].
% 9.81/10.03 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(1647,b,1633,a)].
% 9.81/10.03 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(1647,b,1634,a)].
% 9.81/10.03 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(1647,b,1635,a)].
% 9.81/10.03 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(1647,b,1636,a)].
% 9.81/10.03 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(1647,b,1637,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1647,b,1638,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1647,b,1639,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1647,b,1640,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1647,b,1641,a)].
% 9.81/10.03 1648 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1622,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1648,b,1623,a)].
% 9.81/10.03 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(1648,b,1624,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1625,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1648,b,1626,a)].
% 9.81/10.03 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(1648,b,1627,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1648,b,1628,a)].
% 9.81/10.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1648,b,1629,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1648,b,1630,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1648,b,1631,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1648,b,1632,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1648,b,1633,a)].
% 9.81/10.04 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(1648,b,1634,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1648,b,1635,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1648,b,1636,a)].
% 9.81/10.04 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(1648,b,1637,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1648,b,1638,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1648,b,1639,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1648,b,1640,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1648,b,1641,a)].
% 9.81/10.04 1649 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1622,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1623,a)].
% 9.81/10.04 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(1649,b,1624,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1625,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1626,a)].
% 9.81/10.04 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(1649,b,1627,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1628,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1649,b,1629,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1649,b,1630,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1649,b,1631,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1632,a)].
% 9.81/10.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1633,a)].
% 9.81/10.04 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(1649,b,1634,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1635,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1636,a)].
% 9.81/10.05 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(1649,b,1637,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1649,b,1638,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1649,b,1639,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1649,b,1640,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1649,b,1641,a)].
% 9.81/10.05 1650 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 9.81/10.05 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(1650,b,1622,a)].
% 9.81/10.05 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(1650,b,1623,a)].
% 9.81/10.05 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(1650,b,1624,a)].
% 9.81/10.05 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(1650,b,1625,a)].
% 9.81/10.05 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(1650,b,1626,a)].
% 9.81/10.05 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(1650,b,1627,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1628,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1650,b,1629,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1650,b,1630,a)].
% 9.81/10.05 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1650,b,1631,a)].
% 9.81/10.05 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(1650,b,1632,a)].
% 9.81/10.05 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(1650,b,1633,a)].
% 9.81/10.05 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(1650,b,1634,a)].
% 9.81/10.05 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(1650,b,1635,a)].
% 9.81/10.05 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(1650,b,1636,a)].
% 9.81/10.05 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(1650,b,1637,a)].
% 9.81/10.06 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1650,b,1638,a)].
% 9.81/10.06 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1650,b,1639,a)].
% 9.81/10.06 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1650,b,1640,a)].
% 9.81/10.06 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1650,b,1641,a)].
% 9.81/10.06 1651 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 9.81/10.06 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(1651,b,1622,a)].
% 9.81/10.06 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(1651,b,1623,a)].
% 9.81/10.06 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(1651,b,1624,a)].
% 9.81/10.06 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(1651,b,1625,a)].
% 9.81/10.06 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(1651,b,1626,a)].
% 9.81/10.06 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(1651,b,1627,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1651,b,1628,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1651,b,1629,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1651,b,1630,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1651,b,1631,a)].
% 9.81/10.06 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(1651,b,1632,a)].
% 9.81/10.06 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(1651,b,1633,a)].
% 9.81/10.06 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(1651,b,1634,a)].
% 9.81/10.06 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(1651,b,1635,a)].
% 9.81/10.06 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(1651,b,1636,a)].
% 9.81/10.06 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(1651,b,1637,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1651,b,1638,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1651,b,1639,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1651,b,1640,a)].
% 9.81/10.06 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1651,b,1641,a)].
% 9.81/10.06 1652 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1622,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1623,a)].
% 9.81/10.08 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(1652,b,1624,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1625,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1626,a)].
% 9.81/10.08 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(1652,b,1627,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1628,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1652,b,1629,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1652,b,1630,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1652,b,1631,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1632,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1633,a)].
% 9.81/10.08 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(1652,b,1634,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1635,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1636,a)].
% 9.81/10.08 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(1652,b,1637,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1652,b,1638,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1652,b,1639,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1652,b,1640,a)].
% 9.81/10.08 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1652,b,1641,a)].
% 9.81/10.08 1653 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) # label(axiom). [assumption].
% 9.81/10.08 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(1653,b,1622,a)].
% 9.81/10.08 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(1653,b,1623,a)].
% 9.81/10.08 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(1653,b,1624,a)].
% 9.81/10.08 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(1653,b,1625,a)].
% 9.81/10.08 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(1653,b,1626,a)].
% 9.81/10.08 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(1653,b,1627,a)].
% 9.90/10.09 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(1653,b,1628,a)].
% 9.90/10.09 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(1653,b,1629,a)].
% 9.90/10.09 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(1653,b,1630,a)].
% 9.90/10.09 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(1653,b,1631,a)].
% 9.90/10.09 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(1653,b,1632,a)].
% 9.90/10.09 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(1653,b,1633,a)].
% 9.90/10.09 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(1653,b,1634,a)].
% 9.90/10.09 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(1653,b,1635,a)].
% 9.90/10.09 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(1653,b,1636,a)].
% 9.90/10.09 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(1653,b,1637,a)].
% 9.90/10.09 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(1653,b,1638,a)].
% 9.90/10.09 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(1653,b,1639,a)].
% 9.90/10.09 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(1653,b,1640,a)].
% 9.90/10.09 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(1653,b,1641,a)].
% 9.90/10.09 1654 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1622,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1654,b,1623,a)].
% 9.90/10.09 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(1654,b,1624,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1625,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1654,b,1626,a)].
% 9.90/10.09 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(1654,b,1627,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1654,b,1628,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1654,b,1629,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1654,b,1630,a)].
% 9.90/10.09 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1654,b,1631,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1654,b,1632,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1654,b,1633,a)].
% 9.90/10.10 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(1654,b,1634,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1654,b,1635,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1654,b,1636,a)].
% 9.90/10.10 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(1654,b,1637,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1654,b,1638,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1654,b,1639,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1654,b,1640,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1654,b,1641,a)].
% 9.90/10.10 1655 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1655,b,1622,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1655,b,1623,a)].
% 9.90/10.10 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(1655,b,1624,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1655,b,1625,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1655,b,1626,a)].
% 9.90/10.10 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(1655,b,1627,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1655,b,1628,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1655,b,1629,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1655,b,1630,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1655,b,1631,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1655,b,1632,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1655,b,1633,a)].
% 9.90/10.10 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(1655,b,1634,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1655,b,1635,a)].
% 9.90/10.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1655,b,1636,a)].
% 9.90/10.10 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(1655,b,1637,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1655,b,1638,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1655,b,1639,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1655,b,1640,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1655,b,1641,a)].
% 9.90/10.11 1656 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 9.90/10.11 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(1656,b,1622,a)].
% 9.90/10.11 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(1656,b,1623,a)].
% 9.90/10.11 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(1656,b,1624,a)].
% 9.90/10.11 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(1656,b,1625,a)].
% 9.90/10.11 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(1656,b,1626,a)].
% 9.90/10.11 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(1656,b,1627,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1628,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1656,b,1629,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1656,b,1630,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1656,b,1631,a)].
% 9.90/10.11 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(1656,b,1632,a)].
% 9.90/10.11 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(1656,b,1633,a)].
% 9.90/10.11 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(1656,b,1634,a)].
% 9.90/10.11 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(1656,b,1635,a)].
% 9.90/10.11 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(1656,b,1636,a)].
% 9.90/10.11 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(1656,b,1637,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1656,b,1638,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1656,b,1639,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1656,b,1640,a)].
% 9.90/10.11 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1656,b,1641,a)].
% 9.90/10.11 1657 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) # label(axiom). [assumption].
% 9.95/10.12 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(1657,b,1622,a)].
% 9.95/10.12 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(1657,b,1623,a)].
% 9.95/10.12 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(1657,b,1624,a)].
% 9.95/10.12 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(1657,b,1625,a)].
% 9.95/10.12 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(1657,b,1626,a)].
% 9.95/10.12 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(1657,b,1627,a)].
% 9.95/10.12 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(1657,b,1628,a)].
% 9.95/10.12 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(1657,b,1629,a)].
% 9.95/10.12 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(1657,b,1630,a)].
% 9.95/10.12 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(1657,b,1631,a)].
% 9.95/10.12 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(1657,b,1632,a)].
% 9.95/10.12 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(1657,b,1633,a)].
% 9.95/10.12 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(1657,b,1634,a)].
% 9.95/10.12 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(1657,b,1635,a)].
% 9.95/10.12 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(1657,b,1636,a)].
% 9.95/10.12 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(1657,b,1637,a)].
% 9.95/10.12 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(1657,b,1638,a)].
% 9.95/10.12 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(1657,b,1639,a)].
% 9.95/10.12 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(1657,b,1640,a)].
% 9.95/10.12 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(1657,b,1641,a)].
% 9.95/10.12 1658 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 9.95/10.12 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(1658,b,1622,a)].
% 9.95/10.12 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(1658,b,1623,a)].
% 9.95/10.12 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(1658,b,1624,a)].
% 9.96/10.13 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(1658,b,1625,a)].
% 9.96/10.13 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(1658,b,1626,a)].
% 9.96/10.13 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(1658,b,1627,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1628,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1658,b,1629,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1658,b,1630,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1658,b,1631,a)].
% 9.96/10.13 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(1658,b,1632,a)].
% 9.96/10.13 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(1658,b,1633,a)].
% 9.96/10.13 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(1658,b,1634,a)].
% 9.96/10.13 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(1658,b,1635,a)].
% 9.96/10.13 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(1658,b,1636,a)].
% 9.96/10.13 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(1658,b,1637,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1658,b,1638,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1658,b,1639,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1658,b,1640,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1658,b,1641,a)].
% 9.96/10.13 1659 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 9.96/10.13 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(1659,b,1622,a)].
% 9.96/10.13 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(1659,b,1623,a)].
% 9.96/10.13 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(1659,b,1624,a)].
% 9.96/10.13 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(1659,b,1625,a)].
% 9.96/10.13 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(1659,b,1626,a)].
% 9.96/10.13 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(1659,b,1627,a)].
% 9.96/10.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1628,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1629,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1630,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1631,a)].
% 9.96/10.15 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(1659,b,1632,a)].
% 9.96/10.15 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(1659,b,1633,a)].
% 9.96/10.15 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(1659,b,1634,a)].
% 9.96/10.15 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(1659,b,1635,a)].
% 9.96/10.15 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(1659,b,1636,a)].
% 9.96/10.15 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(1659,b,1637,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1638,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1639,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1640,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1641,a)].
% 9.96/10.15 1660 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 9.96/10.15 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(1660,b,1622,a)].
% 9.96/10.15 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(1660,b,1623,a)].
% 9.96/10.15 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(1660,b,1624,a)].
% 9.96/10.15 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(1660,b,1625,a)].
% 9.96/10.15 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(1660,b,1626,a)].
% 9.96/10.15 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(1660,b,1627,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1628,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1629,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1630,a)].
% 9.96/10.15 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1631,a)].
% 9.96/10.15 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(1660,b,1632,a)].
% 9.96/10.15 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(1660,b,1633,a)].
% 9.96/10.16 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(1660,b,1634,a)].
% 9.96/10.16 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(1660,b,1635,a)].
% 9.96/10.16 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(1660,b,1636,a)].
% 9.96/10.16 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(1660,b,1637,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1638,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1639,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1640,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1641,a)].
% 9.96/10.16 1661 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1622,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1623,a)].
% 9.96/10.16 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(1661,b,1624,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1625,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1626,a)].
% 9.96/10.16 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(1661,b,1627,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1628,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1629,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1630,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1631,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1632,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1633,a)].
% 9.96/10.16 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(1661,b,1634,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1635,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1636,a)].
% 9.96/10.16 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(1661,b,1637,a)].
% 9.96/10.16 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1638,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1639,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1640,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1641,a)].
% 9.96/10.17 1662 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1622,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1623,a)].
% 9.96/10.17 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(1662,b,1624,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1625,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1626,a)].
% 9.96/10.17 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(1662,b,1627,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1628,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1629,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1630,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1631,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1632,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1633,a)].
% 9.96/10.17 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(1662,b,1634,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1635,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1636,a)].
% 9.96/10.17 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(1662,b,1637,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1638,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1639,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1640,a)].
% 9.96/10.17 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1641,a)].
% 9.96/10.17 1663 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 9.96/10.17 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1622,a)].
% 9.96/10.17 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1623,a)].
% 10.26/10.43 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(1663,b,1624,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1625,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1626,a)].
% 10.26/10.43 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(1663,b,1627,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1628,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1663,b,1629,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1663,b,1630,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1663,b,1631,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1632,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1633,a)].
% 10.26/10.43 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(1663,b,1634,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1635,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1636,a)].
% 10.26/10.43 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(1663,b,1637,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1663,b,1638,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1663,b,1639,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1663,b,1640,a)].
% 10.26/10.43 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1663,b,1641,a)].
% 10.26/10.43 1664 class_Orderings_Oord(tc_IntDef_Oint). [resolve(885,a,821,a)].
% 10.26/10.43 1665 class_Orderings_Oord(tc_nat). [resolve(885,a,880,a)].
% 10.26/10.43 1666 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(885,a,881,b)].
% 10.26/10.43 1667 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(893,b,885,a)].
% 10.26/10.43 1668 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1072,b,1070,a)].
% 10.26/10.43 1669 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1078,b,1070,a)].
% 10.26/10.43 1670 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1139,b)].
% 10.26/10.43 1671 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1140,b)].
% 10.26/10.43 1672 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1458,a,1441,a)].
% 10.26/10.43 1673 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1459,a,1441,a)].
% 10.26/10.43 1674 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1460,a,1441,a)].
% 10.26/10.43 1675 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1479,a,1472,b)].
% 10.26/10.43 1676 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1479,a,1473,b)].
% 10.26/10.43 1677 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1479,a,1475,b)].
% 11.25/11.43 1678 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1487,b,1479,a)].
% 11.25/11.43 1679 class_Orderings_Oord(tc_nat). [resolve(1493,a,1479,a)].
% 11.25/11.43 1680 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1496,a,1479,a)].
% 11.25/11.43 1681 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1497,b,1479,a)].
% 11.25/11.43 1682 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1498,b,1479,a)].
% 11.25/11.43 1683 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1560,b,1534,b)].
% 11.25/11.43 1684 class_Orderings_Oord(tc_set(A)). [resolve(1586,a,1578,a)].
% 11.25/11.43 1685 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1586,a,1584,b)].
% 11.25/11.43 1686 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1586,a,1585,b)].
% 11.25/11.43 1687 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1603,a,1586,a)].
% 11.25/11.43 1688 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1604,b,1586,a)].
% 11.25/11.43 1689 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1605,b,1586,a)].
% 11.25/11.43 1690 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1072,b,1068,a)].
% 11.25/11.43 1691 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 11.25/11.43 1692 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 11.25/11.43 1693 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 11.25/11.43 1694 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 11.25/11.43 1695 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 11.25/11.43 1696 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 11.25/11.43 1697 -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].
% 11.25/11.43 1698 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 11.25/11.43 1699 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 11.25/11.43 1700 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 11.25/11.43 1701 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 11.25/11.43 1702 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(882,a,821,a)].
% 11.25/11.43 1703 class_LOrder_Olorder(tc_nat). [resolve(882,a,880,a)].
% 11.25/11.43 1704 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(882,a,881,b)].
% 11.25/11.43 1705 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(893,b,882,a)].
% 11.25/11.43 1706 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1093,b,1091,a)].
% 11.25/11.43 1707 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1151,a,1139,b)].
% 11.25/11.43 1708 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1151,a,1140,b)].
% 11.25/11.43 1709 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1458,a,1439,a)].
% 11.25/11.43 1710 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1459,a,1439,a)].
% 11.25/11.43 1711 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1460,a,1439,a)].
% 11.25/11.43 1712 -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1579,b,1566,a)].
% 11.25/11.43 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1712,a,1691,a)].
% 11.25/11.43 Derived: -c_less(A,A,tc_nat). [resolve(1712,a,1692,a)].
% 11.25/11.43 1713 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1567,a)].
% 11.25/11.43 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1713,a,1691,a)].
% 11.25/11.43 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1713,a,1692,a)].
% 11.25/11.43 1714 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1579,b,1568,a)].
% 11.25/11.43 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1714,a,1691,a)].
% 11.25/11.43 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1714,a,1692,a)].
% 11.25/11.43 1715 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1579,b,1569,a)].
% 11.25/11.43 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1715,a,1691,a)].
% 11.25/11.43 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1715,a,1692,a)].
% 11.25/11.43 1716 -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)].
% 11.25/11.43 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(1716,a,1691,a)].
% 11.25/11.43 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(1716,a,1692,a)].
% 11.25/11.43 1717 -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)].
% 11.25/11.43 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(1717,a,1691,a)].
% 11.25/11.43 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(1717,a,1692,a)].
% 11.25/11.43 1718 -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)].
% 11.25/11.43 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(1718,a,1691,a)].
% 11.25/11.43 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(1718,a,1692,a)].
% 11.25/11.43 1719 -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)].
% 11.25/11.43 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(1719,a,1691,a)].
% 11.25/11.43 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(1719,a,1692,a)].
% 11.25/11.43 1720 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1579,b,1574,a)].
% 11.25/11.43 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1720,a,1691,a)].
% 11.25/11.43 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1720,a,1692,a)].
% 11.25/11.43 1721 -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)].
% 11.25/11.43 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(1721,a,1691,a)].
% 11.25/11.43 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(1721,a,1692,a)].
% 11.25/11.43 1722 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1579,b,1576,a)].
% 11.30/11.48 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1722,a,1691,a)].
% 11.30/11.48 Derived: c_lessequals(A,A,tc_nat). [resolve(1722,a,1692,a)].
% 11.30/11.48 1723 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1599,a,1579,b)].
% 11.30/11.48 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1723,d,1691,a)].
% 11.30/11.48 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1723,d,1692,a)].
% 11.30/11.48 1724 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_LOrder_Olorder(C). [resolve(1600,a,1579,b)].
% 11.30/11.48 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1724,c,1691,a)].
% 11.30/11.48 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1724,c,1692,a)].
% 11.30/11.48 1725 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1622,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1725,a,1691,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1725,a,1692,a)].
% 11.30/11.48 1726 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1623,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1726,a,1691,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1726,a,1692,a)].
% 11.30/11.48 1727 -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(1644,b,1624,a)].
% 11.30/11.48 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(1727,a,1691,a)].
% 11.30/11.48 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1727,a,1692,a)].
% 11.30/11.48 1728 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1625,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1728,a,1691,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1728,a,1692,a)].
% 11.30/11.48 1729 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1626,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1729,a,1691,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1729,a,1692,a)].
% 11.30/11.48 1730 -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(1644,b,1627,a)].
% 11.30/11.48 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1730,a,1691,a)].
% 11.30/11.48 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1730,a,1692,a)].
% 11.30/11.48 1731 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1644,b,1628,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1731,a,1691,a)].
% 11.30/11.48 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1731,a,1692,a)].
% 11.30/11.48 1732 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1644,b,1629,a)].
% 11.30/11.48 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1732,a,1691,a)].
% 11.30/11.48 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1732,a,1692,a)].
% 11.30/11.49 1733 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1644,b,1630,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1733,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1733,a,1692,a)].
% 11.30/11.49 1734 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1644,b,1631,a)].
% 11.30/11.49 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1734,a,1691,a)].
% 11.30/11.49 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1734,a,1692,a)].
% 11.30/11.49 1735 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1632,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1735,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1735,a,1692,a)].
% 11.30/11.49 1736 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1644,b,1633,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1736,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1736,a,1692,a)].
% 11.30/11.49 1737 -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(1644,b,1634,a)].
% 11.30/11.49 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(1737,a,1691,a)].
% 11.30/11.49 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(1737,a,1692,a)].
% 11.30/11.49 1738 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1644,b,1635,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1738,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1738,a,1692,a)].
% 11.30/11.49 1739 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1644,b,1636,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1739,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1739,a,1692,a)].
% 11.30/11.49 1740 -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(1644,b,1637,a)].
% 11.30/11.49 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(1740,a,1691,a)].
% 11.30/11.49 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1740,a,1692,a)].
% 11.30/11.49 1741 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1644,b,1638,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1741,a,1691,a)].
% 11.30/11.49 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1741,a,1692,a)].
% 11.30/11.49 1742 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1644,b,1639,a)].
% 11.30/11.49 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1742,a,1691,a)].
% 11.30/11.49 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1742,a,1692,a)].
% 11.30/11.49 1743 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1644,b,1640,a)].
% 11.48/11.69 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1743,a,1691,a)].
% 11.48/11.69 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1743,a,1692,a)].
% 11.48/11.69 1744 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1644,b,1641,a)].
% 11.48/11.69 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1744,a,1691,a)].
% 11.48/11.69 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1744,a,1692,a)].
% 11.48/11.69 1745 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 11.48/11.69 1746 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 11.48/11.69 1747 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 11.48/11.69 1748 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_7) # label(axiom). [assumption].
% 11.48/11.69 1749 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_7) # label(axiom). [assumption].
% 11.48/11.69 1750 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 11.48/11.69 1751 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_9) # label(axiom). [assumption].
% 11.48/11.69 1752 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom). [assumption].
% 11.48/11.69 1753 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 11.48/11.69 1754 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_9) # label(axiom). [assumption].
% 11.48/11.69 1755 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) # label(axiom). [assumption].
% 11.48/11.69 1756 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_57) # label(axiom). [assumption].
% 11.48/11.69 1757 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_43) # label(axiom). [assumption].
% 11.48/11.69 1758 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_16) # label(axiom). [assumption].
% 11.48/11.69 1759 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) # label(axiom). [assumption].
% 11.48/11.69 1760 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_7) # label(axiom). [assumption].
% 11.48/11.69 1761 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_22) # label(axiom). [assumption].
% 11.48/11.69 1762 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_12) # label(axiom). [assumption].
% 11.77/11.94 1763 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_16) # label(axiom). [assumption].
% 11.77/11.94 1764 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_9) # label(axiom). [assumption].
% 11.77/11.94 1765 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1113,a)].
% 11.77/11.94 1766 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1158,a,1138,a)].
% 11.77/11.94 1767 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1139,b)].
% 11.77/11.94 1768 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1140,b)].
% 11.77/11.94 1769 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1448,a)].
% 11.77/11.94 1770 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1459,a,1448,a)].
% 11.77/11.94 1771 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1460,a,1448,a)].
% 11.77/11.94 1772 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1477,a,1472,b)].
% 11.77/11.94 1773 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1477,a,1473,b)].
% 11.77/11.94 1774 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1477,a,1474,b)].
% 11.77/11.94 1775 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1477,a,1475,b)].
% 11.77/11.94 1776 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1487,b,1477,a)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1776,b,1745,a)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1776,b,1752,a)].
% 11.77/11.94 1777 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1558,b,1499,a)].
% 11.77/11.94 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1777,a,1745,a)].
% 11.77/11.94 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1777,a,1752,a)].
% 11.77/11.94 1778 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1558,b,1534,b)].
% 11.77/11.94 1779 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1558,b,1535,b)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1779,a,1745,a)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1779,a,1752,a)].
% 11.77/11.94 1780 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1558,b,1536,b)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1780,a,1745,a)].
% 11.77/11.94 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1780,a,1752,a)].
% 11.77/11.94 1781 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1584,b,1566,a)].
% 11.77/11.94 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1781,a,1748,b)].
% 11.77/11.94 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1781,a,1749,b)].
% 11.77/11.94 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1781,a,1750,b)].
% 11.77/11.94 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1781,a,1751,b)].
% 11.77/11.94 1782 -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)].
% 11.77/11.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1782,a,1748,b)].
% 11.77/11.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1782,a,1749,b)].
% 11.77/11.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1782,a,1750,b)].
% 11.77/11.95 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1782,a,1751,b)].
% 11.77/11.95 1783 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1584,b,1568,a)].
% 11.77/11.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1783,a,1748,b)].
% 11.77/11.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1783,a,1749,b)].
% 11.77/11.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1783,a,1750,b)].
% 11.77/11.95 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1783,a,1751,b)].
% 11.77/11.95 1784 -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)].
% 11.77/11.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1784,a,1748,b)].
% 11.77/11.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1784,a,1749,b)].
% 11.77/11.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1784,a,1750,b)].
% 11.77/11.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1784,a,1751,b)].
% 11.77/11.95 1785 -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)].
% 11.77/11.95 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(1785,a,1748,b)].
% 11.77/11.95 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(1785,a,1749,b)].
% 11.77/11.95 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(1785,a,1750,b)].
% 11.77/11.95 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(1785,a,1751,b)].
% 11.77/11.95 1786 -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)].
% 11.77/11.95 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(1786,a,1748,b)].
% 11.77/11.95 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(1786,a,1749,b)].
% 11.77/11.95 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(1786,a,1750,b)].
% 11.77/11.95 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(1786,a,1751,b)].
% 11.77/11.95 1787 -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)].
% 11.77/11.97 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(1787,a,1748,b)].
% 11.77/11.97 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(1787,a,1749,b)].
% 11.77/11.97 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(1787,a,1750,b)].
% 11.77/11.97 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(1787,a,1751,b)].
% 11.77/11.97 1788 -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)].
% 11.77/11.97 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(1788,a,1748,b)].
% 11.77/11.97 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(1788,a,1749,b)].
% 11.77/11.97 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(1788,a,1750,b)].
% 11.77/11.97 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(1788,a,1751,b)].
% 11.77/11.97 1789 -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)].
% 11.77/11.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1789,a,1748,b)].
% 11.77/11.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1789,a,1749,b)].
% 11.77/11.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1789,a,1750,b)].
% 11.77/11.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1789,a,1751,b)].
% 11.77/11.97 1790 -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)].
% 11.77/11.97 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1790,a,1748,b)].
% 11.77/11.97 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1790,a,1749,b)].
% 11.77/11.97 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1790,a,1750,b)].
% 11.77/11.97 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1790,a,1751,b)].
% 11.77/11.97 1791 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1584,b,1576,a)].
% 11.77/11.97 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1791,a,1748,b)].
% 11.77/11.97 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1791,a,1749,b)].
% 11.77/11.97 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1791,a,1750,b)].
% 11.77/11.97 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1791,a,1751,b)].
% 11.77/11.97 1792 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1599,a,1584,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1792,d,1748,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1792,d,1749,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1792,d,1750,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1792,d,1751,b)].
% 11.77/12.01 1793 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1600,a,1584,b)].
% 11.77/12.01 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1793,c,1748,b)].
% 11.77/12.01 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1793,c,1749,b)].
% 11.77/12.01 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1793,c,1750,b)].
% 11.77/12.01 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1793,c,1751,b)].
% 11.77/12.01 1794 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1622,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1794,a,1748,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1794,a,1749,b)].
% 11.77/12.01 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(1794,a,1750,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1794,a,1751,b)].
% 11.77/12.01 1795 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1623,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1795,a,1748,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1795,a,1749,b)].
% 11.77/12.01 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(1795,a,1750,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1795,a,1751,b)].
% 11.77/12.01 1796 -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(1649,b,1624,a)].
% 11.77/12.01 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(1796,a,1748,b)].
% 11.77/12.01 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(1796,a,1749,b)].
% 11.77/12.01 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(1796,a,1750,b)].
% 11.77/12.01 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(1796,a,1751,b)].
% 11.77/12.01 1797 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1625,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1797,a,1748,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1797,a,1749,b)].
% 11.77/12.01 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(1797,a,1750,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1797,a,1751,b)].
% 11.77/12.01 1798 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1626,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1798,a,1748,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1798,a,1749,b)].
% 11.77/12.01 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(1798,a,1750,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1798,a,1751,b)].
% 11.77/12.01 1799 -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(1649,b,1627,a)].
% 11.77/12.01 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(1799,a,1748,b)].
% 11.77/12.01 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(1799,a,1749,b)].
% 11.77/12.01 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(1799,a,1750,b)].
% 11.77/12.01 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(1799,a,1751,b)].
% 11.77/12.01 1800 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1649,b,1628,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1748,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1749,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1750,b)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1800,a,1751,b)].
% 11.77/12.01 1801 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1649,b,1629,a)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1801,a,1748,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1801,a,1749,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1801,a,1750,b)].
% 11.77/12.01 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1801,a,1751,b)].
% 11.77/12.01 1802 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1649,b,1630,a)].
% 11.77/12.01 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1802,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1802,a,1749,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1802,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1802,a,1751,b)].
% 11.77/12.02 1803 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1649,b,1631,a)].
% 11.77/12.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1803,a,1748,b)].
% 11.77/12.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1803,a,1749,b)].
% 11.77/12.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1803,a,1750,b)].
% 11.77/12.02 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1803,a,1751,b)].
% 11.77/12.02 1804 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1632,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1804,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1804,a,1749,b)].
% 11.77/12.02 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(1804,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1804,a,1751,b)].
% 11.77/12.02 1805 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1649,b,1633,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1805,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1805,a,1749,b)].
% 11.77/12.02 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(1805,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1805,a,1751,b)].
% 11.77/12.02 1806 -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(1649,b,1634,a)].
% 11.77/12.02 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(1806,a,1748,b)].
% 11.77/12.02 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(1806,a,1749,b)].
% 11.77/12.02 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(1806,a,1750,b)].
% 11.77/12.02 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(1806,a,1751,b)].
% 11.77/12.02 1807 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1649,b,1635,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1807,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1807,a,1749,b)].
% 11.77/12.02 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(1807,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1807,a,1751,b)].
% 11.77/12.02 1808 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1649,b,1636,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1808,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1808,a,1749,b)].
% 11.77/12.02 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(1808,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1808,a,1751,b)].
% 11.77/12.02 1809 -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(1649,b,1637,a)].
% 11.77/12.02 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(1809,a,1748,b)].
% 11.77/12.02 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(1809,a,1749,b)].
% 11.77/12.02 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(1809,a,1750,b)].
% 11.77/12.02 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(1809,a,1751,b)].
% 11.77/12.02 1810 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1649,b,1638,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1810,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1810,a,1749,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1810,a,1750,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1810,a,1751,b)].
% 11.77/12.02 1811 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1649,b,1639,a)].
% 11.77/12.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1811,a,1748,b)].
% 11.77/12.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1811,a,1749,b)].
% 11.77/12.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1811,a,1750,b)].
% 11.77/12.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1811,a,1751,b)].
% 11.77/12.02 1812 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1649,b,1640,a)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1812,a,1748,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1812,a,1749,b)].
% 11.77/12.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1812,a,1750,b)].
% 12.08/12.24 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1812,a,1751,b)].
% 12.08/12.24 1813 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1649,b,1641,a)].
% 12.08/12.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1813,a,1748,b)].
% 12.08/12.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1813,a,1749,b)].
% 12.08/12.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1813,a,1750,b)].
% 12.08/12.24 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1813,a,1751,b)].
% 12.08/12.24 1814 -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].
% 12.08/12.24 1815 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 12.08/12.24 1816 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 12.08/12.24 1817 -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].
% 12.08/12.24 1818 -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].
% 12.08/12.24 1819 -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].
% 12.08/12.24 1820 -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].
% 12.08/12.24 1821 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # label(axiom). [assumption].
% 12.08/12.24 1822 -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].
% 12.08/12.24 1823 -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].
% 12.08/12.24 1824 -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].
% 12.08/12.24 1825 -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].
% 12.08/12.24 1826 -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].
% 12.08/12.24 1827 -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].
% 12.08/12.24 1828 -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)].
% 12.08/12.24 1829 -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)].
% 12.08/12.24 1830 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 12.08/12.24 1831 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 12.33/12.49 1832 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(765,b,724,a)].
% 12.33/12.49 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1832,a,1823,b)].
% 12.33/12.49 1833 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(765,b,731,a)].
% 12.33/12.49 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1833,a,1823,b)].
% 12.33/12.49 1834 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1153,a,1113,a)].
% 12.33/12.49 1835 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1153,a,1138,a)].
% 12.33/12.49 1836 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1153,a,1139,b)].
% 12.33/12.49 1837 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1140,b)].
% 12.33/12.49 1838 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1458,a,1447,a)].
% 12.33/12.49 1839 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1459,a,1447,a)].
% 12.33/12.49 1840 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1460,a,1447,a)].
% 12.33/12.49 1841 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1476,a,1472,b)].
% 12.33/12.49 1842 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1476,a,1473,b)].
% 12.33/12.49 1843 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1476,a,1474,b)].
% 12.33/12.49 1844 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1476,a,1475,b)].
% 12.33/12.49 1845 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1557,b,1499,a)].
% 12.33/12.49 1846 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1557,b,1534,b)].
% 12.33/12.49 1847 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1557,b,1535,b)].
% 12.33/12.49 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1847,a,1828,a)].
% 12.33/12.49 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1847,a,1829,a)].
% 12.33/12.49 1848 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1557,b,1536,b)].
% 12.33/12.49 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1848,a,1828,a)].
% 12.33/12.49 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1848,a,1829,a)].
% 12.33/12.49 1849 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1585,b,1566,a)].
% 12.33/12.49 1850 -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)].
% 12.33/12.49 1851 -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)].
% 12.33/12.49 1852 -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)].
% 12.33/12.49 1853 -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)].
% 12.33/12.49 1854 -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)].
% 12.33/12.49 1855 -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)].
% 12.36/12.56 1856 -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)].
% 12.36/12.56 1857 -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)].
% 12.36/12.56 1858 -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)].
% 12.36/12.56 1859 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1585,b,1576,a)].
% 12.36/12.56 1860 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1599,a,1585,b)].
% 12.36/12.56 1861 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1600,a,1585,b)].
% 12.36/12.56 1862 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1622,a)].
% 12.36/12.56 1863 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1623,a)].
% 12.36/12.56 1864 -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(1650,b,1624,a)].
% 12.36/12.56 1865 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1625,a)].
% 12.36/12.56 1866 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1626,a)].
% 12.36/12.56 1867 -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(1650,b,1627,a)].
% 12.36/12.56 1868 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1650,b,1628,a)].
% 12.36/12.56 1869 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1650,b,1629,a)].
% 12.36/12.56 1870 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1650,b,1630,a)].
% 12.36/12.56 1871 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1650,b,1631,a)].
% 12.36/12.56 1872 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1632,a)].
% 12.36/12.56 1873 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1650,b,1633,a)].
% 12.36/12.56 1874 -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(1650,b,1634,a)].
% 12.36/12.56 1875 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1650,b,1635,a)].
% 12.36/12.56 1876 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1650,b,1636,a)].
% 12.36/12.56 1877 -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(1650,b,1637,a)].
% 12.36/12.56 1878 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1650,b,1638,a)].
% 12.36/12.56 1879 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1650,b,1639,a)].
% 12.66/12.83 1880 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1650,b,1640,a)].
% 12.66/12.83 1881 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1650,b,1641,a)].
% 12.66/12.83 1882 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) # label(axiom). [assumption].
% 12.66/12.83 1883 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 12.66/12.83 1884 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 12.66/12.83 1885 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) # label(axiom). [assumption].
% 12.66/12.83 1886 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) # label(axiom). [assumption].
% 12.66/12.83 1887 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_40) # label(axiom). [assumption].
% 12.66/12.83 1888 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_32) # label(axiom). [assumption].
% 12.66/12.83 1889 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_9) # label(axiom). [assumption].
% 12.66/12.83 1890 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(15,b,1,a)].
% 12.66/12.83 1891 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(15,b,3,a)].
% 12.66/12.83 1892 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 12.66/12.83 1893 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 12.66/12.83 1894 -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)].
% 12.66/12.83 1895 -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)].
% 12.66/12.83 1896 -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)].
% 12.66/12.83 1897 -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)].
% 12.66/12.83 1898 -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)].
% 12.66/12.83 1899 -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)].
% 12.66/12.83 1900 -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)].
% 12.66/12.83 1901 -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)].
% 12.66/12.84 1902 -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)].
% 12.66/12.84 1903 -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)].
% 12.66/12.84 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(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(881,b,832,a)].
% 12.66/12.84 1905 -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)].
% 12.66/12.84 1906 -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)].
% 12.66/12.84 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_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(881,b,835,a)].
% 12.66/12.84 1908 -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)].
% 12.66/12.84 1909 -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)].
% 12.66/12.84 1910 -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)].
% 12.66/12.84 1911 -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)].
% 12.66/12.84 1912 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(881,b,840,a)].
% 12.66/12.84 1913 -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)].
% 12.66/12.84 1914 -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)].
% 12.66/12.84 1915 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(881,b,843,a)].
% 12.66/12.84 1916 -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)].
% 12.66/12.84 1917 -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)].
% 12.66/12.84 1918 -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)].
% 12.66/12.84 1919 -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)].
% 12.66/12.84 1920 -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)].
% 12.66/12.84 1921 -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)].
% 12.66/12.84 1922 -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)].
% 12.66/12.84 1923 -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)].
% 12.66/12.84 1924 -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)].
% 12.66/12.84 1925 -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)].
% 12.66/12.84 1926 -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)].
% 12.66/12.84 1927 -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)].
% 12.66/12.84 1928 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(881,b,856,a)].
% 12.66/12.84 1929 -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)].
% 12.66/12.84 1930 -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)].
% 12.66/12.84 1931 -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)].
% 12.66/12.84 1932 -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)].
% 12.66/12.84 1933 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(881,b,861,a)].
% 12.66/12.84 1934 -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)].
% 12.66/12.84 1935 -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)].
% 12.66/12.84 1936 -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)].
% 12.66/12.84 1937 -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)].
% 12.66/12.84 1938 -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)].
% 12.66/12.84 1939 -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)].
% 12.66/12.84 1940 -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)].
% 12.66/12.84 1941 -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)].
% 12.66/12.84 1942 -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)].
% 12.66/12.84 1943 -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)].
% 12.66/12.84 1944 -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)].
% 12.66/12.84 1945 -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)].
% 12.77/12.98 1946 -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)].
% 12.77/12.98 1947 -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)].
% 12.77/12.98 1948 -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)].
% 12.77/12.98 1949 -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)].
% 12.77/12.98 1950 -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)].
% 12.77/12.98 1951 -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)].
% 12.77/12.98 1952 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1077,b,1068,a)].
% 12.77/12.98 1953 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1100,b,1091,a)].
% 12.77/12.98 1954 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1150,a,1113,a)].
% 12.77/12.98 1955 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1150,a,1138,a)].
% 12.77/12.98 1956 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1150,a,1139,b)].
% 12.77/12.98 1957 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1150,a,1140,b)].
% 12.77/12.98 1958 -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)].
% 12.77/12.98 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1958,a,1884,a)].
% 12.77/12.98 1959 -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)].
% 12.77/12.98 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1959,a,1884,a)].
% 12.77/12.98 1960 -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)].
% 12.77/12.98 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1960,a,1884,a)].
% 12.77/12.98 1961 -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)].
% 12.77/12.98 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1961,a,1884,a)].
% 12.77/12.98 1962 -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)].
% 12.77/12.98 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1962,a,1884,a)].
% 12.77/12.98 1963 -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)].
% 12.77/12.98 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1963,a,1884,a)].
% 12.77/12.98 1964 -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)].
% 12.77/12.98 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1964,a,1884,a)].
% 12.77/12.98 1965 -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)].
% 12.77/12.98 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1965,a,1884,a)].
% 12.85/13.06 1966 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)].
% 12.85/13.06 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1966,c,1886,b)].
% 12.85/13.06 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1966,c,1889,b)].
% 12.85/13.06 1967 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)].
% 12.85/13.06 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1967,c,1886,b)].
% 12.85/13.06 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1967,c,1889,b)].
% 12.85/13.06 1968 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1490,b,1474,b)].
% 12.85/13.06 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1968,b,1884,a)].
% 12.85/13.06 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1968,b,1889,b)].
% 12.85/13.06 1969 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,b,1474,b)].
% 12.85/13.06 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1969,b,1889,b)].
% 12.85/13.06 1970 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1582,b,1566,a)].
% 12.85/13.06 1971 -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)].
% 12.85/13.06 1972 -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)].
% 12.85/13.06 1973 -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)].
% 12.85/13.06 1974 -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)].
% 12.85/13.06 1975 -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)].
% 12.85/13.06 1976 -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)].
% 12.85/13.06 1977 -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)].
% 12.85/13.06 1978 -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)].
% 12.85/13.06 1979 -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)].
% 12.85/13.06 1980 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1582,b,1576,a)].
% 12.85/13.06 1981 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1599,a,1582,b)].
% 12.85/13.06 1982 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1600,a,1582,b)].
% 12.85/13.06 1983 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1622,a)].
% 12.85/13.06 1984 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1623,a)].
% 12.85/13.06 1985 -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(1647,b,1624,a)].
% 12.94/13.12 1986 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1625,a)].
% 12.94/13.12 1987 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1626,a)].
% 12.94/13.12 1988 -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(1647,b,1627,a)].
% 12.94/13.12 1989 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1647,b,1628,a)].
% 12.94/13.12 1990 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1647,b,1629,a)].
% 12.94/13.12 1991 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1647,b,1630,a)].
% 12.94/13.12 1992 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1647,b,1631,a)].
% 12.94/13.12 1993 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1632,a)].
% 12.94/13.12 1994 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1647,b,1633,a)].
% 12.94/13.12 1995 -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(1647,b,1634,a)].
% 12.94/13.12 1996 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1647,b,1635,a)].
% 12.94/13.12 1997 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1647,b,1636,a)].
% 12.94/13.12 1998 -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(1647,b,1637,a)].
% 12.94/13.12 1999 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1647,b,1638,a)].
% 12.94/13.12 2000 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1647,b,1639,a)].
% 12.94/13.12 2001 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1647,b,1640,a)].
% 12.94/13.12 2002 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1647,b,1641,a)].
% 12.94/13.12 2003 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1781,a,1750,b)].
% 12.94/13.12 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2003,b,1883,a)].
% 12.94/13.12 Derived: -c_less(A,A,tc_nat). [resolve(2003,b,1884,a)].
% 12.94/13.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2003,b,1886,b)].
% 12.94/13.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2003,b,1887,b)].
% 12.94/13.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2003,b,1888,b)].
% 12.94/13.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2003,b,1889,b)].
% 12.94/13.12 2004 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1782,a,1750,b)].
% 12.94/13.12 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2004,c,1883,a)].
% 12.94/13.12 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2004,c,1884,a)].
% 12.94/13.12 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2004,c,1886,b)].
% 12.94/13.12 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2004,c,1887,b)].
% 12.94/13.13 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2004,c,1888,b)].
% 12.94/13.13 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2004,c,1889,b)].
% 12.94/13.13 2005 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1783,a,1750,b)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2005,b,1883,a)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2005,b,1884,a)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2005,b,1886,b)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2005,b,1887,b)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2005,b,1888,b)].
% 12.94/13.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2005,b,1889,b)].
% 12.94/13.13 2006 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1784,a,1750,b)].
% 12.94/13.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2006,c,1883,a)].
% 12.94/13.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2006,c,1884,a)].
% 12.94/13.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2006,c,1886,b)].
% 12.94/13.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2006,c,1887,b)].
% 12.94/13.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2006,c,1888,b)].
% 12.94/13.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2006,c,1889,b)].
% 12.94/13.13 2007 -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(1785,a,1750,b)].
% 12.94/13.13 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(2007,c,1883,a)].
% 12.94/13.13 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(2007,c,1884,a)].
% 12.94/13.13 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(2007,c,1886,b)].
% 12.94/13.13 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(2007,c,1887,b)].
% 12.94/13.13 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(2007,c,1888,b)].
% 12.94/13.13 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(2007,c,1889,b)].
% 12.94/13.13 2008 -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(1786,a,1750,b)].
% 12.94/13.13 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(2008,c,1883,a)].
% 12.94/13.13 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(2008,c,1884,a)].
% 12.94/13.13 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(2008,c,1886,b)].
% 12.94/13.13 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(2008,c,1887,b)].
% 12.94/13.13 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(2008,c,1888,b)].
% 12.94/13.13 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(2008,c,1889,b)].
% 12.94/13.13 2009 -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(1787,a,1750,b)].
% 12.94/13.13 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(2009,c,1883,a)].
% 12.94/13.13 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(2009,c,1884,a)].
% 12.94/13.13 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(2009,c,1886,b)].
% 12.94/13.13 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(2009,c,1887,b)].
% 12.94/13.13 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(2009,c,1888,b)].
% 12.94/13.13 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(2009,c,1889,b)].
% 12.94/13.13 2010 -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(1788,a,1750,b)].
% 12.94/13.13 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(2010,c,1883,a)].
% 12.94/13.13 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(2010,c,1884,a)].
% 12.94/13.13 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(2010,c,1886,b)].
% 12.94/13.13 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(2010,c,1887,b)].
% 12.94/13.13 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(2010,c,1888,b)].
% 12.94/13.13 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(2010,c,1889,b)].
% 12.94/13.13 2011 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1789,a,1750,b)].
% 12.94/13.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2011,c,1883,a)].
% 12.94/13.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2011,c,1884,a)].
% 12.94/13.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2011,c,1886,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2011,c,1887,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2011,c,1888,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2011,c,1889,b)].
% 12.94/13.14 2012 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(1790,a,1750,b)].
% 12.94/13.14 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(2012,b,1883,a)].
% 12.94/13.14 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(2012,b,1884,a)].
% 12.94/13.14 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(2012,b,1886,b)].
% 12.94/13.14 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(2012,b,1887,b)].
% 12.94/13.14 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(2012,b,1888,b)].
% 12.94/13.14 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(2012,b,1889,b)].
% 12.94/13.14 2013 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1791,a,1750,b)].
% 12.94/13.14 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2013,b,1883,a)].
% 12.94/13.14 Derived: c_lessequals(A,A,tc_nat). [resolve(2013,b,1884,a)].
% 12.94/13.14 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2013,b,1886,b)].
% 12.94/13.14 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2013,b,1887,b)].
% 12.94/13.14 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2013,b,1888,b)].
% 12.94/13.14 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2013,b,1889,b)].
% 12.94/13.14 2014 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1792,d,1750,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2014,d,1883,a)].
% 12.94/13.14 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2014,d,1884,a)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2014,d,1886,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2014,d,1887,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2014,d,1888,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2014,d,1889,b)].
% 12.94/13.14 2015 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1793,c,1750,b)].
% 12.94/13.14 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2015,c,1883,a)].
% 12.94/13.14 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2015,c,1884,a)].
% 12.94/13.14 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2015,c,1886,b)].
% 12.94/13.14 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2015,c,1887,b)].
% 12.94/13.14 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2015,c,1888,b)].
% 12.94/13.14 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2015,c,1889,b)].
% 12.94/13.14 2016 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1794,a,1750,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2016,c,1883,a)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2016,c,1884,a)].
% 12.94/13.14 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(2016,c,1886,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2016,c,1887,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2016,c,1888,b)].
% 12.94/13.14 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(2016,c,1889,b)].
% 12.94/13.14 2017 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1795,a,1750,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2017,c,1883,a)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2017,c,1884,a)].
% 12.94/13.14 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(2017,c,1886,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2017,c,1887,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2017,c,1888,b)].
% 12.94/13.14 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(2017,c,1889,b)].
% 12.94/13.14 2018 -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(1796,a,1750,b)].
% 12.94/13.14 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(2018,d,1883,a)].
% 12.94/13.14 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(2018,d,1884,a)].
% 12.94/13.14 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(2018,d,1886,b)].
% 12.94/13.14 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(2018,d,1887,b)].
% 12.94/13.14 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(2018,d,1888,b)].
% 12.94/13.14 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(2018,d,1889,b)].
% 12.94/13.14 2019 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1797,a,1750,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2019,c,1883,a)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2019,c,1884,a)].
% 12.94/13.14 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(2019,c,1886,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2019,c,1887,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2019,c,1888,b)].
% 12.94/13.14 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(2019,c,1889,b)].
% 12.94/13.14 2020 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1798,a,1750,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2020,c,1883,a)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2020,c,1884,a)].
% 12.94/13.14 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(2020,c,1886,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2020,c,1887,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2020,c,1888,b)].
% 12.94/13.14 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(2020,c,1889,b)].
% 12.94/13.14 2021 -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(1799,a,1750,b)].
% 12.94/13.14 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(2021,d,1883,a)].
% 12.94/13.14 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(2021,d,1884,a)].
% 12.94/13.14 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(2021,d,1886,b)].
% 12.94/13.14 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(2021,d,1887,b)].
% 12.94/13.14 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(2021,d,1888,b)].
% 12.94/13.14 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(2021,d,1889,b)].
% 12.94/13.14 2022 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1750,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2022,c,1883,a)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2022,c,1884,a)].
% 12.94/13.14 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(2022,c,1886,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2022,c,1887,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2022,c,1888,b)].
% 12.94/13.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2022,c,1889,b)].
% 12.94/13.14 2023 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1801,a,1750,b)].
% 12.94/13.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2023,c,1883,a)].
% 12.94/13.15 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2023,c,1884,a)].
% 12.94/13.15 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(2023,c,1886,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2023,c,1887,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2023,c,1888,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2023,c,1889,b)].
% 12.94/13.15 2024 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1802,a,1750,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2024,c,1883,a)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2024,c,1884,a)].
% 12.94/13.15 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(2024,c,1886,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2024,c,1887,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2024,c,1888,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2024,c,1889,b)].
% 12.94/13.15 2025 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1803,a,1750,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2025,c,1883,a)].
% 12.94/13.15 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2025,c,1884,a)].
% 12.94/13.15 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(2025,c,1886,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2025,c,1887,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2025,c,1888,b)].
% 12.94/13.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1889,b)].
% 12.94/13.15 2026 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1804,a,1750,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2026,c,1883,a)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2026,c,1884,a)].
% 12.94/13.15 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(2026,c,1886,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2026,c,1887,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2026,c,1888,b)].
% 12.94/13.15 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(2026,c,1889,b)].
% 12.94/13.15 2027 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1805,a,1750,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2027,c,1883,a)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2027,c,1884,a)].
% 12.94/13.15 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(2027,c,1886,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2027,c,1887,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2027,c,1888,b)].
% 12.94/13.15 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(2027,c,1889,b)].
% 12.94/13.15 2028 -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(1806,a,1750,b)].
% 12.94/13.15 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(2028,d,1883,a)].
% 12.94/13.15 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(2028,d,1884,a)].
% 12.94/13.15 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(2028,d,1886,b)].
% 12.94/13.15 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(2028,d,1887,b)].
% 12.94/13.15 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(2028,d,1888,b)].
% 12.94/13.15 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(2028,d,1889,b)].
% 12.94/13.15 2029 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1807,a,1750,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2029,c,1883,a)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2029,c,1884,a)].
% 12.94/13.15 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(2029,c,1886,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2029,c,1887,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2029,c,1888,b)].
% 12.94/13.15 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(2029,c,1889,b)].
% 12.94/13.15 2030 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1808,a,1750,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2030,c,1883,a)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2030,c,1884,a)].
% 12.94/13.15 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(2030,c,1886,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2030,c,1887,b)].
% 12.94/13.15 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2030,c,1888,b)].
% 12.94/13.15 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(2030,c,1889,b)].
% 12.94/13.16 2031 -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(1809,a,1750,b)].
% 12.94/13.16 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(2031,d,1883,a)].
% 12.94/13.16 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(2031,d,1884,a)].
% 12.94/13.16 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(2031,d,1886,b)].
% 12.94/13.16 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(2031,d,1887,b)].
% 12.94/13.16 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(2031,d,1888,b)].
% 12.94/13.16 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(2031,d,1889,b)].
% 12.94/13.16 2032 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1810,a,1750,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2032,c,1883,a)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2032,c,1884,a)].
% 12.94/13.16 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(2032,c,1886,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2032,c,1887,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2032,c,1888,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1889,b)].
% 12.94/13.16 2033 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1811,a,1750,b)].
% 12.94/13.16 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2033,c,1883,a)].
% 12.94/13.16 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2033,c,1884,a)].
% 12.94/13.16 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(2033,c,1886,b)].
% 12.94/13.16 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2033,c,1887,b)].
% 12.94/13.16 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2033,c,1888,b)].
% 12.94/13.16 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2033,c,1889,b)].
% 12.94/13.16 2034 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1812,a,1750,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2034,c,1883,a)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2034,c,1884,a)].
% 12.94/13.16 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(2034,c,1886,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2034,c,1887,b)].
% 12.94/13.16 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2034,c,1888,b)].
% 13.15/13.32 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2034,c,1889,b)].
% 13.15/13.32 2035 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1813,a,1750,b)].
% 13.15/13.32 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2035,c,1883,a)].
% 13.15/13.32 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2035,c,1884,a)].
% 13.15/13.32 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(2035,c,1886,b)].
% 13.15/13.32 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2035,c,1887,b)].
% 13.15/13.32 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2035,c,1888,b)].
% 13.15/13.32 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,c,1889,b)].
% 13.15/13.32 2036 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 13.15/13.32 2037 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 13.15/13.32 2038 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 13.15/13.32 2039 -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].
% 13.15/13.32 2040 -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].
% 13.15/13.32 2041 -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].
% 13.15/13.32 2042 -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].
% 13.15/13.32 2043 -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].
% 13.15/13.32 2044 -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].
% 13.15/13.32 2045 -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].
% 13.15/13.32 2046 -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].
% 13.15/13.32 2047 -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].
% 13.15/13.32 2048 -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].
% 13.15/13.32 2049 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom). [assumption].
% 13.15/13.32 2050 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 13.15/13.32 2051 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 13.15/13.32 2052 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom). [assumption].
% 13.15/13.34 2053 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom). [assumption].
% 13.15/13.34 2054 -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].
% 13.15/13.34 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(2054,a,2037,a)].
% 13.15/13.34 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(2054,a,2038,a)].
% 13.15/13.34 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(2054,a,2039,b)].
% 13.15/13.34 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(2054,a,2040,b)].
% 13.15/13.34 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(2054,a,2041,b)].
% 13.15/13.34 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(2054,a,2042,b)].
% 13.15/13.34 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(2054,a,2043,b)].
% 13.15/13.34 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(2054,a,2044,b)].
% 13.15/13.34 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(2054,a,2045,b)].
% 13.15/13.34 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(2054,a,2046,b)].
% 13.15/13.34 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(2054,a,2047,b)].
% 13.15/13.34 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(2054,a,2048,b)].
% 13.15/13.34 2055 -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)].
% 13.15/13.34 2056 -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)].
% 13.15/13.34 2057 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,161,b)].
% 13.15/13.34 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2057,b,2047,b)].
% 13.15/13.34 2058 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,161,b)].
% 13.15/13.34 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2058,b,2047,b)].
% 13.15/13.34 2059 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(167,a,161,b)].
% 13.15/13.34 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2059,b,2040,b)].
% 13.15/13.34 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2059,b,2043,b)].
% 13.15/13.34 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2059,b,2044,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2059,b,2045,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2059,b,2047,b)].
% 13.15/13.36 2060 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(168,a,161,b)].
% 13.15/13.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2060,b,2040,b)].
% 13.15/13.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2060,b,2043,b)].
% 13.15/13.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2060,b,2044,b)].
% 13.15/13.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2060,b,2045,b)].
% 13.15/13.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2060,b,2047,b)].
% 13.15/13.36 2061 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2061,b,2040,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2061,b,2043,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2061,b,2044,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2061,b,2045,b)].
% 13.15/13.36 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2061,b,2047,b)].
% 13.15/13.36 2062 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 13.15/13.36 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2062,b,2040,b)].
% 13.15/13.36 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2062,b,2043,b)].
% 13.15/13.36 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2062,b,2044,b)].
% 13.15/13.36 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2062,b,2045,b)].
% 13.15/13.36 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2062,b,2047,b)].
% 13.15/13.36 2063 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 13.15/13.36 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(2063,c,2040,b)].
% 13.15/13.36 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(2063,c,2043,b)].
% 13.15/13.36 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(2063,c,2044,b)].
% 13.15/13.36 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(2063,c,2045,b)].
% 13.15/13.36 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(2063,c,2047,b)].
% 13.15/13.36 2064 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 13.37/13.58 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(2064,c,2040,b)].
% 13.37/13.58 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(2064,c,2043,b)].
% 13.37/13.58 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(2064,c,2044,b)].
% 13.37/13.58 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(2064,c,2045,b)].
% 13.37/13.58 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(2064,c,2047,b)].
% 13.37/13.58 2065 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1157,a,1113,a)].
% 13.37/13.58 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2065,a,2036,a)].
% 13.37/13.58 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2065,a,2049,a)].
% 13.37/13.58 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2065,a,2055,a)].
% 13.37/13.58 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2065,a,2056,a)].
% 13.37/13.58 2066 class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1157,a,1138,a)].
% 13.37/13.58 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2066,a,2036,a)].
% 13.37/13.58 Derived: class_HOL_Otimes(tc_nat). [resolve(2066,a,2049,a)].
% 13.37/13.58 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2066,a,2050,a)].
% 13.37/13.58 Derived: class_HOL_Ozero(tc_nat). [resolve(2066,a,2053,a)].
% 13.37/13.58 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(2066,a,2055,a)].
% 13.37/13.58 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(2066,a,2056,a)].
% 13.37/13.58 2067 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1139,b)].
% 13.37/13.58 2068 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1140,b)].
% 13.37/13.58 2069 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1597,b,1566,a)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2069,a,2039,b)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2069,a,2044,b)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2069,a,2045,b)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2069,a,2046,b)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2069,a,2047,b)].
% 13.37/13.58 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2069,a,2048,b)].
% 13.37/13.58 2070 -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)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2070,a,2039,b)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2070,a,2044,b)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2070,a,2045,b)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2070,a,2046,b)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2070,a,2047,b)].
% 13.37/13.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2070,a,2048,b)].
% 13.37/13.58 2071 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1568,a)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2071,a,2039,b)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2071,a,2044,b)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2071,a,2045,b)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2071,a,2046,b)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2071,a,2047,b)].
% 13.37/13.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2071,a,2048,b)].
% 13.37/13.58 2072 -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)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2072,a,2039,b)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2072,a,2044,b)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2072,a,2045,b)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2072,a,2046,b)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2072,a,2047,b)].
% 13.37/13.58 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2072,a,2048,b)].
% 13.37/13.58 2073 -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)].
% 13.37/13.58 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(2073,a,2039,b)].
% 13.37/13.58 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(2073,a,2044,b)].
% 13.37/13.58 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(2073,a,2045,b)].
% 13.37/13.59 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(2073,a,2046,b)].
% 13.37/13.59 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(2073,a,2047,b)].
% 13.37/13.59 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(2073,a,2048,b)].
% 13.37/13.59 2074 -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)].
% 13.37/13.59 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(2074,a,2039,b)].
% 13.37/13.59 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(2074,a,2044,b)].
% 13.37/13.59 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(2074,a,2045,b)].
% 13.37/13.59 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(2074,a,2046,b)].
% 13.37/13.59 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(2074,a,2047,b)].
% 13.37/13.59 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(2074,a,2048,b)].
% 13.37/13.59 2075 -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)].
% 13.37/13.59 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(2075,a,2039,b)].
% 13.37/13.59 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(2075,a,2044,b)].
% 13.37/13.59 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(2075,a,2045,b)].
% 13.37/13.59 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(2075,a,2046,b)].
% 13.37/13.59 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(2075,a,2047,b)].
% 13.37/13.59 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(2075,a,2048,b)].
% 13.37/13.59 2076 -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)].
% 13.37/13.59 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(2076,a,2039,b)].
% 13.37/13.59 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(2076,a,2044,b)].
% 13.37/13.59 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(2076,a,2045,b)].
% 13.37/13.60 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(2076,a,2046,b)].
% 13.37/13.60 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(2076,a,2047,b)].
% 13.37/13.60 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(2076,a,2048,b)].
% 13.37/13.60 2077 -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)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2039,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2044,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2045,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2077,a,2046,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2047,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2048,b)].
% 13.37/13.60 2078 -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)].
% 13.37/13.60 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(2078,a,2039,b)].
% 13.37/13.60 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(2078,a,2044,b)].
% 13.37/13.60 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(2078,a,2045,b)].
% 13.37/13.60 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(2078,a,2046,b)].
% 13.37/13.60 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(2078,a,2047,b)].
% 13.37/13.60 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(2078,a,2048,b)].
% 13.37/13.60 2079 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1597,b,1576,a)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2079,a,2039,b)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2079,a,2044,b)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2079,a,2045,b)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2079,a,2046,b)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2079,a,2047,b)].
% 13.37/13.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2079,a,2048,b)].
% 13.37/13.60 2080 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1599,a,1597,b)].
% 13.37/13.60 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2080,d,2039,b)].
% 13.47/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2080,d,2044,b)].
% 13.47/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2080,d,2045,b)].
% 13.47/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2080,d,2046,b)].
% 13.47/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2080,d,2047,b)].
% 13.47/13.66 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2080,d,2048,b)].
% 13.47/13.66 2081 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1600,a,1597,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2081,c,2039,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2081,c,2044,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2081,c,2045,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2081,c,2046,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2081,c,2047,b)].
% 13.47/13.66 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2081,c,2048,b)].
% 13.47/13.66 2082 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1622,a)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2082,a,2039,b)].
% 13.47/13.66 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(2082,a,2044,b)].
% 13.47/13.66 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(2082,a,2045,b)].
% 13.47/13.66 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(2082,a,2046,b)].
% 13.47/13.66 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(2082,a,2047,b)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2082,a,2048,b)].
% 13.47/13.66 2083 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1623,a)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2083,a,2039,b)].
% 13.47/13.66 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(2083,a,2044,b)].
% 13.47/13.66 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(2083,a,2045,b)].
% 13.47/13.66 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(2083,a,2046,b)].
% 13.47/13.66 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(2083,a,2047,b)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2083,a,2048,b)].
% 13.47/13.66 2084 -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(1662,b,1624,a)].
% 13.47/13.66 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(2084,a,2039,b)].
% 13.47/13.66 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(2084,a,2044,b)].
% 13.47/13.66 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(2084,a,2045,b)].
% 13.47/13.66 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(2084,a,2046,b)].
% 13.47/13.66 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(2084,a,2047,b)].
% 13.47/13.66 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(2084,a,2048,b)].
% 13.47/13.66 2085 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1625,a)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2085,a,2039,b)].
% 13.47/13.66 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(2085,a,2044,b)].
% 13.47/13.66 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(2085,a,2045,b)].
% 13.47/13.66 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(2085,a,2046,b)].
% 13.47/13.66 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(2085,a,2047,b)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2085,a,2048,b)].
% 13.47/13.66 2086 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1626,a)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2086,a,2039,b)].
% 13.47/13.66 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(2086,a,2044,b)].
% 13.47/13.66 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(2086,a,2045,b)].
% 13.47/13.66 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(2086,a,2046,b)].
% 13.47/13.66 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(2086,a,2047,b)].
% 13.47/13.66 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2086,a,2048,b)].
% 13.47/13.66 2087 -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(1662,b,1627,a)].
% 13.47/13.66 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(2087,a,2039,b)].
% 13.47/13.66 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(2087,a,2044,b)].
% 13.47/13.66 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(2087,a,2045,b)].
% 13.47/13.66 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(2087,a,2046,b)].
% 13.47/13.67 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(2087,a,2047,b)].
% 13.47/13.67 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(2087,a,2048,b)].
% 13.47/13.67 2088 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1628,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2088,a,2039,b)].
% 13.47/13.67 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(2088,a,2044,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2088,a,2045,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2088,a,2046,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2088,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2088,a,2048,b)].
% 13.47/13.67 2089 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1629,a)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2089,a,2039,b)].
% 13.47/13.67 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(2089,a,2044,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,a,2045,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2089,a,2046,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,a,2047,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2089,a,2048,b)].
% 13.47/13.67 2090 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1630,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2090,a,2039,b)].
% 13.47/13.67 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(2090,a,2044,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2090,a,2045,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2090,a,2046,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2090,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2090,a,2048,b)].
% 13.47/13.67 2091 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1631,a)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2091,a,2039,b)].
% 13.47/13.67 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(2091,a,2044,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2091,a,2045,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2091,a,2046,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2091,a,2047,b)].
% 13.47/13.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2091,a,2048,b)].
% 13.47/13.67 2092 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1632,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2092,a,2039,b)].
% 13.47/13.67 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(2092,a,2044,b)].
% 13.47/13.67 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(2092,a,2045,b)].
% 13.47/13.67 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(2092,a,2046,b)].
% 13.47/13.67 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(2092,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2092,a,2048,b)].
% 13.47/13.67 2093 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1633,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2093,a,2039,b)].
% 13.47/13.67 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(2093,a,2044,b)].
% 13.47/13.67 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(2093,a,2045,b)].
% 13.47/13.67 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(2093,a,2046,b)].
% 13.47/13.67 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(2093,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2093,a,2048,b)].
% 13.47/13.67 2094 -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(1662,b,1634,a)].
% 13.47/13.67 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(2094,a,2039,b)].
% 13.47/13.67 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(2094,a,2044,b)].
% 13.47/13.67 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(2094,a,2045,b)].
% 13.47/13.67 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(2094,a,2046,b)].
% 13.47/13.67 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(2094,a,2047,b)].
% 13.47/13.67 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(2094,a,2048,b)].
% 13.47/13.67 2095 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1635,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2095,a,2039,b)].
% 13.47/13.67 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(2095,a,2044,b)].
% 13.47/13.67 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(2095,a,2045,b)].
% 13.47/13.67 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(2095,a,2046,b)].
% 13.47/13.67 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(2095,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2095,a,2048,b)].
% 13.47/13.67 2096 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1636,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2096,a,2039,b)].
% 13.47/13.67 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(2096,a,2044,b)].
% 13.47/13.67 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(2096,a,2045,b)].
% 13.47/13.67 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(2096,a,2046,b)].
% 13.47/13.67 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(2096,a,2047,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2096,a,2048,b)].
% 13.47/13.67 2097 -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(1662,b,1637,a)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,a,2039,b)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,a,2044,b)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2097,a,2045,b)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2097,a,2046,b)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2097,a,2047,b)].
% 13.47/13.67 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2097,a,2048,b)].
% 13.47/13.67 2098 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1638,a)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2098,a,2039,b)].
% 13.47/13.67 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(2098,a,2044,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2098,a,2045,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2098,a,2046,b)].
% 13.47/13.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2098,a,2047,b)].
% 13.68/13.91 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2098,a,2048,b)].
% 13.68/13.91 2099 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1639,a)].
% 13.68/13.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2099,a,2039,b)].
% 13.68/13.91 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(2099,a,2044,b)].
% 13.68/13.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2099,a,2045,b)].
% 13.68/13.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2099,a,2046,b)].
% 13.68/13.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2099,a,2047,b)].
% 13.68/13.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2099,a,2048,b)].
% 13.68/13.91 2100 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1640,a)].
% 13.68/13.91 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2100,a,2039,b)].
% 13.68/13.91 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(2100,a,2044,b)].
% 13.68/13.91 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2100,a,2045,b)].
% 13.68/13.91 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2100,a,2046,b)].
% 13.68/13.91 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2100,a,2047,b)].
% 13.68/13.92 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2100,a,2048,b)].
% 13.68/13.92 2101 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1641,a)].
% 13.68/13.92 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2101,a,2039,b)].
% 13.68/13.92 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(2101,a,2044,b)].
% 13.68/13.92 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2101,a,2045,b)].
% 13.68/13.92 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2101,a,2046,b)].
% 13.68/13.92 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2101,a,2047,b)].
% 13.68/13.92 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2101,a,2048,b)].
% 13.68/13.92 2102 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_10) # label(axiom). [assumption].
% 13.68/13.92 2103 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 13.68/13.92 2104 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 13.68/13.92 2105 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_7) # label(axiom). [assumption].
% 13.68/13.92 2106 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) # label(axiom). [assumption].
% 13.78/13.95 2107 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_45) # label(axiom). [assumption].
% 13.78/13.95 2108 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_40) # label(axiom). [assumption].
% 13.78/13.95 2109 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_22) # label(axiom). [assumption].
% 13.78/13.95 2110 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) # label(axiom). [assumption].
% 13.78/13.95 2111 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_3) # label(axiom). [assumption].
% 13.78/13.95 2112 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_4) # label(axiom). [assumption].
% 13.78/13.95 2113 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_5) # label(axiom). [assumption].
% 13.78/13.95 2114 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # label(axiom). [assumption].
% 13.78/13.95 2115 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_9) # label(axiom). [assumption].
% 13.78/13.95 2116 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_22) # label(axiom). [assumption].
% 13.78/13.95 2117 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(34,b,1,a)].
% 13.78/13.95 2118 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(34,b,3,a)].
% 13.78/13.95 2119 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 13.78/13.95 2120 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 13.78/13.95 2121 -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)].
% 13.78/13.95 2122 -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)].
% 13.78/13.95 2123 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(167,a,157,b)].
% 13.78/13.95 2124 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(168,a,157,b)].
% 13.78/13.95 2125 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 13.78/13.95 2126 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 13.78/13.95 2127 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 13.78/13.95 2128 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 13.78/13.95 2129 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,286,a)].
% 14.00/14.18 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2129,a,2106,b)].
% 14.00/14.18 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2129,a,2109,b)].
% 14.00/14.18 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2129,a,2110,b)].
% 14.00/14.18 2130 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,288,a)].
% 14.00/14.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2130,a,2106,b)].
% 14.00/14.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2130,a,2109,b)].
% 14.00/14.18 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2130,a,2110,b)].
% 14.00/14.18 2131 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)].
% 14.00/14.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2131,c,2110,b)].
% 14.00/14.18 2132 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)].
% 14.00/14.18 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2132,c,2110,b)].
% 14.00/14.18 2133 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(324,a,307,b)].
% 14.00/14.18 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2133,b,2110,b)].
% 14.00/14.18 2134 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(780,a,724,a)].
% 14.00/14.18 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2134,a,2110,b)].
% 14.00/14.18 2135 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1155,a,1113,a)].
% 14.00/14.18 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2135,a,2129,a)].
% 14.00/14.18 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2135,a,2130,a)].
% 14.00/14.18 2136 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1155,a,1138,a)].
% 14.00/14.18 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2136,a,2129,a)].
% 14.00/14.18 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2136,a,2130,a)].
% 14.00/14.18 2137 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1155,a,1139,b)].
% 14.00/14.18 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(2137,a,2129,a)].
% 14.00/14.18 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(2137,a,2130,a)].
% 14.00/14.18 2138 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1155,a,1140,b)].
% 14.00/14.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(2138,a,2129,a)].
% 14.00/14.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(2138,a,2130,a)].
% 14.00/14.18 2139 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1593,b,1566,a)].
% 14.00/14.18 2140 -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)].
% 14.00/14.18 2141 -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)].
% 14.00/14.18 2142 -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)].
% 14.00/14.18 2143 -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)].
% 14.00/14.18 2144 -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)].
% 14.00/14.18 2145 -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)].
% 14.08/14.25 2146 -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)].
% 14.08/14.25 2147 -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)].
% 14.08/14.25 2148 -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)].
% 14.08/14.25 2149 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1593,b,1576,a)].
% 14.08/14.25 2150 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1599,a,1593,b)].
% 14.08/14.25 2151 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1600,a,1593,b)].
% 14.08/14.25 2152 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1622,a)].
% 14.08/14.25 2153 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1658,b,1623,a)].
% 14.08/14.25 2154 -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(1658,b,1624,a)].
% 14.08/14.25 2155 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1625,a)].
% 14.08/14.25 2156 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1658,b,1626,a)].
% 14.08/14.25 2157 -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(1658,b,1627,a)].
% 14.08/14.25 2158 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1658,b,1628,a)].
% 14.08/14.25 2159 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1658,b,1629,a)].
% 14.08/14.25 2160 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1658,b,1630,a)].
% 14.08/14.25 2161 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1658,b,1631,a)].
% 14.08/14.25 2162 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1658,b,1632,a)].
% 14.08/14.25 2163 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1658,b,1633,a)].
% 14.08/14.25 2164 -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(1658,b,1634,a)].
% 14.08/14.25 2165 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1658,b,1635,a)].
% 14.08/14.25 2166 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1658,b,1636,a)].
% 14.08/14.25 2167 -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(1658,b,1637,a)].
% 14.08/14.25 2168 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1658,b,1638,a)].
% 14.08/14.25 2169 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1658,b,1639,a)].
% 14.08/14.25 2170 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1658,b,1640,a)].
% 14.08/14.25 2171 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1658,b,1641,a)].
% 14.13/14.33 2172 -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(2054,a,2045,b)].
% 14.13/14.33 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(2172,d,2103,a)].
% 14.13/14.33 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(2172,d,2104,a)].
% 14.13/14.33 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(2172,d,2105,b)].
% 14.13/14.33 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(2172,d,2106,b)].
% 14.13/14.33 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(2172,d,2107,b)].
% 14.13/14.33 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(2172,d,2108,b)].
% 14.13/14.33 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(2172,d,2109,b)].
% 14.13/14.33 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(2172,d,2110,b)].
% 14.13/14.33 2173 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2059,b,2045,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2173,b,2105,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2173,b,2106,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2173,b,2107,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2173,b,2108,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2173,b,2109,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2173,b,2110,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2173,b,2116,b)].
% 14.13/14.33 2174 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2060,b,2045,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2174,b,2105,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2174,b,2106,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2174,b,2107,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2174,b,2108,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2174,b,2109,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2174,b,2110,b)].
% 14.13/14.33 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2174,b,2116,b)].
% 14.13/14.33 2175 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2061,b,2045,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2175,b,2103,a)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2175,b,2105,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2175,b,2106,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2175,b,2107,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2175,b,2108,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2175,b,2109,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2175,b,2110,b)].
% 14.13/14.33 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2175,b,2116,b)].
% 14.13/14.33 2176 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2062,b,2045,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2176,b,2103,a)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2176,b,2105,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2176,b,2106,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2176,b,2107,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2176,b,2108,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2176,b,2109,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2176,b,2110,b)].
% 14.13/14.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2176,b,2116,b)].
% 14.13/14.33 2177 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2063,c,2045,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2177,c,2105,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2177,c,2106,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2177,c,2107,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2177,c,2108,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2177,c,2109,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2177,c,2110,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2177,c,2116,b)].
% 14.13/14.33 2178 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2064,c,2045,b)].
% 14.13/14.33 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2178,c,2105,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2178,c,2106,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2178,c,2107,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2178,c,2108,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2178,c,2109,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2178,c,2110,b)].
% 14.13/14.34 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2178,c,2116,b)].
% 14.13/14.34 2179 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2069,a,2045,b)].
% 14.13/14.34 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2179,b,2103,a)].
% 14.13/14.34 Derived: -c_less(A,A,tc_nat). [resolve(2179,b,2104,a)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2179,b,2105,b)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2179,b,2106,b)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2179,b,2107,b)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2179,b,2108,b)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2179,b,2109,b)].
% 14.13/14.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2179,b,2110,b)].
% 14.13/14.34 2180 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2070,a,2045,b)].
% 14.13/14.34 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2180,c,2103,a)].
% 14.13/14.34 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2180,c,2104,a)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2180,c,2105,b)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2180,c,2106,b)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2180,c,2107,b)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2180,c,2108,b)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2180,c,2109,b)].
% 14.13/14.34 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2180,c,2110,b)].
% 14.13/14.34 2181 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2071,a,2045,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2181,b,2103,a)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2181,b,2104,a)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2181,b,2105,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2181,b,2106,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2181,b,2107,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2181,b,2108,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2181,b,2109,b)].
% 14.13/14.34 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2181,b,2110,b)].
% 14.13/14.34 2182 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2072,a,2045,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2182,c,2103,a)].
% 14.13/14.34 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2182,c,2104,a)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2182,c,2105,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2182,c,2106,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2182,c,2107,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2182,c,2108,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2182,c,2109,b)].
% 14.13/14.34 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2182,c,2110,b)].
% 14.13/14.34 2183 -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(2073,a,2045,b)].
% 14.13/14.34 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(2183,c,2103,a)].
% 14.13/14.34 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(2183,c,2104,a)].
% 14.13/14.34 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(2183,c,2105,b)].
% 14.13/14.34 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(2183,c,2106,b)].
% 14.13/14.34 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(2183,c,2107,b)].
% 14.13/14.34 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(2183,c,2108,b)].
% 14.13/14.34 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(2183,c,2109,b)].
% 14.13/14.34 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(2183,c,2110,b)].
% 14.13/14.35 2184 -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(2074,a,2045,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2184,c,2103,a)].
% 14.13/14.35 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2184,c,2104,a)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2184,c,2105,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2184,c,2106,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2184,c,2107,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2184,c,2108,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2184,c,2109,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2184,c,2110,b)].
% 14.13/14.35 2185 -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(2075,a,2045,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2185,c,2103,a)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2185,c,2104,a)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2185,c,2105,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2185,c,2106,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2185,c,2107,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2185,c,2108,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2185,c,2109,b)].
% 14.13/14.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2185,c,2110,b)].
% 14.13/14.35 2186 -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(2076,a,2045,b)].
% 14.13/14.35 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(2186,c,2103,a)].
% 14.13/14.35 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(2186,c,2104,a)].
% 14.13/14.35 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(2186,c,2105,b)].
% 14.13/14.35 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(2186,c,2106,b)].
% 14.13/14.35 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(2186,c,2107,b)].
% 14.13/14.35 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(2186,c,2108,b)].
% 14.13/14.35 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(2186,c,2109,b)].
% 14.13/14.35 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(2186,c,2110,b)].
% 14.13/14.35 2187 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2045,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2187,c,2103,a)].
% 14.13/14.35 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2187,c,2104,a)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2187,c,2105,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2187,c,2106,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2187,c,2107,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2187,c,2108,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2187,c,2109,b)].
% 14.13/14.35 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2187,c,2110,b)].
% 14.13/14.35 2188 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(2078,a,2045,b)].
% 14.13/14.35 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(2188,b,2103,a)].
% 14.13/14.35 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(2188,b,2104,a)].
% 14.13/14.35 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(2188,b,2105,b)].
% 14.13/14.35 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(2188,b,2106,b)].
% 14.13/14.35 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(2188,b,2107,b)].
% 14.13/14.35 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(2188,b,2108,b)].
% 14.13/14.35 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(2188,b,2109,b)].
% 14.13/14.35 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(2188,b,2110,b)].
% 14.22/14.36 2189 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2079,a,2045,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2189,b,2103,a)].
% 14.22/14.36 Derived: c_lessequals(A,A,tc_nat). [resolve(2189,b,2104,a)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2189,b,2105,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2189,b,2106,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2189,b,2107,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2189,b,2108,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2189,b,2109,b)].
% 14.22/14.36 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2189,b,2110,b)].
% 14.22/14.36 2190 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2080,d,2045,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2190,d,2103,a)].
% 14.22/14.36 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2190,d,2104,a)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2190,d,2105,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2190,d,2106,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2190,d,2107,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2190,d,2108,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2190,d,2109,b)].
% 14.22/14.36 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2190,d,2110,b)].
% 14.22/14.36 2191 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2081,c,2045,b)].
% 14.22/14.36 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2191,c,2103,a)].
% 14.22/14.36 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2191,c,2104,a)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2191,c,2105,b)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2191,c,2106,b)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2191,c,2107,b)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2191,c,2108,b)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2191,c,2109,b)].
% 14.22/14.36 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2191,c,2110,b)].
% 14.22/14.36 2192 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2082,a,2045,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2192,c,2103,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2192,c,2104,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2192,c,2105,b)].
% 14.22/14.36 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(2192,c,2106,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2192,c,2107,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2192,c,2108,b)].
% 14.22/14.36 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(2192,c,2109,b)].
% 14.22/14.36 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(2192,c,2110,b)].
% 14.22/14.36 2193 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2083,a,2045,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2193,c,2103,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2193,c,2104,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2193,c,2105,b)].
% 14.22/14.36 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(2193,c,2106,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2193,c,2107,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2193,c,2108,b)].
% 14.22/14.36 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(2193,c,2109,b)].
% 14.22/14.36 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(2193,c,2110,b)].
% 14.22/14.36 2194 -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(2084,a,2045,b)].
% 14.22/14.36 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(2194,d,2103,a)].
% 14.22/14.36 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(2194,d,2104,a)].
% 14.22/14.36 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(2194,d,2105,b)].
% 14.22/14.36 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(2194,d,2106,b)].
% 14.22/14.36 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(2194,d,2107,b)].
% 14.22/14.36 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(2194,d,2108,b)].
% 14.22/14.36 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(2194,d,2109,b)].
% 14.22/14.36 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(2194,d,2110,b)].
% 14.22/14.36 2195 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2085,a,2045,b)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2195,c,2103,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2195,c,2104,a)].
% 14.22/14.36 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2195,c,2105,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2195,c,2106,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2195,c,2107,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2195,c,2108,b)].
% 14.22/14.37 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(2195,c,2109,b)].
% 14.22/14.37 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(2195,c,2110,b)].
% 14.22/14.37 2196 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2086,a,2045,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2196,c,2103,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2196,c,2104,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2196,c,2105,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2196,c,2106,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2196,c,2107,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2196,c,2108,b)].
% 14.22/14.37 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(2196,c,2109,b)].
% 14.22/14.37 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(2196,c,2110,b)].
% 14.22/14.37 2197 -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(2087,a,2045,b)].
% 14.22/14.37 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(2197,d,2103,a)].
% 14.22/14.37 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(2197,d,2104,a)].
% 14.22/14.37 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(2197,d,2105,b)].
% 14.22/14.37 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(2197,d,2106,b)].
% 14.22/14.37 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(2197,d,2107,b)].
% 14.22/14.37 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(2197,d,2108,b)].
% 14.22/14.37 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(2197,d,2109,b)].
% 14.22/14.37 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(2197,d,2110,b)].
% 14.22/14.37 2198 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2088,a,2045,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2198,c,2103,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2198,c,2104,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2198,c,2105,b)].
% 14.22/14.37 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(2198,c,2106,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2198,c,2107,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2198,c,2108,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2198,c,2109,b)].
% 14.22/14.37 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(2198,c,2110,b)].
% 14.22/14.37 2199 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,a,2045,b)].
% 14.22/14.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2199,c,2103,a)].
% 14.22/14.37 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2199,c,2104,a)].
% 14.22/14.37 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2199,c,2105,b)].
% 14.22/14.37 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(2199,c,2106,b)].
% 14.22/14.37 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2199,c,2107,b)].
% 14.22/14.37 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2199,c,2108,b)].
% 14.22/14.37 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2199,c,2109,b)].
% 14.22/14.37 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(2199,c,2110,b)].
% 14.22/14.37 2200 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2090,a,2045,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2200,c,2103,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2200,c,2104,a)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2200,c,2105,b)].
% 14.22/14.37 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(2200,c,2106,b)].
% 14.22/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2200,c,2107,b)].
% 14.24/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2200,c,2108,b)].
% 14.24/14.37 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2200,c,2109,b)].
% 14.24/14.37 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(2200,c,2110,b)].
% 14.24/14.37 2201 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2091,a,2045,b)].
% 14.24/14.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2201,c,2103,a)].
% 14.24/14.37 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2201,c,2104,a)].
% 14.24/14.37 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,c,2105,b)].
% 14.24/14.38 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(2201,c,2106,b)].
% 14.24/14.38 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2201,c,2107,b)].
% 14.24/14.38 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2201,c,2108,b)].
% 14.24/14.38 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,c,2109,b)].
% 14.24/14.38 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(2201,c,2110,b)].
% 14.24/14.38 2202 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2092,a,2045,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2202,c,2103,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2202,c,2104,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2202,c,2105,b)].
% 14.24/14.38 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(2202,c,2106,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2202,c,2107,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2202,c,2108,b)].
% 14.24/14.38 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(2202,c,2109,b)].
% 14.24/14.38 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(2202,c,2110,b)].
% 14.24/14.38 2203 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2093,a,2045,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2203,c,2103,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2203,c,2104,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2203,c,2105,b)].
% 14.24/14.38 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(2203,c,2106,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2203,c,2107,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2203,c,2108,b)].
% 14.24/14.38 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(2203,c,2109,b)].
% 14.24/14.38 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(2203,c,2110,b)].
% 14.24/14.38 2204 -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(2094,a,2045,b)].
% 14.24/14.38 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(2204,d,2103,a)].
% 14.24/14.38 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(2204,d,2104,a)].
% 14.24/14.38 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(2204,d,2105,b)].
% 14.24/14.38 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(2204,d,2106,b)].
% 14.24/14.38 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(2204,d,2107,b)].
% 14.24/14.38 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(2204,d,2108,b)].
% 14.24/14.38 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(2204,d,2109,b)].
% 14.24/14.38 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(2204,d,2110,b)].
% 14.24/14.38 2205 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2095,a,2045,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2205,c,2103,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2205,c,2104,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2205,c,2105,b)].
% 14.24/14.38 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(2205,c,2106,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2205,c,2107,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2205,c,2108,b)].
% 14.24/14.38 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(2205,c,2109,b)].
% 14.24/14.38 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(2205,c,2110,b)].
% 14.24/14.38 2206 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2096,a,2045,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2206,c,2103,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2206,c,2104,a)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,c,2105,b)].
% 14.24/14.38 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(2206,c,2106,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2206,c,2107,b)].
% 14.24/14.38 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2206,c,2108,b)].
% 14.24/14.38 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(2206,c,2109,b)].
% 14.24/14.38 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(2206,c,2110,b)].
% 14.24/14.38 2207 -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(2097,a,2045,b)].
% 14.24/14.38 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(2207,d,2103,a)].
% 14.24/14.39 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(2207,d,2104,a)].
% 14.24/14.39 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(2207,d,2105,b)].
% 14.24/14.39 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(2207,d,2106,b)].
% 14.24/14.39 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(2207,d,2107,b)].
% 14.24/14.39 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(2207,d,2108,b)].
% 14.24/14.39 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(2207,d,2109,b)].
% 14.24/14.39 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(2207,d,2110,b)].
% 14.24/14.39 2208 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2098,a,2045,b)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2208,c,2103,a)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2208,c,2104,a)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2208,c,2105,b)].
% 14.24/14.39 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(2208,c,2106,b)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2208,c,2107,b)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2208,c,2108,b)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2208,c,2109,b)].
% 14.24/14.39 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(2208,c,2110,b)].
% 14.24/14.39 2209 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2099,a,2045,b)].
% 14.24/14.39 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2209,c,2103,a)].
% 14.24/14.39 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2209,c,2104,a)].
% 14.24/14.39 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2105,b)].
% 14.24/14.39 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(2209,c,2106,b)].
% 14.24/14.39 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2209,c,2107,b)].
% 14.24/14.39 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2209,c,2108,b)].
% 14.24/14.39 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2109,b)].
% 14.24/14.39 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(2209,c,2110,b)].
% 14.24/14.39 2210 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2100,a,2045,b)].
% 14.24/14.39 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2210,c,2103,a)].
% 14.44/14.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2210,c,2104,a)].
% 14.44/14.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2210,c,2105,b)].
% 14.44/14.58 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(2210,c,2106,b)].
% 14.44/14.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2210,c,2107,b)].
% 14.44/14.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2210,c,2108,b)].
% 14.44/14.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2210,c,2109,b)].
% 14.44/14.58 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(2210,c,2110,b)].
% 14.44/14.58 2211 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2101,a,2045,b)].
% 14.44/14.58 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2211,c,2103,a)].
% 14.44/14.58 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2211,c,2104,a)].
% 14.44/14.58 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2105,b)].
% 14.44/14.58 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(2211,c,2106,b)].
% 14.44/14.58 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2211,c,2107,b)].
% 14.44/14.58 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2211,c,2108,b)].
% 14.44/14.58 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2109,b)].
% 14.44/14.58 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(2211,c,2110,b)].
% 14.44/14.58 2212 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_2) # label(axiom). [assumption].
% 14.44/14.58 2213 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 14.44/14.58 2214 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 14.44/14.58 2215 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) # label(axiom). [assumption].
% 14.44/14.58 2216 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_39) # label(axiom). [assumption].
% 14.44/14.58 2217 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_31) # label(axiom). [assumption].
% 14.44/14.58 2218 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_3) # label(axiom). [assumption].
% 14.44/14.58 2219 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_4) # label(axiom). [assumption].
% 14.44/14.58 2220 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_6) # label(axiom). [assumption].
% 14.44/14.58 2221 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_7) # label(axiom). [assumption].
% 14.44/14.58 2222 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_8) # label(axiom). [assumption].
% 14.53/14.67 2223 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(32,b,1,a)].
% 14.53/14.67 2224 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(32,b,3,a)].
% 14.53/14.67 2225 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 14.53/14.67 2226 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 14.53/14.67 2227 -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)].
% 14.53/14.67 2228 -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)].
% 14.53/14.67 2229 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(167,a,155,b)].
% 14.53/14.67 2230 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(168,a,155,b)].
% 14.53/14.67 2231 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 14.53/14.67 2232 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 14.53/14.67 2233 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.53/14.67 2234 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 14.53/14.67 2235 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,286,a)].
% 14.53/14.67 2236 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,288,a)].
% 14.53/14.67 2237 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)].
% 14.53/14.67 2238 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)].
% 14.53/14.67 2239 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(779,a,724,a)].
% 14.53/14.67 2240 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(779,a,731,a)].
% 14.53/14.67 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(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(892,b,822,a)].
% 14.53/14.67 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(2241,a,2215,b)].
% 14.53/14.68 2242 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2242,a,2215,b)].
% 14.53/14.68 2243 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2243,a,2215,b)].
% 14.53/14.68 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_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(892,b,825,a)].
% 14.53/14.68 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2244,a,2215,b)].
% 14.53/14.68 2245 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2245,a,2215,b)].
% 14.53/14.68 2246 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2246,a,2215,b)].
% 14.53/14.68 2247 -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)].
% 14.53/14.68 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2247,a,2215,b)].
% 14.53/14.68 2248 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2248,a,2215,b)].
% 14.53/14.68 2249 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2249,a,2215,b)].
% 14.53/14.68 2250 -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)].
% 14.53/14.68 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2250,a,2215,b)].
% 14.53/14.68 2251 -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)].
% 14.53/14.68 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2251,a,2215,b)].
% 14.53/14.68 2252 -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)].
% 14.53/14.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2252,a,2215,b)].
% 14.53/14.68 2253 -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)].
% 14.55/14.69 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(2253,a,2215,b)].
% 14.55/14.69 2254 -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)].
% 14.55/14.69 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(2254,a,2215,b)].
% 14.55/14.69 2255 -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)].
% 14.55/14.69 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2255,a,2215,b)].
% 14.55/14.69 2256 -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)].
% 14.55/14.69 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2256,a,2215,b)].
% 14.55/14.69 2257 -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)].
% 14.55/14.69 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2257,a,2215,b)].
% 14.55/14.69 2258 -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)].
% 14.55/14.69 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2258,a,2215,b)].
% 14.55/14.69 2259 -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)].
% 14.55/14.69 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2259,a,2215,b)].
% 14.55/14.69 2260 -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)].
% 14.55/14.69 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2260,a,2215,b)].
% 14.55/14.69 2261 -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)].
% 14.55/14.69 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2261,a,2215,b)].
% 14.55/14.69 2262 -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)].
% 14.55/14.69 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2262,a,2215,b)].
% 14.55/14.70 2263 -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)].
% 14.55/14.70 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(2263,a,2215,b)].
% 14.55/14.70 2264 -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)].
% 14.55/14.70 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(2264,a,2215,b)].
% 14.55/14.70 2265 -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)].
% 14.55/14.70 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(2265,a,2215,b)].
% 14.55/14.70 2266 -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)].
% 14.55/14.70 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(2266,a,2215,b)].
% 14.55/14.70 2267 -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)].
% 14.55/14.70 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(2267,a,2215,b)].
% 14.55/14.70 2268 -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)].
% 14.55/14.70 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(2268,a,2215,b)].
% 14.55/14.70 2269 -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)].
% 14.55/14.70 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(2269,a,2215,b)].
% 14.55/14.70 2270 -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)].
% 14.55/14.70 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(2270,a,2215,b)].
% 14.55/14.70 2271 -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)].
% 14.55/14.70 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(2271,a,2215,b)].
% 14.55/14.70 2272 -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)].
% 14.55/14.70 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(2272,a,2215,b)].
% 14.55/14.70 2273 -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)].
% 14.55/14.70 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(2273,a,2215,b)].
% 14.55/14.70 2274 -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)].
% 14.55/14.70 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2274,a,2215,b)].
% 14.55/14.71 2275 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(892,b,856,a)].
% 14.55/14.71 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2275,a,2215,b)].
% 14.55/14.71 2276 -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)].
% 14.55/14.71 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(2276,a,2215,b)].
% 14.55/14.71 2277 -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)].
% 14.55/14.71 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(2277,a,2215,b)].
% 14.55/14.71 2278 -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)].
% 14.55/14.71 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(2278,a,2215,b)].
% 14.55/14.71 2279 -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)].
% 14.55/14.71 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(2279,a,2215,b)].
% 14.55/14.71 2280 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(892,b,861,a)].
% 14.55/14.71 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2280,a,2215,b)].
% 14.55/14.71 2281 -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)].
% 14.55/14.71 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(2281,a,2215,b)].
% 14.55/14.71 2282 -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)].
% 14.55/14.71 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(2282,a,2215,b)].
% 14.55/14.71 2283 -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)].
% 14.55/14.71 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(2283,a,2215,b)].
% 14.55/14.71 2284 -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)].
% 14.55/14.71 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(2284,a,2215,b)].
% 14.55/14.71 2285 -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)].
% 14.55/14.71 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(2285,a,2215,b)].
% 14.55/14.71 2286 -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)].
% 14.55/14.71 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2286,a,2215,b)].
% 14.55/14.71 2287 -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)].
% 14.55/14.71 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2287,a,2215,b)].
% 14.55/14.71 2288 -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)].
% 14.55/14.71 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2288,a,2215,b)].
% 14.55/14.71 2289 -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)].
% 14.55/14.71 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(2289,a,2215,b)].
% 14.55/14.71 2290 -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)].
% 14.55/14.71 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(2290,a,2215,b)].
% 14.55/14.71 2291 -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)].
% 14.55/14.71 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(2291,a,2215,b)].
% 14.55/14.71 2292 -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)].
% 14.55/14.71 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(2292,a,2215,b)].
% 14.55/14.71 2293 -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)].
% 14.55/14.71 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(2293,a,2215,b)].
% 14.55/14.71 2294 -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)].
% 14.55/14.71 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(2294,a,2215,b)].
% 14.55/14.71 2295 -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)].
% 14.55/14.71 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(2295,a,2215,b)].
% 14.55/14.71 2296 -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)].
% 14.55/14.71 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2296,a,2215,b)].
% 14.55/14.71 2297 -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)].
% 14.67/14.83 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2297,a,2215,b)].
% 14.67/14.83 2298 -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)].
% 14.67/14.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2298,a,2215,b)].
% 14.67/14.83 2299 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1068,a)].
% 14.67/14.83 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2299,a,2215,b)].
% 14.67/14.83 2300 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1091,a)].
% 14.67/14.83 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2300,a,2215,b)].
% 14.67/14.83 2301 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1149,a,1113,a)].
% 14.67/14.83 2302 class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1149,a,1138,a)].
% 14.67/14.83 2303 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1149,a,1139,b)].
% 14.67/14.83 2304 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1149,a,1140,b)].
% 14.67/14.83 2305 -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)].
% 14.67/14.83 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(2305,a,2215,b)].
% 14.67/14.83 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(2305,a,2216,b)].
% 14.67/14.83 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(2305,a,2217,b)].
% 14.67/14.83 2306 -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)].
% 14.67/14.83 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(2306,a,2215,b)].
% 14.67/14.83 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(2306,a,2216,b)].
% 14.67/14.83 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(2306,a,2217,b)].
% 14.67/14.83 2307 -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)].
% 14.67/14.83 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(2307,a,2215,b)].
% 14.67/14.83 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(2307,a,2216,b)].
% 14.67/14.83 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(2307,a,2217,b)].
% 14.67/14.83 2308 -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)].
% 14.67/14.83 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(2308,a,2215,b)].
% 14.67/14.83 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(2308,a,2216,b)].
% 14.67/14.83 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(2308,a,2217,b)].
% 14.67/14.83 2309 -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)].
% 14.73/14.89 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(2309,a,2215,b)].
% 14.73/14.89 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(2309,a,2216,b)].
% 14.73/14.89 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(2309,a,2217,b)].
% 14.73/14.89 2310 -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)].
% 14.73/14.89 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(2310,a,2215,b)].
% 14.73/14.89 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(2310,a,2216,b)].
% 14.73/14.89 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(2310,a,2217,b)].
% 14.73/14.89 2311 -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)].
% 14.73/14.89 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(2311,a,2215,b)].
% 14.73/14.89 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(2311,a,2216,b)].
% 14.73/14.89 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(2311,a,2217,b)].
% 14.73/14.89 2312 -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)].
% 14.73/14.89 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(2312,a,2215,b)].
% 14.73/14.89 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(2312,a,2216,b)].
% 14.73/14.89 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(2312,a,2217,b)].
% 14.73/14.89 2313 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1591,b,1566,a)].
% 14.73/14.89 2314 -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)].
% 14.73/14.89 2315 -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)].
% 14.73/14.89 2316 -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)].
% 14.73/14.89 2317 -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)].
% 14.73/14.89 2318 -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)].
% 14.73/14.89 2319 -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)].
% 14.73/14.89 2320 -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)].
% 14.73/14.89 2321 -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)].
% 14.73/14.89 2322 -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)].
% 14.73/14.89 2323 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1591,b,1576,a)].
% 14.73/14.89 2324 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1599,a,1591,b)].
% 14.82/14.98 2325 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1600,a,1591,b)].
% 14.82/14.98 2326 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1622,a)].
% 14.82/14.98 2327 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1656,b,1623,a)].
% 14.82/14.98 2328 -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(1656,b,1624,a)].
% 14.82/14.98 2329 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1625,a)].
% 14.82/14.98 2330 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1656,b,1626,a)].
% 14.82/14.98 2331 -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(1656,b,1627,a)].
% 14.82/14.98 2332 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1656,b,1628,a)].
% 14.82/14.98 2333 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1656,b,1629,a)].
% 14.82/14.98 2334 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1656,b,1630,a)].
% 14.82/14.98 2335 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1656,b,1631,a)].
% 14.82/14.98 2336 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1656,b,1632,a)].
% 14.82/14.98 2337 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1656,b,1633,a)].
% 14.82/14.98 2338 -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(1656,b,1634,a)].
% 14.82/14.98 2339 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1656,b,1635,a)].
% 14.82/14.98 2340 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1656,b,1636,a)].
% 14.82/14.98 2341 -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(1656,b,1637,a)].
% 14.82/14.98 2342 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1656,b,1638,a)].
% 14.82/14.98 2343 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1656,b,1639,a)].
% 14.82/14.98 2344 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1656,b,1640,a)].
% 14.82/14.98 2345 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1656,b,1641,a)].
% 14.82/14.98 2346 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1966,c,1889,b)].
% 14.82/14.98 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2346,c,2213,a)].
% 14.82/14.98 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2346,c,2214,a)].
% 14.82/14.98 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2346,c,2215,b)].
% 14.82/14.98 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2346,c,2216,b)].
% 14.82/14.98 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2346,c,2217,b)].
% 14.85/15.00 2347 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1967,c,1889,b)].
% 14.85/15.00 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2347,c,2213,a)].
% 14.85/15.00 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2347,c,2214,a)].
% 14.85/15.00 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2347,c,2215,b)].
% 14.85/15.00 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2347,c,2216,b)].
% 14.85/15.00 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2347,c,2217,b)].
% 14.85/15.00 2348 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1968,b,1889,b)].
% 14.85/15.00 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2348,b,2213,a)].
% 14.85/15.00 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2348,b,2214,a)].
% 14.85/15.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2348,b,2215,b)].
% 14.85/15.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2348,b,2216,b)].
% 14.85/15.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2348,b,2217,b)].
% 14.85/15.00 2349 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1969,b,1889,b)].
% 14.85/15.00 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2349,b,2213,a)].
% 14.85/15.00 Derived: class_HOL_Oplus(tc_nat). [resolve(2349,b,2214,a)].
% 14.85/15.00 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2349,b,2215,b)].
% 14.85/15.00 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2349,b,2216,b)].
% 14.85/15.00 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2349,b,2217,b)].
% 14.85/15.00 2350 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2003,b,1889,b)].
% 14.85/15.00 2351 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2004,c,1889,b)].
% 14.85/15.00 2352 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2005,b,1889,b)].
% 14.85/15.00 2353 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2006,c,1889,b)].
% 14.85/15.00 2354 -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(2007,c,1889,b)].
% 14.85/15.00 2355 -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(2008,c,1889,b)].
% 14.85/15.00 2356 -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(2009,c,1889,b)].
% 14.85/15.00 2357 -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(2010,c,1889,b)].
% 14.85/15.00 2358 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2011,c,1889,b)].
% 14.85/15.00 2359 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(2012,b,1889,b)].
% 14.85/15.00 2360 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2013,b,1889,b)].
% 14.85/15.00 2361 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2014,d,1889,b)].
% 14.85/15.00 2362 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2015,c,1889,b)].
% 14.85/15.00 2363 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2016,c,1889,b)].
% 14.91/15.04 2364 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2017,c,1889,b)].
% 14.91/15.04 2365 -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(2018,d,1889,b)].
% 14.91/15.04 2366 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2019,c,1889,b)].
% 14.91/15.04 2367 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2020,c,1889,b)].
% 14.91/15.04 2368 -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(2021,d,1889,b)].
% 14.91/15.04 2369 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2022,c,1889,b)].
% 14.91/15.04 2370 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2023,c,1889,b)].
% 14.91/15.04 2371 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2024,c,1889,b)].
% 14.91/15.04 2372 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1889,b)].
% 14.91/15.04 2373 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2026,c,1889,b)].
% 14.91/15.04 2374 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2027,c,1889,b)].
% 14.91/15.04 2375 -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(2028,d,1889,b)].
% 14.91/15.04 2376 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2029,c,1889,b)].
% 14.91/15.04 2377 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2030,c,1889,b)].
% 14.91/15.04 2378 -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(2031,d,1889,b)].
% 14.91/15.04 2379 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1889,b)].
% 14.91/15.04 2380 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2033,c,1889,b)].
% 14.91/15.04 2381 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2034,c,1889,b)].
% 14.91/15.04 2382 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,c,1889,b)].
% 14.91/15.04 2383 -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(2054,a,2043,b)].
% 14.91/15.04 2384 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2059,b,2043,b)].
% 14.91/15.04 2385 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2060,b,2043,b)].
% 14.91/15.04 2386 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2061,b,2043,b)].
% 14.91/15.04 2387 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2062,b,2043,b)].
% 14.91/15.04 2388 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2063,c,2043,b)].
% 14.91/15.04 2389 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2064,c,2043,b)].
% 14.91/15.08 2390 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2129,a,2109,b)].
% 14.91/15.08 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2390,b,2215,b)].
% 14.91/15.08 2391 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2130,a,2109,b)].
% 14.91/15.08 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2391,b,2215,b)].
% 14.91/15.08 2392 -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(2172,d,2109,b)].
% 14.91/15.08 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(2392,d,2213,a)].
% 14.91/15.08 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(2392,d,2214,a)].
% 14.91/15.08 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(2392,d,2215,b)].
% 14.91/15.08 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(2392,d,2216,b)].
% 14.91/15.08 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(2392,d,2217,b)].
% 14.91/15.08 2393 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2173,b,2109,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2393,b,2213,a)].
% 14.91/15.08 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2393,b,2214,a)].
% 14.91/15.08 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2393,b,2215,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2393,b,2216,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2393,b,2217,b)].
% 14.91/15.08 2394 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2174,b,2109,b)].
% 14.91/15.08 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2394,b,2213,a)].
% 14.91/15.08 Derived: class_HOL_Otimes(tc_nat). [resolve(2394,b,2214,a)].
% 14.91/15.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2394,b,2215,b)].
% 14.91/15.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2394,b,2216,b)].
% 14.91/15.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2394,b,2217,b)].
% 14.91/15.08 2395 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2175,b,2109,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2395,b,2213,a)].
% 14.91/15.08 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2395,b,2214,a)].
% 14.91/15.08 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2395,b,2215,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2395,b,2216,b)].
% 14.91/15.08 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2395,b,2217,b)].
% 14.91/15.08 2396 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2176,b,2109,b)].
% 14.91/15.08 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2396,b,2213,a)].
% 14.91/15.08 Derived: class_HOL_Ozero(tc_nat). [resolve(2396,b,2214,a)].
% 14.91/15.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2396,b,2215,b)].
% 14.91/15.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2396,b,2216,b)].
% 14.91/15.09 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2396,b,2217,b)].
% 14.91/15.09 2397 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2177,c,2109,b)].
% 14.91/15.09 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(2397,c,2213,a)].
% 14.91/15.09 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(2397,c,2214,a)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2397,c,2215,b)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2397,c,2216,b)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2397,c,2217,b)].
% 14.91/15.09 2398 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2178,c,2109,b)].
% 14.91/15.09 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(2398,c,2213,a)].
% 14.91/15.09 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(2398,c,2214,a)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2398,c,2215,b)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2398,c,2216,b)].
% 14.91/15.09 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2398,c,2217,b)].
% 14.91/15.09 2399 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2179,b,2109,b)].
% 14.91/15.09 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2399,b,2213,a)].
% 14.91/15.09 Derived: -c_less(A,A,tc_nat). [resolve(2399,b,2214,a)].
% 14.91/15.09 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2399,b,2215,b)].
% 14.91/15.09 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2399,b,2216,b)].
% 14.91/15.09 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2399,b,2217,b)].
% 14.91/15.09 2400 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2180,c,2109,b)].
% 14.91/15.09 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2400,c,2213,a)].
% 14.91/15.10 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2400,c,2214,a)].
% 14.91/15.10 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2400,c,2215,b)].
% 14.91/15.10 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2400,c,2216,b)].
% 14.91/15.10 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2400,c,2217,b)].
% 14.91/15.10 2401 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2181,b,2109,b)].
% 14.91/15.10 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2401,b,2213,a)].
% 14.91/15.10 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2401,b,2214,a)].
% 14.91/15.10 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2401,b,2215,b)].
% 14.91/15.10 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2401,b,2216,b)].
% 14.91/15.10 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2401,b,2217,b)].
% 14.91/15.10 2402 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2182,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2402,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2402,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2402,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2402,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2402,c,2217,b)].
% 14.91/15.10 2403 -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(2183,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2403,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2403,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2403,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2403,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2403,c,2217,b)].
% 14.91/15.10 2404 -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(2184,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2404,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2404,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2404,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2404,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2404,c,2217,b)].
% 14.91/15.10 2405 -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(2185,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2405,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2405,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2405,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2405,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2405,c,2217,b)].
% 14.91/15.10 2406 -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(2186,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2406,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(2406,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2406,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2406,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2406,c,2217,b)].
% 14.91/15.10 2407 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2187,c,2109,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2407,c,2213,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2407,c,2214,a)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2407,c,2215,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2407,c,2216,b)].
% 14.91/15.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2407,c,2217,b)].
% 14.91/15.10 2408 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(2188,b,2109,b)].
% 14.91/15.10 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(2408,b,2213,a)].
% 14.91/15.10 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(2408,b,2214,a)].
% 14.97/15.11 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2408,b,2215,b)].
% 14.97/15.11 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2408,b,2216,b)].
% 14.97/15.11 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2408,b,2217,b)].
% 14.97/15.11 2409 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2189,b,2109,b)].
% 14.97/15.11 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2409,b,2213,a)].
% 14.97/15.11 Derived: c_lessequals(A,A,tc_nat). [resolve(2409,b,2214,a)].
% 14.97/15.11 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2409,b,2215,b)].
% 14.97/15.11 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2409,b,2216,b)].
% 14.97/15.11 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2409,b,2217,b)].
% 14.97/15.11 2410 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2190,d,2109,b)].
% 14.97/15.11 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2410,d,2213,a)].
% 14.97/15.11 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2410,d,2214,a)].
% 14.97/15.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2410,d,2215,b)].
% 14.97/15.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2410,d,2216,b)].
% 14.97/15.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2410,d,2217,b)].
% 14.97/15.11 2411 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2191,c,2109,b)].
% 14.97/15.11 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2411,c,2213,a)].
% 14.97/15.11 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2411,c,2214,a)].
% 14.97/15.11 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2411,c,2215,b)].
% 14.97/15.11 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2411,c,2216,b)].
% 14.97/15.11 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2411,c,2217,b)].
% 14.97/15.11 2412 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2192,c,2109,b)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2412,c,2213,a)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2412,c,2214,a)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2412,c,2215,b)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2412,c,2216,b)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2412,c,2217,b)].
% 14.97/15.11 2413 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2193,c,2109,b)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2413,c,2213,a)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2413,c,2214,a)].
% 14.97/15.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2413,c,2215,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2413,c,2216,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2413,c,2217,b)].
% 14.97/15.12 2414 -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(2194,d,2109,b)].
% 14.97/15.12 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(2414,d,2213,a)].
% 14.97/15.12 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(2414,d,2214,a)].
% 14.97/15.12 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(2414,d,2215,b)].
% 14.97/15.12 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(2414,d,2216,b)].
% 14.97/15.12 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(2414,d,2217,b)].
% 14.97/15.12 2415 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2195,c,2109,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2415,c,2213,a)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2415,c,2214,a)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2415,c,2215,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2415,c,2216,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2415,c,2217,b)].
% 14.97/15.12 2416 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2196,c,2109,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2416,c,2213,a)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2416,c,2214,a)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2416,c,2215,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2416,c,2216,b)].
% 14.97/15.12 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2416,c,2217,b)].
% 14.97/15.12 2417 -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(2197,d,2109,b)].
% 14.97/15.12 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2417,d,2213,a)].
% 14.97/15.12 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2417,d,2214,a)].
% 14.97/15.12 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2417,d,2215,b)].
% 14.97/15.12 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2417,d,2216,b)].
% 14.97/15.13 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(2417,d,2217,b)].
% 14.97/15.13 2418 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2198,c,2109,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2418,c,2213,a)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2418,c,2214,a)].
% 14.97/15.13 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(2418,c,2215,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2418,c,2216,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2418,c,2217,b)].
% 14.97/15.13 2419 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2199,c,2109,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2419,c,2213,a)].
% 14.97/15.13 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2419,c,2214,a)].
% 14.97/15.13 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(2419,c,2215,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2419,c,2216,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2419,c,2217,b)].
% 14.97/15.13 2420 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2200,c,2109,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2420,c,2213,a)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2420,c,2214,a)].
% 14.97/15.13 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(2420,c,2215,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2420,c,2216,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2420,c,2217,b)].
% 14.97/15.13 2421 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,c,2109,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2421,c,2213,a)].
% 14.97/15.13 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2421,c,2214,a)].
% 14.97/15.13 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2421,c,2215,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2421,c,2216,b)].
% 14.97/15.13 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2421,c,2217,b)].
% 14.97/15.13 2422 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2202,c,2109,b)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2422,c,2213,a)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2422,c,2214,a)].
% 14.97/15.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2422,c,2215,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2422,c,2216,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2422,c,2217,b)].
% 14.97/15.14 2423 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2203,c,2109,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2423,c,2213,a)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2423,c,2214,a)].
% 14.97/15.14 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(2423,c,2215,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2423,c,2216,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2423,c,2217,b)].
% 14.97/15.14 2424 -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(2204,d,2109,b)].
% 14.97/15.14 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(2424,d,2213,a)].
% 14.97/15.14 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2424,d,2214,a)].
% 14.97/15.14 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(2424,d,2215,b)].
% 14.97/15.14 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(2424,d,2216,b)].
% 14.97/15.14 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(2424,d,2217,b)].
% 14.97/15.14 2425 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2205,c,2109,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2425,c,2213,a)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2425,c,2214,a)].
% 14.97/15.14 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(2425,c,2215,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2425,c,2216,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2425,c,2217,b)].
% 14.97/15.14 2426 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2206,c,2109,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2426,c,2213,a)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2426,c,2214,a)].
% 14.97/15.14 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(2426,c,2215,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2426,c,2216,b)].
% 14.97/15.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2426,c,2217,b)].
% 14.97/15.15 2427 -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(2207,d,2109,b)].
% 14.97/15.15 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(2427,d,2213,a)].
% 14.97/15.15 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(2427,d,2214,a)].
% 14.97/15.15 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(2427,d,2215,b)].
% 14.97/15.15 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(2427,d,2216,b)].
% 14.97/15.15 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(2427,d,2217,b)].
% 14.97/15.15 2428 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2208,c,2109,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2428,c,2213,a)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2428,c,2214,a)].
% 14.97/15.15 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(2428,c,2215,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2428,c,2216,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2428,c,2217,b)].
% 14.97/15.15 2429 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2109,b)].
% 14.97/15.15 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2429,c,2213,a)].
% 14.97/15.15 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2429,c,2214,a)].
% 14.97/15.15 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(2429,c,2215,b)].
% 14.97/15.15 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2429,c,2216,b)].
% 14.97/15.15 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2429,c,2217,b)].
% 14.97/15.15 2430 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2210,c,2109,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2430,c,2213,a)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2430,c,2214,a)].
% 14.97/15.15 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(2430,c,2215,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2430,c,2216,b)].
% 14.97/15.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2430,c,2217,b)].
% 14.97/15.15 2431 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2109,b)].
% 14.97/15.15 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2431,c,2213,a)].
% 14.97/15.15 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2431,c,2214,a)].
% 14.97/15.15 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(2431,c,2215,b)].
% 14.97/15.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2431,c,2216,b)].
% 15.22/15.36 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2431,c,2217,b)].
% 15.22/15.36 2432 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_10) # label(axiom). [assumption].
% 15.22/15.36 2433 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 15.22/15.36 2434 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 15.22/15.36 2435 -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].
% 15.22/15.36 2436 -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].
% 15.22/15.36 2437 -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].
% 15.22/15.36 2438 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) # label(axiom). [assumption].
% 15.22/15.36 2439 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_20) # label(axiom). [assumption].
% 15.22/15.36 2440 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_11) # label(axiom). [assumption].
% 15.22/15.36 2441 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_5) # label(axiom). [assumption].
% 15.22/15.36 2442 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_6) # label(axiom). [assumption].
% 15.22/15.36 2443 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_7) # label(axiom). [assumption].
% 15.22/15.36 2444 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_9) # label(axiom). [assumption].
% 15.22/15.36 2445 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(108,a,107,b)].
% 15.22/15.36 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2445,b,2435,b)].
% 15.22/15.36 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2445,b,2438,b)].
% 15.22/15.36 2446 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)].
% 15.22/15.36 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(2446,b,2435,b)].
% 15.22/15.36 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(2446,b,2438,b)].
% 15.22/15.36 2447 -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)].
% 15.22/15.36 2448 -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)].
% 15.22/15.36 2449 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,159,b)].
% 15.22/15.36 2450 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,159,b)].
% 15.45/15.59 2451 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(167,a,159,b)].
% 15.45/15.59 2452 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(168,a,159,b)].
% 15.45/15.59 2453 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 15.45/15.59 2454 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 15.45/15.59 2455 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.45/15.59 2456 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 15.45/15.59 2457 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1156,a,1113,a)].
% 15.45/15.59 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(2457,a,2445,b)].
% 15.45/15.59 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(2457,a,2446,b)].
% 15.45/15.59 2458 class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1156,a,1138,a)].
% 15.45/15.59 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(2458,a,2445,b)].
% 15.45/15.59 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(2458,a,2446,b)].
% 15.45/15.59 2459 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1139,b)].
% 15.45/15.59 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) = c_times(C,B,A). [resolve(2459,a,2445,b)].
% 15.45/15.59 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(2459,a,2446,b)].
% 15.45/15.59 2460 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1140,b)].
% 15.45/15.59 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) = c_times(C,B,A). [resolve(2460,a,2445,b)].
% 15.45/15.59 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(2460,a,2446,b)].
% 15.45/15.59 2461 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1595,b,1566,a)].
% 15.45/15.59 2462 -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)].
% 15.45/15.59 2463 -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)].
% 15.45/15.59 2464 -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)].
% 15.45/15.59 2465 -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)].
% 15.45/15.59 2466 -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)].
% 15.45/15.59 2467 -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)].
% 15.45/15.59 2468 -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)].
% 15.45/15.59 2469 -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)].
% 15.45/15.59 2470 -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)].
% 15.52/15.71 2471 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1595,b,1576,a)].
% 15.52/15.71 2472 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1599,a,1595,b)].
% 15.52/15.71 2473 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1600,a,1595,b)].
% 15.52/15.71 2474 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1622,a)].
% 15.52/15.71 2475 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1623,a)].
% 15.52/15.71 2476 -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(1660,b,1624,a)].
% 15.52/15.71 2477 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1625,a)].
% 15.52/15.71 2478 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1626,a)].
% 15.52/15.71 2479 -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(1660,b,1627,a)].
% 15.52/15.71 2480 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1628,a)].
% 15.52/15.71 2481 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1629,a)].
% 15.52/15.71 2482 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1630,a)].
% 15.52/15.71 2483 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1631,a)].
% 15.52/15.71 2484 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1632,a)].
% 15.52/15.71 2485 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1633,a)].
% 15.52/15.71 2486 -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(1660,b,1634,a)].
% 15.52/15.71 2487 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1635,a)].
% 15.52/15.71 2488 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1636,a)].
% 15.52/15.71 2489 -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(1660,b,1637,a)].
% 15.52/15.71 2490 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1638,a)].
% 15.52/15.71 2491 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1639,a)].
% 15.52/15.71 2492 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1640,a)].
% 15.52/15.71 2493 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1641,a)].
% 15.52/15.71 2494 -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(2054,a,2047,b)].
% 15.52/15.71 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(2494,d,2439,b)].
% 15.52/15.71 2495 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2057,b,2047,b)].
% 15.52/15.71 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2495,b,2439,b)].
% 15.52/15.72 2496 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2058,b,2047,b)].
% 15.52/15.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2496,b,2439,b)].
% 15.52/15.72 2497 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2059,b,2047,b)].
% 15.52/15.72 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2497,b,2439,b)].
% 15.52/15.72 2498 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2060,b,2047,b)].
% 15.52/15.72 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2498,b,2439,b)].
% 15.52/15.72 2499 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2061,b,2047,b)].
% 15.52/15.72 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2499,b,2439,b)].
% 15.52/15.72 2500 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2062,b,2047,b)].
% 15.52/15.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2500,b,2439,b)].
% 15.52/15.72 2501 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2063,c,2047,b)].
% 15.52/15.72 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(2501,c,2439,b)].
% 15.52/15.72 2502 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2064,c,2047,b)].
% 15.52/15.72 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(2502,c,2439,b)].
% 15.52/15.72 2503 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2069,a,2047,b)].
% 15.52/15.72 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2503,b,2439,b)].
% 15.52/15.72 2504 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2070,a,2047,b)].
% 15.52/15.72 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2504,c,2439,b)].
% 15.52/15.72 2505 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2071,a,2047,b)].
% 15.52/15.72 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2505,b,2439,b)].
% 15.52/15.72 2506 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2072,a,2047,b)].
% 15.52/15.72 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2506,c,2439,b)].
% 15.52/15.72 2507 -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(2073,a,2047,b)].
% 15.52/15.72 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(2507,c,2439,b)].
% 15.52/15.72 2508 -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(2074,a,2047,b)].
% 15.52/15.72 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(2508,c,2439,b)].
% 15.61/15.74 2509 -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(2075,a,2047,b)].
% 15.61/15.74 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(2509,c,2439,b)].
% 15.61/15.74 2510 -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(2076,a,2047,b)].
% 15.61/15.74 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(2510,c,2439,b)].
% 15.61/15.74 2511 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2047,b)].
% 15.61/15.74 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2511,c,2439,b)].
% 15.61/15.74 2512 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(2078,a,2047,b)].
% 15.61/15.74 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(2512,b,2439,b)].
% 15.61/15.74 2513 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2079,a,2047,b)].
% 15.61/15.74 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2513,b,2439,b)].
% 15.61/15.74 2514 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2080,d,2047,b)].
% 15.61/15.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2514,d,2439,b)].
% 15.61/15.74 2515 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2081,c,2047,b)].
% 15.61/15.74 Derived: -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2515,c,2439,b)].
% 15.61/15.74 2516 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2082,a,2047,b)].
% 15.61/15.74 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(2516,c,2439,b)].
% 15.61/15.74 2517 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2083,a,2047,b)].
% 15.61/15.74 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(2517,c,2439,b)].
% 15.61/15.74 2518 -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(2084,a,2047,b)].
% 15.61/15.74 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(2518,d,2439,b)].
% 15.61/15.74 2519 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2085,a,2047,b)].
% 15.61/15.74 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(2519,c,2439,b)].
% 15.61/15.74 2520 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2086,a,2047,b)].
% 15.61/15.74 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(2520,c,2439,b)].
% 15.61/15.74 2521 -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(2087,a,2047,b)].
% 15.61/15.74 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(2521,d,2439,b)].
% 15.61/15.76 2522 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2088,a,2047,b)].
% 15.61/15.76 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2522,c,2439,b)].
% 15.61/15.76 2523 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,a,2047,b)].
% 15.61/15.76 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2523,c,2439,b)].
% 15.61/15.76 2524 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2090,a,2047,b)].
% 15.61/15.76 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2524,c,2439,b)].
% 15.61/15.76 2525 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2091,a,2047,b)].
% 15.61/15.76 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2525,c,2439,b)].
% 15.61/15.76 2526 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2092,a,2047,b)].
% 15.61/15.76 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(2526,c,2439,b)].
% 15.61/15.76 2527 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2093,a,2047,b)].
% 15.61/15.76 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(2527,c,2439,b)].
% 15.61/15.76 2528 -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(2094,a,2047,b)].
% 15.61/15.76 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(2528,d,2439,b)].
% 15.61/15.76 2529 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2095,a,2047,b)].
% 15.61/15.76 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(2529,c,2439,b)].
% 15.61/15.76 2530 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2096,a,2047,b)].
% 15.61/15.76 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(2530,c,2439,b)].
% 15.61/15.76 2531 -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(2097,a,2047,b)].
% 15.61/15.76 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(2531,d,2439,b)].
% 15.61/15.76 2532 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2098,a,2047,b)].
% 15.61/15.76 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2532,c,2439,b)].
% 15.61/15.76 2533 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2099,a,2047,b)].
% 15.61/15.76 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2533,c,2439,b)].
% 15.61/15.76 2534 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2100,a,2047,b)].
% 15.61/15.76 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2534,c,2439,b)].
% 15.90/16.02 2535 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2101,a,2047,b)].
% 15.90/16.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2535,c,2439,b)].
% 15.90/16.02 2536 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) # label(axiom). [assumption].
% 15.90/16.02 2537 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 15.90/16.02 2538 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 15.90/16.02 2539 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) # label(axiom). [assumption].
% 15.90/16.02 2540 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_36) # label(axiom). [assumption].
% 15.90/16.02 2541 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_39) # label(axiom). [assumption].
% 15.90/16.02 2542 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) # label(axiom). [assumption].
% 15.90/16.02 2543 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) # label(axiom). [assumption].
% 15.90/16.02 2544 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) # label(axiom). [assumption].
% 15.90/16.02 2545 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) # label(axiom). [assumption].
% 15.90/16.02 2546 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) # label(axiom). [assumption].
% 15.90/16.02 2547 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(33,b,1,a)].
% 15.90/16.02 2548 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(33,b,3,a)].
% 15.90/16.02 2549 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 15.90/16.02 2550 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 15.90/16.02 2551 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(108,a,105,b)].
% 15.90/16.02 2552 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)].
% 15.90/16.02 2553 -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)].
% 15.90/16.02 2554 -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)].
% 15.90/16.02 2555 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(167,a,156,b)].
% 15.90/16.02 2556 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(168,a,156,b)].
% 15.90/16.02 2557 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(203,b,195,b)].
% 16.10/16.27 2558 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(204,b,195,b)].
% 16.10/16.27 2559 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 16.10/16.27 2560 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 16.10/16.27 2561 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 16.10/16.27 2562 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 16.10/16.27 2563 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,286,a)].
% 16.10/16.27 2564 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,288,a)].
% 16.10/16.27 2565 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)].
% 16.10/16.27 2566 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)].
% 16.10/16.27 2567 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1154,a,1113,a)].
% 16.10/16.27 2568 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1154,a,1138,a)].
% 16.10/16.27 2569 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1154,a,1139,b)].
% 16.10/16.27 2570 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1154,a,1140,b)].
% 16.10/16.27 2571 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1592,b,1566,a)].
% 16.10/16.27 2572 -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)].
% 16.10/16.27 2573 -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)].
% 16.10/16.27 2574 -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)].
% 16.10/16.27 2575 -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)].
% 16.10/16.27 2576 -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)].
% 16.10/16.27 2577 -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)].
% 16.10/16.27 2578 -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)].
% 16.10/16.27 2579 -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)].
% 16.10/16.27 2580 -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)].
% 16.10/16.27 2581 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1592,b,1576,a)].
% 16.10/16.27 2582 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1599,a,1592,b)].
% 16.10/16.27 2583 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1600,a,1592,b)].
% 16.10/16.27 2584 -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(1657,b,1622,a)].
% 16.21/16.35 2585 -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(1657,b,1623,a)].
% 16.21/16.35 2586 -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(1657,b,1624,a)].
% 16.21/16.35 2587 -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(1657,b,1625,a)].
% 16.21/16.35 2588 -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(1657,b,1626,a)].
% 16.21/16.35 2589 -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(1657,b,1627,a)].
% 16.21/16.35 2590 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1657,b,1628,a)].
% 16.21/16.35 2591 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1657,b,1629,a)].
% 16.21/16.35 2592 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1657,b,1630,a)].
% 16.21/16.35 2593 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1657,b,1631,a)].
% 16.21/16.35 2594 -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(1657,b,1632,a)].
% 16.21/16.35 2595 -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(1657,b,1633,a)].
% 16.21/16.35 2596 -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(1657,b,1634,a)].
% 16.21/16.35 2597 -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(1657,b,1635,a)].
% 16.21/16.35 2598 -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(1657,b,1636,a)].
% 16.21/16.35 2599 -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(1657,b,1637,a)].
% 16.21/16.35 2600 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1657,b,1638,a)].
% 16.21/16.35 2601 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1657,b,1639,a)].
% 16.21/16.35 2602 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1657,b,1640,a)].
% 16.21/16.35 2603 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1657,b,1641,a)].
% 16.21/16.35 2604 -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(2054,a,2044,b)].
% 16.21/16.35 2605 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2059,b,2044,b)].
% 16.21/16.35 2606 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2060,b,2044,b)].
% 16.21/16.35 2607 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2061,b,2044,b)].
% 16.21/16.35 2608 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2062,b,2044,b)].
% 16.21/16.35 2609 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2063,c,2044,b)].
% 16.21/16.37 2610 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2064,c,2044,b)].
% 16.21/16.37 2611 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2069,a,2044,b)].
% 16.21/16.37 2612 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2070,a,2044,b)].
% 16.21/16.37 2613 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2071,a,2044,b)].
% 16.21/16.37 2614 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2072,a,2044,b)].
% 16.21/16.37 2615 -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(2073,a,2044,b)].
% 16.21/16.37 2616 -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(2074,a,2044,b)].
% 16.21/16.37 2617 -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(2075,a,2044,b)].
% 16.21/16.37 2618 -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(2076,a,2044,b)].
% 16.21/16.37 2619 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2044,b)].
% 16.21/16.37 2620 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(2078,a,2044,b)].
% 16.21/16.37 2621 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2079,a,2044,b)].
% 16.21/16.37 2622 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2080,d,2044,b)].
% 16.21/16.37 2623 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2081,c,2044,b)].
% 16.21/16.37 2624 -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(2082,a,2044,b)].
% 16.21/16.37 2625 -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(2083,a,2044,b)].
% 16.21/16.37 2626 -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(2084,a,2044,b)].
% 16.21/16.37 2627 -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(2085,a,2044,b)].
% 16.21/16.37 2628 -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(2086,a,2044,b)].
% 16.21/16.37 2629 -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(2087,a,2044,b)].
% 16.21/16.37 2630 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2088,a,2044,b)].
% 16.21/16.37 2631 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2089,a,2044,b)].
% 16.21/16.37 2632 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2090,a,2044,b)].
% 16.21/16.37 2633 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2091,a,2044,b)].
% 16.21/16.40 2634 -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(2092,a,2044,b)].
% 16.21/16.40 2635 -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(2093,a,2044,b)].
% 16.21/16.40 2636 -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(2094,a,2044,b)].
% 16.21/16.40 2637 -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(2095,a,2044,b)].
% 16.21/16.40 2638 -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(2096,a,2044,b)].
% 16.21/16.40 2639 -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(2097,a,2044,b)].
% 16.21/16.40 2640 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2098,a,2044,b)].
% 16.21/16.40 2641 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2099,a,2044,b)].
% 16.21/16.40 2642 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2100,a,2044,b)].
% 16.21/16.40 2643 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2101,a,2044,b)].
% 16.21/16.40 2644 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2129,a,2110,b)].
% 16.21/16.40 2645 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2130,a,2110,b)].
% 16.21/16.40 2646 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2131,c,2110,b)].
% 16.21/16.40 2647 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2132,c,2110,b)].
% 16.21/16.40 2648 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2133,b,2110,b)].
% 16.21/16.40 2649 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2134,a,2110,b)].
% 16.21/16.40 2650 -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(2172,d,2110,b)].
% 16.21/16.40 2651 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2173,b,2110,b)].
% 16.21/16.40 2652 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2174,b,2110,b)].
% 16.21/16.40 2653 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2175,b,2110,b)].
% 16.21/16.40 2654 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2176,b,2110,b)].
% 16.21/16.40 2655 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2177,c,2110,b)].
% 16.21/16.40 2656 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2178,c,2110,b)].
% 16.21/16.40 2657 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2179,b,2110,b)].
% 16.21/16.40 2658 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2180,c,2110,b)].
% 16.21/16.40 2659 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2181,b,2110,b)].
% 16.29/16.44 2660 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2182,c,2110,b)].
% 16.29/16.44 2661 -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(2183,c,2110,b)].
% 16.29/16.44 2662 -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(2184,c,2110,b)].
% 16.29/16.44 2663 -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(2185,c,2110,b)].
% 16.29/16.44 2664 -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(2186,c,2110,b)].
% 16.29/16.44 2665 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2187,c,2110,b)].
% 16.29/16.44 2666 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(2188,b,2110,b)].
% 16.29/16.44 2667 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2189,b,2110,b)].
% 16.29/16.44 2668 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2190,d,2110,b)].
% 16.29/16.44 2669 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2191,c,2110,b)].
% 16.29/16.44 2670 -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(2192,c,2110,b)].
% 16.29/16.44 2671 -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(2193,c,2110,b)].
% 16.29/16.44 2672 -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(2194,d,2110,b)].
% 16.29/16.44 2673 -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(2195,c,2110,b)].
% 16.29/16.44 2674 -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(2196,c,2110,b)].
% 16.29/16.44 2675 -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(2197,d,2110,b)].
% 16.29/16.44 2676 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2198,c,2110,b)].
% 16.29/16.44 2677 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2199,c,2110,b)].
% 16.29/16.44 2678 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2200,c,2110,b)].
% 16.29/16.44 2679 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2201,c,2110,b)].
% 16.29/16.44 2680 -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(2202,c,2110,b)].
% 16.29/16.44 2681 -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(2203,c,2110,b)].
% 16.29/16.44 2682 -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(2204,d,2110,b)].
% 16.29/16.44 2683 -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(2205,c,2110,b)].
% 16.50/16.65 2684 -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(2206,c,2110,b)].
% 16.50/16.65 2685 -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(2207,d,2110,b)].
% 16.50/16.65 2686 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2208,c,2110,b)].
% 16.50/16.65 2687 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2209,c,2110,b)].
% 16.50/16.65 2688 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2210,c,2110,b)].
% 16.50/16.65 2689 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2211,c,2110,b)].
% 16.50/16.65 2690 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2445,b,2438,b)].
% 16.50/16.65 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2690,b,2539,b)].
% 16.50/16.65 2691 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(2446,b,2438,b)].
% 16.50/16.65 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(2691,b,2539,b)].
% 16.50/16.65 2692 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) # label(axiom). [assumption].
% 16.50/16.65 2693 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 16.50/16.65 2694 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 16.50/16.65 2695 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) # label(axiom). [assumption].
% 16.50/16.65 2696 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) # label(axiom). [assumption].
% 16.50/16.65 2697 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) # label(axiom). [assumption].
% 16.50/16.65 2698 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) # label(axiom). [assumption].
% 16.50/16.65 2699 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) # label(axiom). [assumption].
% 16.50/16.65 2700 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_35) # label(axiom). [assumption].
% 16.50/16.65 2701 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_30) # label(axiom). [assumption].
% 16.50/16.65 2702 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(27,b,1,a)].
% 16.50/16.65 2703 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(27,b,3,a)].
% 16.50/16.65 2704 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 16.50/16.65 2705 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 16.50/16.65 2706 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(108,a,101,b)].
% 16.50/16.65 2707 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)].
% 16.50/16.70 2708 -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)].
% 16.50/16.70 2709 -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)].
% 16.50/16.70 2710 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(167,a,150,b)].
% 16.50/16.70 2711 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(168,a,150,b)].
% 16.50/16.70 2712 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(203,b,191,b)].
% 16.50/16.70 2713 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(204,b,191,b)].
% 16.50/16.70 2714 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 16.50/16.70 2715 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 16.50/16.70 2716 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 16.50/16.70 2717 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 16.50/16.70 2718 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,286,a)].
% 16.50/16.70 2719 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,288,a)].
% 16.50/16.70 2720 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)].
% 16.50/16.70 2721 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)].
% 16.50/16.70 2722 -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)].
% 16.50/16.70 2723 -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)].
% 16.50/16.70 2724 -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)].
% 16.50/16.70 2725 -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)].
% 16.50/16.70 2726 -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)].
% 16.50/16.70 2727 -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)].
% 16.50/16.70 2728 -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)].
% 16.50/16.70 2729 -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)].
% 16.60/16.71 2730 -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)].
% 16.60/16.71 2731 -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)].
% 16.60/16.71 2732 -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)].
% 16.60/16.71 2733 -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)].
% 16.60/16.71 2734 -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)].
% 16.60/16.71 2735 -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)].
% 16.60/16.71 2736 -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)].
% 16.60/16.71 2737 -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)].
% 16.60/16.71 2738 -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)].
% 16.60/16.71 2739 -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)].
% 16.60/16.71 2740 -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)].
% 16.60/16.71 2741 -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)].
% 16.60/16.71 2742 -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)].
% 16.60/16.71 2743 -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)].
% 16.60/16.71 2744 -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)].
% 16.60/16.71 2745 -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)].
% 16.60/16.71 2746 -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)].
% 16.60/16.71 2747 -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)].
% 16.60/16.71 2748 -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)].
% 16.60/16.71 2749 -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)].
% 16.60/16.72 2750 -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)].
% 16.60/16.72 2751 -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)].
% 16.60/16.72 2752 -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)].
% 16.60/16.72 2753 -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)].
% 16.60/16.72 2754 -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)].
% 16.60/16.72 2755 -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)].
% 16.60/16.72 2756 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(887,b,856,a)].
% 16.60/16.72 2757 -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)].
% 16.60/16.72 2758 -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)].
% 16.60/16.72 2759 -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)].
% 16.60/16.72 2760 -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)].
% 16.60/16.72 2761 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(887,b,861,a)].
% 16.60/16.72 2762 -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)].
% 16.60/16.72 2763 -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)].
% 16.60/16.72 2764 -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)].
% 16.60/16.72 2765 -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)].
% 16.60/16.72 2766 -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)].
% 16.60/16.72 2767 -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)].
% 16.60/16.72 2768 -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)].
% 16.60/16.72 2769 -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)].
% 16.60/16.72 2770 -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)].
% 16.60/16.72 2771 -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)].
% 16.60/16.72 2772 -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)].
% 16.60/16.72 2773 -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)].
% 16.68/16.88 2774 -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)].
% 16.68/16.88 2775 -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)].
% 16.68/16.88 2776 -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)].
% 16.68/16.88 2777 -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)].
% 16.68/16.88 2778 -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)].
% 16.77/16.88 2779 -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)].
% 16.77/16.88 2780 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1079,b,1068,a)].
% 16.77/16.88 2781 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1102,b,1091,a)].
% 16.77/16.88 2782 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1148,a,1113,a)].
% 16.77/16.88 2783 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1148,a,1138,a)].
% 16.77/16.88 2784 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1148,a,1139,b)].
% 16.77/16.88 2785 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1148,a,1140,b)].
% 16.77/16.88 2786 -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)].
% 16.77/16.88 2787 -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)].
% 16.77/16.88 2788 -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)].
% 16.77/16.88 2789 -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)].
% 16.77/16.88 2790 -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)].
% 16.77/16.88 2791 -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)].
% 16.77/16.88 2792 -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)].
% 16.77/16.88 2793 -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)].
% 16.77/16.88 2794 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1588,b,1566,a)].
% 16.77/16.88 2795 -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)].
% 16.77/16.88 2796 -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)].
% 16.77/16.88 2797 -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)].
% 16.77/16.88 2798 -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)].
% 16.81/16.92 2799 -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)].
% 16.81/16.92 2800 -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)].
% 16.81/16.92 2801 -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)].
% 16.81/16.92 2802 -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)].
% 16.81/16.92 2803 -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)].
% 16.81/16.92 2804 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1588,b,1576,a)].
% 16.81/16.92 2805 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1599,a,1588,b)].
% 16.81/16.92 2806 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1600,a,1588,b)].
% 16.81/16.92 2807 -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(1653,b,1622,a)].
% 16.81/16.92 2808 -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(1653,b,1623,a)].
% 16.81/16.92 2809 -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(1653,b,1624,a)].
% 16.81/16.92 2810 -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(1653,b,1625,a)].
% 16.81/16.92 2811 -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(1653,b,1626,a)].
% 16.81/16.92 2812 -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(1653,b,1627,a)].
% 16.81/16.92 2813 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1653,b,1628,a)].
% 16.81/16.92 2814 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1653,b,1629,a)].
% 16.81/16.92 2815 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1653,b,1630,a)].
% 16.81/16.92 2816 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1653,b,1631,a)].
% 16.81/16.92 2817 -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(1653,b,1632,a)].
% 16.81/16.92 2818 -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(1653,b,1633,a)].
% 16.81/16.92 2819 -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(1653,b,1634,a)].
% 16.81/16.92 2820 -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(1653,b,1635,a)].
% 16.81/16.92 2821 -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(1653,b,1636,a)].
% 16.81/16.92 2822 -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(1653,b,1637,a)].
% 16.81/16.92 2823 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1653,b,1638,a)].
% 16.82/16.98 2824 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1653,b,1639,a)].
% 16.82/16.98 2825 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1653,b,1640,a)].
% 16.82/16.98 2826 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1653,b,1641,a)].
% 16.82/16.98 2827 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1832,a,1823,b)].
% 16.82/16.98 2828 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1833,a,1823,b)].
% 16.82/16.98 2829 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1966,c,1886,b)].
% 16.82/16.98 2830 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1967,c,1886,b)].
% 16.82/16.98 2831 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2003,b,1886,b)].
% 16.82/16.98 2832 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2004,c,1886,b)].
% 16.82/16.98 2833 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2005,b,1886,b)].
% 16.82/16.98 2834 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2006,c,1886,b)].
% 16.82/16.98 2835 -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(2007,c,1886,b)].
% 16.82/16.98 2836 -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(2008,c,1886,b)].
% 16.82/16.98 2837 -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(2009,c,1886,b)].
% 16.82/16.98 2838 -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(2010,c,1886,b)].
% 16.82/16.98 2839 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2011,c,1886,b)].
% 16.82/16.98 2840 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(2012,b,1886,b)].
% 16.82/16.98 2841 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2013,b,1886,b)].
% 16.82/16.98 2842 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2014,d,1886,b)].
% 16.82/16.98 2843 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2015,c,1886,b)].
% 16.82/16.98 2844 -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(2016,c,1886,b)].
% 16.82/16.98 2845 -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(2017,c,1886,b)].
% 16.82/16.98 2846 -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(2018,d,1886,b)].
% 16.82/16.98 2847 -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(2019,c,1886,b)].
% 16.82/16.98 2848 -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(2020,c,1886,b)].
% 16.82/17.02 2849 -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(2021,d,1886,b)].
% 16.82/17.02 2850 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2022,c,1886,b)].
% 16.82/17.02 2851 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2023,c,1886,b)].
% 16.82/17.02 2852 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2024,c,1886,b)].
% 16.82/17.02 2853 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2025,c,1886,b)].
% 16.82/17.02 2854 -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(2026,c,1886,b)].
% 16.82/17.02 2855 -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(2027,c,1886,b)].
% 16.82/17.02 2856 -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(2028,d,1886,b)].
% 16.82/17.02 2857 -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(2029,c,1886,b)].
% 16.82/17.02 2858 -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(2030,c,1886,b)].
% 16.82/17.02 2859 -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(2031,d,1886,b)].
% 16.82/17.02 2860 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2032,c,1886,b)].
% 16.82/17.02 2861 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2033,c,1886,b)].
% 16.82/17.02 2862 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2034,c,1886,b)].
% 16.82/17.02 2863 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2035,c,1886,b)].
% 16.82/17.02 2864 -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(2054,a,2040,b)].
% 16.82/17.02 2865 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2059,b,2040,b)].
% 16.82/17.02 2866 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2060,b,2040,b)].
% 16.82/17.02 2867 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2061,b,2040,b)].
% 16.82/17.02 2868 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2062,b,2040,b)].
% 16.82/17.02 2869 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2063,c,2040,b)].
% 16.82/17.02 2870 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2064,c,2040,b)].
% 16.82/17.02 2871 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2129,a,2106,b)].
% 16.82/17.02 2872 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2130,a,2106,b)].
% 16.82/17.02 2873 -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(2172,d,2106,b)].
% 16.82/17.02 2874 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2173,b,2106,b)].
% 16.91/17.04 2875 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2174,b,2106,b)].
% 16.91/17.04 2876 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2175,b,2106,b)].
% 16.91/17.04 2877 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2176,b,2106,b)].
% 16.91/17.04 2878 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2177,c,2106,b)].
% 16.91/17.04 2879 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2178,c,2106,b)].
% 16.91/17.04 2880 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2179,b,2106,b)].
% 16.91/17.04 2881 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2180,c,2106,b)].
% 16.91/17.04 2882 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2181,b,2106,b)].
% 16.91/17.04 2883 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2182,c,2106,b)].
% 16.91/17.04 2884 -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(2183,c,2106,b)].
% 16.91/17.04 2885 -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(2184,c,2106,b)].
% 16.91/17.04 2886 -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(2185,c,2106,b)].
% 16.91/17.04 2887 -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(2186,c,2106,b)].
% 16.91/17.04 2888 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2187,c,2106,b)].
% 16.91/17.04 2889 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(2188,b,2106,b)].
% 16.91/17.04 2890 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2189,b,2106,b)].
% 16.91/17.04 2891 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2190,d,2106,b)].
% 16.91/17.04 2892 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2191,c,2106,b)].
% 16.91/17.04 2893 -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(2192,c,2106,b)].
% 16.91/17.04 2894 -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(2193,c,2106,b)].
% 16.91/17.04 2895 -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(2194,d,2106,b)].
% 16.91/17.04 2896 -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(2195,c,2106,b)].
% 16.91/17.04 2897 -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(2196,c,2106,b)].
% 16.91/17.04 2898 -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(2197,d,2106,b)].
% 16.91/17.06 2899 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2198,c,2106,b)].
% 16.91/17.06 2900 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2199,c,2106,b)].
% 16.91/17.06 2901 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2200,c,2106,b)].
% 16.91/17.06 2902 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,c,2106,b)].
% 16.91/17.06 2903 -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(2202,c,2106,b)].
% 16.91/17.06 2904 -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(2203,c,2106,b)].
% 16.91/17.06 2905 -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(2204,d,2106,b)].
% 16.91/17.06 2906 -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(2205,c,2106,b)].
% 16.91/17.06 2907 -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(2206,c,2106,b)].
% 16.91/17.06 2908 -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(2207,d,2106,b)].
% 16.91/17.06 2909 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2208,c,2106,b)].
% 16.91/17.06 2910 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2209,c,2106,b)].
% 16.91/17.06 2911 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2210,c,2106,b)].
% 16.91/17.06 2912 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2211,c,2106,b)].
% 16.91/17.06 2913 -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(2241,a,2215,b)].
% 16.91/17.06 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(2913,e,2693,a)].
% 16.91/17.06 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(2913,e,2694,a)].
% 16.91/17.06 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(2913,e,2700,b)].
% 16.91/17.06 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(2913,e,2701,b)].
% 16.91/17.06 2914 -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(2242,a,2215,b)].
% 16.91/17.06 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(2914,d,2693,a)].
% 16.91/17.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2914,d,2694,a)].
% 16.91/17.06 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(2914,d,2700,b)].
% 16.91/17.06 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(2914,d,2701,b)].
% 16.91/17.06 2915 -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(2243,a,2215,b)].
% 16.91/17.06 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(2915,d,2693,a)].
% 16.91/17.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(2915,d,2694,a)].
% 16.91/17.06 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(2915,d,2700,b)].
% 16.91/17.06 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(2915,d,2701,b)].
% 16.91/17.06 2916 -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(2244,a,2215,b)].
% 16.91/17.06 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(2916,f,2693,a)].
% 16.91/17.06 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(2916,f,2694,a)].
% 16.91/17.06 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(2916,f,2700,b)].
% 16.91/17.06 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(2916,f,2701,b)].
% 16.91/17.06 2917 -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(2245,a,2215,b)].
% 16.91/17.06 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(2917,e,2693,a)].
% 16.91/17.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2917,e,2694,a)].
% 16.91/17.06 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(2917,e,2700,b)].
% 16.91/17.06 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(2917,e,2701,b)].
% 16.91/17.06 2918 -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(2246,a,2215,b)].
% 16.91/17.06 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(2918,e,2693,a)].
% 16.91/17.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2918,e,2694,a)].
% 16.91/17.07 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(2918,e,2700,b)].
% 16.91/17.07 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(2918,e,2701,b)].
% 16.91/17.07 2919 -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(2247,a,2215,b)].
% 16.91/17.07 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(2919,f,2693,a)].
% 16.91/17.07 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(2919,f,2694,a)].
% 16.91/17.07 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(2919,f,2700,b)].
% 16.91/17.07 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(2919,f,2701,b)].
% 16.91/17.07 2920 -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(2248,a,2215,b)].
% 16.91/17.07 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(2920,e,2693,a)].
% 16.91/17.07 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(2920,e,2694,a)].
% 16.91/17.07 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(2920,e,2700,b)].
% 16.91/17.07 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(2920,e,2701,b)].
% 16.91/17.07 2921 -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(2249,a,2215,b)].
% 16.91/17.07 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(2921,e,2693,a)].
% 16.91/17.07 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(2921,e,2694,a)].
% 16.91/17.07 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(2921,e,2700,b)].
% 16.91/17.07 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(2921,e,2701,b)].
% 16.91/17.07 2922 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2250,a,2215,b)].
% 16.91/17.07 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2922,b,2693,a)].
% 16.91/17.07 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2922,b,2694,a)].
% 16.91/17.07 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2922,b,2700,b)].
% 16.91/17.07 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2922,b,2701,b)].
% 16.91/17.07 2923 -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(2251,a,2215,b)].
% 16.91/17.07 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(2923,f,2693,a)].
% 16.91/17.07 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(2923,f,2694,a)].
% 16.91/17.07 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(2923,f,2700,b)].
% 16.91/17.07 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(2923,f,2701,b)].
% 16.91/17.07 2924 -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(2252,a,2215,b)].
% 16.91/17.07 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(2924,e,2693,a)].
% 16.91/17.07 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(2924,e,2694,a)].
% 16.91/17.07 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(2924,e,2700,b)].
% 16.91/17.07 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(2924,e,2701,b)].
% 16.91/17.07 2925 -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(2253,a,2215,b)].
% 16.91/17.07 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(2925,e,2693,a)].
% 16.91/17.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2925,e,2694,a)].
% 16.91/17.07 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(2925,e,2700,b)].
% 16.91/17.07 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(2925,e,2701,b)].
% 16.91/17.07 2926 -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(2254,a,2215,b)].
% 16.91/17.07 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(2926,f,2693,a)].
% 16.91/17.07 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(2926,f,2694,a)].
% 16.91/17.07 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(2926,f,2700,b)].
% 16.91/17.07 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(2926,f,2701,b)].
% 16.91/17.07 2927 -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(2255,a,2215,b)].
% 16.91/17.07 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(2927,e,2693,a)].
% 16.91/17.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2927,e,2694,a)].
% 16.91/17.07 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(2927,e,2700,b)].
% 16.91/17.07 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(2927,e,2701,b)].
% 16.91/17.07 2928 -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(2256,a,2215,b)].
% 16.91/17.07 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(2928,e,2693,a)].
% 16.91/17.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2928,e,2694,a)].
% 16.91/17.07 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(2928,e,2700,b)].
% 16.91/17.07 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(2928,e,2701,b)].
% 16.91/17.07 2929 -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(2257,a,2215,b)].
% 16.91/17.07 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(2929,d,2693,a)].
% 16.91/17.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2929,d,2694,a)].
% 16.91/17.07 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(2929,d,2700,b)].
% 16.91/17.07 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(2929,d,2701,b)].
% 16.91/17.08 2930 -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(2258,a,2215,b)].
% 16.91/17.08 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(2930,d,2693,a)].
% 16.91/17.08 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(2930,d,2694,a)].
% 16.91/17.08 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(2930,d,2700,b)].
% 16.91/17.08 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(2930,d,2701,b)].
% 16.91/17.08 2931 -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(2259,a,2215,b)].
% 16.91/17.08 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(2931,e,2693,a)].
% 16.91/17.08 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(2931,e,2694,a)].
% 16.91/17.08 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(2931,e,2700,b)].
% 16.91/17.08 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(2931,e,2701,b)].
% 16.91/17.08 2932 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2260,a,2215,b)].
% 16.91/17.08 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2932,b,2693,a)].
% 16.91/17.08 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2932,b,2694,a)].
% 16.91/17.08 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2932,b,2700,b)].
% 16.91/17.08 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2932,b,2701,b)].
% 16.91/17.08 2933 -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(2261,a,2215,b)].
% 16.91/17.08 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(2933,d,2693,a)].
% 16.91/17.08 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(2933,d,2694,a)].
% 16.91/17.08 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(2933,d,2700,b)].
% 16.91/17.08 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(2933,d,2701,b)].
% 16.91/17.08 2934 -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(2262,a,2215,b)].
% 16.91/17.08 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(2934,e,2693,a)].
% 16.91/17.08 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(2934,e,2694,a)].
% 16.91/17.08 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(2934,e,2700,b)].
% 16.91/17.08 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(2934,e,2701,b)].
% 16.91/17.08 2935 -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(2263,a,2215,b)].
% 16.91/17.08 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(2935,e,2693,a)].
% 16.91/17.08 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(2935,e,2694,a)].
% 16.91/17.08 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(2935,e,2700,b)].
% 16.91/17.08 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(2935,e,2701,b)].
% 16.91/17.08 2936 -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(2264,a,2215,b)].
% 16.91/17.08 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(2936,d,2693,a)].
% 16.91/17.08 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(2936,d,2694,a)].
% 16.91/17.08 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(2936,d,2700,b)].
% 16.91/17.08 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(2936,d,2701,b)].
% 16.91/17.08 2937 -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(2265,a,2215,b)].
% 16.91/17.08 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(2937,d,2693,a)].
% 16.91/17.08 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(2937,d,2694,a)].
% 16.91/17.08 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(2937,d,2700,b)].
% 16.91/17.08 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(2937,d,2701,b)].
% 16.91/17.08 2938 -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(2266,a,2215,b)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2938,c,2693,a)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2938,c,2694,a)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2938,c,2700,b)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2938,c,2701,b)].
% 16.91/17.08 2939 -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(2267,a,2215,b)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2939,c,2693,a)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2939,c,2694,a)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2939,c,2700,b)].
% 16.91/17.08 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2939,c,2701,b)].
% 16.91/17.08 2940 -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(2268,a,2215,b)].
% 16.91/17.08 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(2940,d,2693,a)].
% 16.91/17.08 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(2940,d,2694,a)].
% 16.91/17.08 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(2940,d,2700,b)].
% 16.91/17.08 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(2940,d,2701,b)].
% 16.91/17.08 2941 -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(2269,a,2215,b)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2941,c,2693,a)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2941,c,2694,a)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2941,c,2700,b)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2941,c,2701,b)].
% 16.91/17.08 2942 -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(2270,a,2215,b)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2942,c,2693,a)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2942,c,2694,a)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2942,c,2700,b)].
% 16.91/17.08 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2942,c,2701,b)].
% 16.91/17.08 2943 -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(2271,a,2215,b)].
% 16.91/17.08 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(2943,d,2693,a)].
% 16.91/17.08 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(2943,d,2694,a)].
% 16.91/17.08 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(2943,d,2700,b)].
% 16.91/17.08 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(2943,d,2701,b)].
% 16.91/17.08 2944 -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(2272,a,2215,b)].
% 16.91/17.08 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2944,c,2693,a)].
% 16.91/17.08 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2944,c,2694,a)].
% 16.91/17.08 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2944,c,2700,b)].
% 16.98/17.09 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2944,c,2701,b)].
% 16.98/17.09 2945 -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(2273,a,2215,b)].
% 16.98/17.09 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2945,c,2693,a)].
% 16.98/17.09 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2945,c,2694,a)].
% 16.98/17.09 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2945,c,2700,b)].
% 16.98/17.09 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2945,c,2701,b)].
% 16.98/17.09 2946 -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(2274,a,2215,b)].
% 16.98/17.09 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(2946,d,2693,a)].
% 16.98/17.09 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(2946,d,2694,a)].
% 16.98/17.09 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(2946,d,2700,b)].
% 16.98/17.09 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(2946,d,2701,b)].
% 16.98/17.09 2947 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2275,a,2215,b)].
% 16.98/17.09 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2947,b,2693,a)].
% 16.98/17.09 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2947,b,2694,a)].
% 16.98/17.09 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2947,b,2700,b)].
% 16.98/17.09 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2947,b,2701,b)].
% 16.98/17.09 2948 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(2276,a,2215,b)].
% 16.98/17.09 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(2948,b,2693,a)].
% 16.98/17.09 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2948,b,2694,a)].
% 16.98/17.09 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(2948,b,2700,b)].
% 16.98/17.09 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(2948,b,2701,b)].
% 16.98/17.09 2949 -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(2277,a,2215,b)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2949,c,2693,a)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2949,c,2694,a)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2949,c,2700,b)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2949,c,2701,b)].
% 16.98/17.09 2950 -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(2278,a,2215,b)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2950,c,2693,a)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2950,c,2694,a)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2950,c,2700,b)].
% 16.98/17.09 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2950,c,2701,b)].
% 16.98/17.09 2951 -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(2279,a,2215,b)].
% 16.98/17.09 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(2951,d,2693,a)].
% 16.98/17.09 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(2951,d,2694,a)].
% 16.98/17.09 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(2951,d,2700,b)].
% 16.98/17.09 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(2951,d,2701,b)].
% 16.98/17.09 2952 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2280,a,2215,b)].
% 16.98/17.09 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2952,b,2693,a)].
% 16.98/17.09 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2952,b,2694,a)].
% 16.98/17.09 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2952,b,2700,b)].
% 16.98/17.09 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2952,b,2701,b)].
% 16.98/17.09 2953 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(2281,a,2215,b)].
% 16.98/17.09 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(2953,b,2693,a)].
% 16.98/17.09 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(2953,b,2694,a)].
% 16.98/17.09 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(2953,b,2700,b)].
% 16.98/17.09 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(2953,b,2701,b)].
% 16.98/17.09 2954 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(2282,a,2215,b)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(2954,b,2693,a)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2954,b,2694,a)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2954,b,2700,b)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2954,b,2701,b)].
% 16.98/17.09 2955 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(2283,a,2215,b)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(2955,b,2693,a)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2955,b,2694,a)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2955,b,2700,b)].
% 16.98/17.09 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2955,b,2701,b)].
% 16.98/17.09 2956 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(2284,a,2215,b)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(2956,b,2693,a)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2956,b,2694,a)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2956,b,2700,b)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2956,b,2701,b)].
% 16.98/17.10 2957 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(2285,a,2215,b)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(2957,b,2693,a)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2957,b,2694,a)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2957,b,2700,b)].
% 16.98/17.10 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2957,b,2701,b)].
% 16.98/17.10 2958 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2286,a,2215,b)].
% 16.98/17.10 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2958,c,2693,a)].
% 16.98/17.10 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2958,c,2694,a)].
% 16.98/17.10 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2958,c,2700,b)].
% 16.98/17.10 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2958,c,2701,b)].
% 16.98/17.10 2959 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2287,a,2215,b)].
% 16.98/17.10 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2959,c,2693,a)].
% 16.98/17.10 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2959,c,2694,a)].
% 16.98/17.10 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2959,c,2700,b)].
% 16.98/17.10 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2959,c,2701,b)].
% 16.98/17.10 2960 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2288,a,2215,b)].
% 16.98/17.10 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2960,c,2693,a)].
% 16.98/17.10 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2960,c,2694,a)].
% 16.98/17.10 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2960,c,2700,b)].
% 16.98/17.10 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2960,c,2701,b)].
% 16.98/17.10 2961 -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(2289,a,2215,b)].
% 16.98/17.10 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(2961,c,2693,a)].
% 16.98/17.10 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(2961,c,2694,a)].
% 16.98/17.10 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(2961,c,2700,b)].
% 16.98/17.10 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(2961,c,2701,b)].
% 16.98/17.10 2962 -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(2290,a,2215,b)].
% 16.98/17.10 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(2962,c,2693,a)].
% 16.98/17.10 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(2962,c,2694,a)].
% 16.98/17.10 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(2962,c,2700,b)].
% 16.98/17.10 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(2962,c,2701,b)].
% 16.98/17.10 2963 -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(2291,a,2215,b)].
% 16.98/17.10 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(2963,c,2693,a)].
% 16.98/17.10 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(2963,c,2694,a)].
% 16.98/17.10 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(2963,c,2700,b)].
% 16.98/17.10 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(2963,c,2701,b)].
% 16.98/17.10 2964 -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(2292,a,2215,b)].
% 16.98/17.10 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(2964,d,2693,a)].
% 16.98/17.10 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(2964,d,2694,a)].
% 16.98/17.10 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(2964,d,2700,b)].
% 16.98/17.10 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(2964,d,2701,b)].
% 16.98/17.10 2965 -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(2293,a,2215,b)].
% 16.98/17.10 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(2965,d,2693,a)].
% 16.98/17.10 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(2965,d,2694,a)].
% 16.98/17.10 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(2965,d,2700,b)].
% 16.98/17.10 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(2965,d,2701,b)].
% 16.98/17.10 2966 -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(2294,a,2215,b)].
% 16.98/17.10 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(2966,c,2693,a)].
% 16.98/17.10 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(2966,c,2694,a)].
% 16.98/17.10 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(2966,c,2700,b)].
% 16.98/17.10 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(2966,c,2701,b)].
% 16.98/17.10 2967 -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(2295,a,2215,b)].
% 16.98/17.10 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(2967,d,2693,a)].
% 16.98/17.10 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(2967,d,2694,a)].
% 16.98/17.10 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(2967,d,2700,b)].
% 16.98/17.10 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(2967,d,2701,b)].
% 16.98/17.10 2968 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2296,a,2215,b)].
% 16.98/17.10 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2968,c,2693,a)].
% 16.98/17.10 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2968,c,2694,a)].
% 16.98/17.10 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2968,c,2700,b)].
% 16.98/17.10 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2968,c,2701,b)].
% 16.98/17.10 2969 -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(2297,a,2215,b)].
% 16.98/17.10 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(2969,c,2693,a)].
% 16.98/17.11 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(2969,c,2694,a)].
% 16.98/17.11 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(2969,c,2700,b)].
% 16.98/17.11 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(2969,c,2701,b)].
% 16.98/17.11 2970 -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(2298,a,2215,b)].
% 16.98/17.11 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(2970,c,2693,a)].
% 16.98/17.11 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(2970,c,2694,a)].
% 16.98/17.11 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(2970,c,2700,b)].
% 16.98/17.11 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(2970,c,2701,b)].
% 16.98/17.11 2971 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2299,a,2215,b)].
% 16.98/17.11 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2971,b,2693,a)].
% 16.98/17.11 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2971,b,2694,a)].
% 16.98/17.11 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2971,b,2700,b)].
% 16.98/17.11 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2971,b,2701,b)].
% 16.98/17.11 2972 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2300,a,2215,b)].
% 16.98/17.11 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2972,b,2693,a)].
% 16.98/17.11 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2972,b,2694,a)].
% 16.98/17.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2972,b,2700,b)].
% 16.98/17.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2972,b,2701,b)].
% 16.98/17.11 2973 -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(2305,a,2215,b)].
% 16.98/17.11 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(2973,c,2693,a)].
% 16.98/17.11 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2973,c,2694,a)].
% 16.98/17.11 2974 -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(2306,a,2215,b)].
% 16.98/17.11 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(2974,c,2693,a)].
% 16.98/17.11 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2974,c,2694,a)].
% 16.98/17.11 2975 -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(2307,a,2215,b)].
% 16.98/17.11 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(2975,c,2693,a)].
% 16.98/17.11 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2975,c,2694,a)].
% 16.98/17.11 2976 -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(2308,a,2215,b)].
% 16.98/17.11 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(2976,c,2693,a)].
% 16.98/17.11 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2976,c,2694,a)].
% 16.98/17.12 2977 -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(2309,a,2215,b)].
% 16.98/17.12 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(2977,c,2693,a)].
% 16.98/17.12 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(2977,c,2694,a)].
% 16.98/17.12 2978 -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(2310,a,2215,b)].
% 16.98/17.12 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(2978,c,2693,a)].
% 16.98/17.12 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2978,c,2694,a)].
% 16.98/17.12 2979 -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(2311,a,2215,b)].
% 16.98/17.12 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(2979,c,2693,a)].
% 16.98/17.12 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2979,c,2694,a)].
% 16.98/17.12 2980 -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(2312,a,2215,b)].
% 16.98/17.12 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(2980,c,2693,a)].
% 16.98/17.12 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2980,c,2694,a)].
% 16.98/17.12 2981 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2346,c,2215,b)].
% 16.98/17.12 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2981,c,2693,a)].
% 16.98/17.12 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2981,c,2694,a)].
% 16.98/17.12 2982 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2347,c,2215,b)].
% 16.98/17.12 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2982,c,2693,a)].
% 16.98/17.12 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2982,c,2694,a)].
% 16.98/17.12 2983 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2348,b,2215,b)].
% 16.98/17.12 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2983,b,2693,a)].
% 16.98/17.12 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2983,b,2694,a)].
% 16.98/17.12 2984 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2349,b,2215,b)].
% 16.98/17.12 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2984,b,2693,a)].
% 16.98/17.12 Derived: class_HOL_Oplus(tc_nat). [resolve(2984,b,2694,a)].
% 16.98/17.12 2985 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2390,b,2215,b)].
% 16.98/17.12 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2985,b,2693,a)].
% 16.98/17.12 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2985,b,2694,a)].
% 16.98/17.12 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2985,b,2700,b)].
% 16.98/17.12 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2985,b,2701,b)].
% 16.98/17.12 2986 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2391,b,2215,b)].
% 16.98/17.12 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2986,b,2693,a)].
% 16.98/17.12 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2986,b,2694,a)].
% 16.98/17.12 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2986,b,2700,b)].
% 16.98/17.12 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2986,b,2701,b)].
% 16.98/17.12 2987 -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(2392,d,2215,b)].
% 16.98/17.12 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(2987,d,2693,a)].
% 16.98/17.13 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(2987,d,2694,a)].
% 16.98/17.13 2988 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2393,b,2215,b)].
% 16.98/17.13 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2988,b,2693,a)].
% 16.98/17.13 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2988,b,2694,a)].
% 16.98/17.13 2989 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2394,b,2215,b)].
% 16.98/17.13 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2989,b,2693,a)].
% 16.98/17.13 Derived: class_HOL_Otimes(tc_nat). [resolve(2989,b,2694,a)].
% 16.98/17.13 2990 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2395,b,2215,b)].
% 16.98/17.13 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2990,b,2693,a)].
% 16.98/17.13 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2990,b,2694,a)].
% 16.98/17.13 2991 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2396,b,2215,b)].
% 16.98/17.13 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2991,b,2693,a)].
% 16.98/17.13 Derived: class_HOL_Ozero(tc_nat). [resolve(2991,b,2694,a)].
% 16.98/17.13 2992 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2397,c,2215,b)].
% 16.98/17.13 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(2992,c,2693,a)].
% 16.98/17.13 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(2992,c,2694,a)].
% 16.98/17.13 2993 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2398,c,2215,b)].
% 16.98/17.13 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(2993,c,2693,a)].
% 16.98/17.13 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(2993,c,2694,a)].
% 16.98/17.13 2994 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2399,b,2215,b)].
% 16.98/17.13 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2994,b,2693,a)].
% 16.98/17.13 Derived: -c_less(A,A,tc_nat). [resolve(2994,b,2694,a)].
% 16.98/17.13 2995 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2400,c,2215,b)].
% 16.98/17.13 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2995,c,2693,a)].
% 16.98/17.13 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2995,c,2694,a)].
% 16.98/17.13 2996 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2401,b,2215,b)].
% 16.98/17.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2996,b,2693,a)].
% 16.98/17.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2996,b,2694,a)].
% 16.98/17.14 2997 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2402,c,2215,b)].
% 16.98/17.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2997,c,2693,a)].
% 16.98/17.14 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2997,c,2694,a)].
% 16.98/17.14 2998 -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(2403,c,2215,b)].
% 16.98/17.14 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(2998,c,2693,a)].
% 16.98/17.14 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(2998,c,2694,a)].
% 16.98/17.14 2999 -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(2404,c,2215,b)].
% 16.98/17.14 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(2999,c,2693,a)].
% 16.98/17.14 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(2999,c,2694,a)].
% 16.98/17.14 3000 -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(2405,c,2215,b)].
% 16.98/17.14 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(3000,c,2693,a)].
% 16.98/17.14 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(3000,c,2694,a)].
% 16.98/17.14 3001 -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(2406,c,2215,b)].
% 16.98/17.14 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(3001,c,2693,a)].
% 16.98/17.14 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(3001,c,2694,a)].
% 16.98/17.14 3002 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2407,c,2215,b)].
% 16.98/17.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3002,c,2693,a)].
% 16.98/17.14 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(3002,c,2694,a)].
% 16.98/17.14 3003 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(2408,b,2215,b)].
% 16.98/17.14 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(3003,b,2693,a)].
% 16.98/17.14 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(3003,b,2694,a)].
% 16.98/17.14 3004 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2409,b,2215,b)].
% 16.98/17.14 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3004,b,2693,a)].
% 16.98/17.14 Derived: c_lessequals(A,A,tc_nat). [resolve(3004,b,2694,a)].
% 16.98/17.14 3005 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2410,d,2215,b)].
% 16.98/17.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(3005,d,2693,a)].
% 16.98/17.15 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(3005,d,2694,a)].
% 16.98/17.15 3006 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2411,c,2215,b)].
% 16.98/17.15 Derived: -c_less(A,B,tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3006,c,2693,a)].
% 16.98/17.15 Derived: -c_less(A,B,tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3006,c,2694,a)].
% 16.98/17.15 3007 -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(2412,c,2215,b)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3007,c,2693,a)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3007,c,2694,a)].
% 16.98/17.15 3008 -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(2413,c,2215,b)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3008,c,2693,a)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3008,c,2694,a)].
% 16.98/17.15 3009 -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(2414,d,2215,b)].
% 16.98/17.15 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(3009,d,2693,a)].
% 16.98/17.15 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(3009,d,2694,a)].
% 16.98/17.15 3010 -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(2415,c,2215,b)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3010,c,2693,a)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3010,c,2694,a)].
% 16.98/17.15 3011 -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(2416,c,2215,b)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3011,c,2693,a)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3011,c,2694,a)].
% 16.98/17.15 3012 -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(2417,d,2215,b)].
% 16.98/17.15 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(3012,d,2693,a)].
% 16.98/17.15 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(3012,d,2694,a)].
% 16.98/17.15 3013 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2418,c,2215,b)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3013,c,2693,a)].
% 16.98/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3013,c,2694,a)].
% 16.98/17.15 3014 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2419,c,2215,b)].
% 16.98/17.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3014,c,2693,a)].
% 16.98/17.15 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3014,c,2694,a)].
% 16.98/17.15 3015 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2420,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3015,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3015,c,2694,a)].
% 16.98/17.16 3016 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2421,c,2215,b)].
% 16.98/17.16 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3016,c,2693,a)].
% 16.98/17.16 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3016,c,2694,a)].
% 16.98/17.16 3017 -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(2422,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3017,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3017,c,2694,a)].
% 16.98/17.16 3018 -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(2423,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3018,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3018,c,2694,a)].
% 16.98/17.16 3019 -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(2424,d,2215,b)].
% 16.98/17.16 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(3019,d,2693,a)].
% 16.98/17.16 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(3019,d,2694,a)].
% 16.98/17.16 3020 -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(2425,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3020,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3020,c,2694,a)].
% 16.98/17.16 3021 -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(2426,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3021,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3021,c,2694,a)].
% 16.98/17.16 3022 -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(2427,d,2215,b)].
% 16.98/17.16 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(3022,d,2693,a)].
% 16.98/17.16 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(3022,d,2694,a)].
% 16.98/17.16 3023 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2428,c,2215,b)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3023,c,2693,a)].
% 16.98/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3023,c,2694,a)].
% 16.98/17.16 3024 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2429,c,2215,b)].
% 16.98/17.16 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3024,c,2693,a)].
% 17.44/17.60 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3024,c,2694,a)].
% 17.44/17.60 3025 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2430,c,2215,b)].
% 17.44/17.60 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(3025,c,2693,a)].
% 17.44/17.60 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3025,c,2694,a)].
% 17.44/17.60 3026 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2431,c,2215,b)].
% 17.44/17.60 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3026,c,2693,a)].
% 17.44/17.60 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3026,c,2694,a)].
% 17.44/17.60 3027 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2445,b,2435,b)].
% 17.44/17.60 3028 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(2446,b,2435,b)].
% 17.44/17.60 3029 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2690,b,2539,b)].
% 17.44/17.60 Derived: c_times(A,B,tc_IntDef_Oint) = c_times(B,A,tc_IntDef_Oint). [resolve(3029,b,2693,a)].
% 17.44/17.60 Derived: c_times(A,B,tc_nat) = c_times(B,A,tc_nat). [resolve(3029,b,2694,a)].
% 17.44/17.60 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3029,b,2700,b)].
% 17.44/17.60 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3029,b,2701,b)].
% 17.44/17.60 3030 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(2691,b,2539,b)].
% 17.44/17.60 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(3030,b,2693,a)].
% 17.44/17.60 Derived: c_times(A,c_times(B,C,tc_nat),tc_nat) = c_times(B,c_times(A,C,tc_nat),tc_nat). [resolve(3030,b,2694,a)].
% 17.44/17.60 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(3030,b,2700,b)].
% 17.44/17.60 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(3030,b,2701,b)].
% 17.44/17.60 3031 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_0) # label(axiom). [assumption].
% 17.44/17.60 3032 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 17.44/17.60 3033 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_2) # label(axiom). [assumption].
% 17.44/17.60 3034 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__field_42) # label(axiom). [assumption].
% 17.44/17.60 3035 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__idom_46) # label(axiom). [assumption].
% 17.44/17.60 3036 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1311,a,1267,a)].
% 17.44/17.60 3037 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1311,a,1293,b)].
% 17.44/17.60 3038 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1311,a,1294,b)].
% 17.44/17.60 3039 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1651,b,1622,a)].
% 17.44/17.60 3040 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1651,b,1623,a)].
% 17.44/17.60 3041 -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(1651,b,1624,a)].
% 17.44/17.60 3042 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1651,b,1625,a)].
% 17.82/17.95 3043 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1651,b,1626,a)].
% 17.82/17.95 3044 -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(1651,b,1627,a)].
% 17.82/17.95 3045 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1651,b,1628,a)].
% 17.82/17.95 3046 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1651,b,1629,a)].
% 17.82/17.95 3047 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1651,b,1630,a)].
% 17.82/17.95 3048 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1651,b,1631,a)].
% 17.82/17.95 3049 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1651,b,1632,a)].
% 17.82/17.95 3050 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1651,b,1633,a)].
% 17.82/17.95 3051 -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(1651,b,1634,a)].
% 17.82/17.95 3052 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1651,b,1635,a)].
% 17.82/17.95 3053 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1651,b,1636,a)].
% 17.82/17.95 3054 -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(1651,b,1637,a)].
% 17.82/17.95 3055 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1651,b,1638,a)].
% 17.82/17.95 3056 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1651,b,1639,a)].
% 17.82/17.95 3057 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1651,b,1640,a)].
% 17.82/17.95 3058 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1651,b,1641,a)].
% 17.82/17.95 3059 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 17.82/17.95 3060 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 17.82/17.95 3061 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Olordered__ring_0) # label(axiom). [assumption].
% 17.82/17.95 3062 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_44) # label(axiom). [assumption].
% 17.82/17.95 3063 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_49) # label(axiom). [assumption].
% 17.82/17.95 3064 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 17.82/17.95 3065 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 17.82/17.95 3066 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom). [assumption].
% 17.82/17.95 3067 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom). [assumption].
% 17.82/17.95 3068 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_19) # label(axiom). [assumption].
% 17.82/17.97 3069 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom). [assumption].
% 17.82/17.97 3070 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 17.82/17.97 3071 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom). [assumption].
% 17.82/17.97 3072 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(36,b,1,a)].
% 17.82/17.97 3073 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(36,b,3,a)].
% 17.82/17.97 3074 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 17.82/17.97 3075 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 17.82/17.97 3076 -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)].
% 17.82/17.97 3077 -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)].
% 17.82/17.97 3078 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(167,a,160,b)].
% 17.82/17.97 3079 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(168,a,160,b)].
% 17.82/17.97 3080 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 17.82/17.97 3081 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 17.82/17.97 3082 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 17.82/17.97 3083 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 17.82/17.97 3084 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,286,a)].
% 17.82/17.97 3085 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,288,a)].
% 17.82/17.97 3086 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(320,a,309,b)].
% 17.82/17.97 3087 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(321,a,309,b)].
% 17.82/17.97 3088 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(323,a,309,b)].
% 17.82/17.97 3089 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,309,b)].
% 17.82/17.97 3090 -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)].
% 17.82/17.97 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(3090,a,3061,b)].
% 17.82/17.97 3091 -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)].
% 17.82/17.97 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(3091,a,3061,b)].
% 17.82/17.97 3092 -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)].
% 17.99/18.10 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(3092,a,3061,b)].
% 17.99/18.10 3093 -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)].
% 17.99/18.10 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(3093,a,3061,b)].
% 17.99/18.10 3094 -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)].
% 17.99/18.10 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(3094,a,3061,b)].
% 17.99/18.10 3095 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(350,a,344,b)].
% 17.99/18.10 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3095,b,3061,b)].
% 17.99/18.10 3096 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(351,a,344,b)].
% 17.99/18.10 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3096,b,3061,b)].
% 17.99/18.10 3097 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(362,b,344,b)].
% 17.99/18.10 3098 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(363,b,344,b)].
% 17.99/18.10 3099 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(364,b,344,b)].
% 17.99/18.10 3100 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(365,b,344,b)].
% 17.99/18.10 3101 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 17.99/18.10 3102 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 17.99/18.10 3103 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(368,a,344,b)].
% 17.99/18.10 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3103,b,3061,b)].
% 17.99/18.10 3104 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(369,a,344,b)].
% 17.99/18.10 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3104,b,3061,b)].
% 17.99/18.10 3105 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(370,c,344,b)].
% 17.99/18.10 3106 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(371,c,344,b)].
% 17.99/18.10 3107 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(804,a,724,a)].
% 17.99/18.10 3108 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(804,a,731,a)].
% 17.99/18.10 3109 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1315,a,1267,a)].
% 17.99/18.10 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(3109,a,3090,a)].
% 17.99/18.10 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(3109,a,3091,a)].
% 17.99/18.10 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(3109,a,3092,a)].
% 17.99/18.10 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(3109,a,3093,a)].
% 17.99/18.10 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(3109,a,3094,a)].
% 17.99/18.10 3110 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1315,a,1293,b)].
% 18.04/18.13 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(3110,a,3090,a)].
% 18.04/18.13 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(3110,a,3091,a)].
% 18.04/18.13 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(3110,a,3092,a)].
% 18.04/18.13 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(3110,a,3093,a)].
% 18.04/18.13 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(3110,a,3094,a)].
% 18.04/18.13 3111 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1315,a,1294,b)].
% 18.04/18.13 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(3111,a,3090,a)].
% 18.04/18.13 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(3111,a,3091,a)].
% 18.04/18.13 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(3111,a,3092,a)].
% 18.04/18.13 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(3111,a,3093,a)].
% 18.04/18.13 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(3111,a,3094,a)].
% 18.04/18.13 3112 -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)].
% 18.04/18.13 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(3112,a,3061,b)].
% 18.04/18.13 3113 -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)].
% 18.04/18.13 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(3113,a,3061,b)].
% 18.04/18.13 3114 -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)].
% 18.04/18.13 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(3114,a,3061,b)].
% 18.04/18.13 3115 -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)].
% 18.04/18.13 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(3115,a,3061,b)].
% 18.04/18.13 3116 -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)].
% 18.04/18.13 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(3116,a,3061,b)].
% 18.04/18.13 3117 -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)].
% 18.04/18.13 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(3117,a,3061,b)].
% 18.04/18.13 3118 -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)].
% 18.04/18.13 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(3118,a,3061,b)].
% 18.04/18.13 3119 -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)].
% 18.12/18.21 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(3119,a,3061,b)].
% 18.12/18.21 3120 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1596,b,1566,a)].
% 18.12/18.21 3121 -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)].
% 18.12/18.21 3122 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1568,a)].
% 18.12/18.21 3123 -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)].
% 18.12/18.21 3124 -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)].
% 18.12/18.21 3125 -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)].
% 18.12/18.21 3126 -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)].
% 18.12/18.21 3127 -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)].
% 18.12/18.21 3128 -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)].
% 18.12/18.21 3129 -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)].
% 18.12/18.21 3130 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1596,b,1576,a)].
% 18.12/18.21 3131 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1599,a,1596,b)].
% 18.12/18.21 3132 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1600,a,1596,b)].
% 18.12/18.21 3133 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1622,a)].
% 18.12/18.21 3134 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1623,a)].
% 18.12/18.21 3135 -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(1661,b,1624,a)].
% 18.12/18.21 3136 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1625,a)].
% 18.12/18.21 3137 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1626,a)].
% 18.12/18.21 3138 -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(1661,b,1627,a)].
% 18.12/18.21 3139 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1628,a)].
% 18.12/18.21 3140 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1629,a)].
% 18.12/18.21 3141 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1630,a)].
% 18.12/18.21 3142 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1631,a)].
% 18.12/18.21 3143 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1632,a)].
% 18.12/18.21 3144 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1633,a)].
% 18.12/18.21 3145 -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(1661,b,1634,a)].
% 18.18/18.27 3146 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1635,a)].
% 18.18/18.27 3147 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1636,a)].
% 18.18/18.27 3148 -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(1661,b,1637,a)].
% 18.18/18.27 3149 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1638,a)].
% 18.18/18.27 3150 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1639,a)].
% 18.18/18.27 3151 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1640,a)].
% 18.18/18.27 3152 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1641,a)].
% 18.18/18.27 3153 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1776,b,1745,a)].
% 18.18/18.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3153,a,3061,b)].
% 18.18/18.27 3154 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1776,b,1752,a)].
% 18.18/18.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3154,a,3061,b)].
% 18.18/18.27 3155 -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(2054,a,2048,b)].
% 18.18/18.27 3156 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2069,a,2048,b)].
% 18.18/18.27 3157 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2070,a,2048,b)].
% 18.18/18.27 3158 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2071,a,2048,b)].
% 18.18/18.27 3159 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2072,a,2048,b)].
% 18.18/18.27 3160 -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(2073,a,2048,b)].
% 18.18/18.27 3161 -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(2074,a,2048,b)].
% 18.18/18.27 3162 -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(2075,a,2048,b)].
% 18.18/18.27 3163 -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(2076,a,2048,b)].
% 18.18/18.27 3164 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2048,b)].
% 18.18/18.27 3165 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(2078,a,2048,b)].
% 18.18/18.27 3166 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2079,a,2048,b)].
% 18.18/18.27 3167 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2080,d,2048,b)].
% 18.18/18.27 3168 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2081,c,2048,b)].
% 18.18/18.27 3169 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2082,a,2048,b)].
% 18.18/18.27 3170 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2083,a,2048,b)].
% 18.18/18.27 3171 -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(2084,a,2048,b)].
% 18.18/18.27 3172 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2085,a,2048,b)].
% 18.18/18.29 3173 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2086,a,2048,b)].
% 18.18/18.29 3174 -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(2087,a,2048,b)].
% 18.18/18.29 3175 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2088,a,2048,b)].
% 18.18/18.29 3176 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2089,a,2048,b)].
% 18.18/18.29 3177 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2090,a,2048,b)].
% 18.18/18.29 3178 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2091,a,2048,b)].
% 18.18/18.29 3179 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2092,a,2048,b)].
% 18.18/18.29 3180 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2093,a,2048,b)].
% 18.18/18.29 3181 -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(2094,a,2048,b)].
% 18.18/18.29 3182 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2095,a,2048,b)].
% 18.18/18.29 3183 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2096,a,2048,b)].
% 18.18/18.29 3184 -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(2097,a,2048,b)].
% 18.18/18.29 3185 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2098,a,2048,b)].
% 18.18/18.29 3186 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2099,a,2048,b)].
% 18.18/18.29 3187 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2100,a,2048,b)].
% 18.18/18.29 3188 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2101,a,2048,b)].
% 18.18/18.29 3189 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2173,b,2116,b)].
% 18.18/18.29 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3189,b,3061,b)].
% 18.18/18.29 3190 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2174,b,2116,b)].
% 18.18/18.29 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3190,b,3061,b)].
% 18.18/18.29 3191 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2175,b,2116,b)].
% 18.18/18.29 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3191,b,3061,b)].
% 18.18/18.29 3192 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2176,b,2116,b)].
% 18.18/18.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3192,b,3061,b)].
% 18.18/18.29 3193 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2177,c,2116,b)].
% 18.18/18.29 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(3193,c,3061,b)].
% 18.18/18.29 3194 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2178,c,2116,b)].
% 18.18/18.29 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(3194,c,3061,b)].
% 18.61/18.70 3195 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_0) # label(axiom). [assumption].
% 18.61/18.70 3196 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 18.61/18.70 3197 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 18.61/18.70 3198 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 18.61/18.70 3199 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom). [assumption].
% 18.61/18.70 3200 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom). [assumption].
% 18.61/18.70 3201 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 18.61/18.70 3202 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom). [assumption].
% 18.61/18.70 3203 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Olordered__ring_29) # label(axiom). [assumption].
% 18.61/18.70 3204 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__field_48) # label(axiom). [assumption].
% 18.61/18.70 3205 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__idom_51) # label(axiom). [assumption].
% 18.61/18.70 3206 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(14,b,1,a)].
% 18.61/18.70 3207 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(14,b,3,a)].
% 18.61/18.70 3208 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 18.61/18.70 3209 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 18.61/18.70 3210 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1076,b,1068,a)].
% 18.61/18.70 3211 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1099,b,1091,a)].
% 18.61/18.70 3212 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1317,a,1267,a)].
% 18.61/18.70 3213 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1317,a,1293,b)].
% 18.61/18.70 3214 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1317,a,1294,b)].
% 18.61/18.70 3215 -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)].
% 18.61/18.70 3216 -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)].
% 18.61/18.70 3217 -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)].
% 18.61/18.70 3218 -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)].
% 18.61/18.70 3219 -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)].
% 18.61/18.70 3220 -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)].
% 18.61/18.70 3221 -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)].
% 18.61/18.72 3222 -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)].
% 18.61/18.72 3223 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1488,a,1473,b)].
% 18.61/18.72 3224 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1489,a,1473,b)].
% 18.61/18.72 3225 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1490,b,1473,b)].
% 18.61/18.72 3226 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,b,1473,b)].
% 18.61/18.72 3227 -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)].
% 18.61/18.72 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3227,a,3196,a)].
% 18.61/18.72 3228 -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)].
% 18.61/18.72 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3228,a,3196,a)].
% 18.61/18.72 3229 -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)].
% 18.61/18.72 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3229,a,3196,a)].
% 18.61/18.72 3230 -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)].
% 18.61/18.72 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3230,a,3196,a)].
% 18.61/18.72 3231 -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)].
% 18.61/18.72 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3231,a,3196,a)].
% 18.61/18.72 3232 -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)].
% 18.61/18.72 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3232,a,3196,a)].
% 18.61/18.72 3233 -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)].
% 18.61/18.72 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(3233,a,3196,a)].
% 18.61/18.72 3234 -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)].
% 18.61/18.72 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(3234,a,3196,a)].
% 18.61/18.72 3235 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1533,b,1508,a)].
% 18.61/18.72 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3235,a,3196,a)].
% 18.61/18.72 3236 -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)].
% 18.61/18.72 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(3236,a,3196,a)].
% 18.61/18.72 3237 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1533,b,1510,a)].
% 18.61/18.72 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(3237,a,3196,a)].
% 18.61/18.72 3238 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1533,b,1511,a)].
% 18.61/18.72 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3238,a,3196,a)].
% 18.61/18.72 3239 -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)].
% 18.61/18.72 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(3239,a,3196,a)].
% 18.64/18.75 3240 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1533,b,1513,a)].
% 18.64/18.75 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3240,a,3196,a)].
% 18.64/18.75 3241 -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)].
% 18.64/18.75 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(3241,a,3196,a)].
% 18.64/18.75 3242 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1533,b,1515,a)].
% 18.64/18.75 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(3242,a,3196,a)].
% 18.64/18.75 3243 -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)].
% 18.64/18.75 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(3243,a,3196,a)].
% 18.64/18.75 3244 -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)].
% 18.64/18.75 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3244,a,3196,a)].
% 18.64/18.75 3245 -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)].
% 18.64/18.75 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3245,a,3196,a)].
% 18.64/18.75 3246 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1533,b,1519,a)].
% 18.64/18.75 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3246,a,3196,a)].
% 18.64/18.75 3247 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1533,b,1520,a)].
% 18.64/18.75 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3247,a,3196,a)].
% 18.64/18.75 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3247,a,3203,b)].
% 18.64/18.75 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3247,a,3204,b)].
% 18.64/18.75 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3247,a,3205,b)].
% 18.64/18.75 3248 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1533,b,1521,a)].
% 18.64/18.75 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(3248,a,3196,a)].
% 18.64/18.75 3249 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1581,b,1566,a)].
% 18.64/18.75 3250 -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)].
% 18.64/18.75 3251 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1581,b,1568,a)].
% 18.64/18.75 3252 -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)].
% 18.64/18.75 3253 -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)].
% 18.64/18.75 3254 -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)].
% 18.64/18.75 3255 -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)].
% 18.64/18.75 3256 -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)].
% 18.64/18.80 3257 -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)].
% 18.64/18.80 3258 -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)].
% 18.64/18.80 3259 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1581,b,1576,a)].
% 18.64/18.80 3260 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1599,a,1581,b)].
% 18.64/18.80 3261 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1600,a,1581,b)].
% 18.64/18.80 3262 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1622,a)].
% 18.64/18.80 3263 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1623,a)].
% 18.64/18.80 3264 -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(1646,b,1624,a)].
% 18.64/18.80 3265 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1625,a)].
% 18.64/18.80 3266 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1626,a)].
% 18.64/18.80 3267 -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(1646,b,1627,a)].
% 18.64/18.80 3268 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1646,b,1628,a)].
% 18.64/18.80 3269 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1646,b,1629,a)].
% 18.64/18.80 3270 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1646,b,1630,a)].
% 18.64/18.80 3271 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1646,b,1631,a)].
% 18.64/18.80 3272 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1632,a)].
% 18.64/18.80 3273 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1646,b,1633,a)].
% 18.64/18.80 3274 -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(1646,b,1634,a)].
% 18.64/18.80 3275 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1646,b,1635,a)].
% 18.64/18.80 3276 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1646,b,1636,a)].
% 18.64/18.80 3277 -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(1646,b,1637,a)].
% 18.64/18.80 3278 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1646,b,1638,a)].
% 18.64/18.80 3279 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1646,b,1639,a)].
% 18.64/18.80 3280 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1646,b,1640,a)].
% 18.64/18.80 3281 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1646,b,1641,a)].
% 18.64/18.80 3282 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1781,a,1749,b)].
% 18.64/18.80 3283 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1782,a,1749,b)].
% 18.64/18.81 3284 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1783,a,1749,b)].
% 18.64/18.81 3285 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1784,a,1749,b)].
% 18.64/18.81 3286 -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(1785,a,1749,b)].
% 18.64/18.81 3287 -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(1786,a,1749,b)].
% 18.64/18.81 3288 -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(1787,a,1749,b)].
% 18.64/18.81 3289 -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(1788,a,1749,b)].
% 18.64/18.81 3290 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1789,a,1749,b)].
% 18.64/18.81 3291 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(1790,a,1749,b)].
% 18.64/18.81 3292 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1791,a,1749,b)].
% 18.64/18.81 3293 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1792,d,1749,b)].
% 18.64/18.81 3294 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1793,c,1749,b)].
% 18.64/18.81 3295 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1794,a,1749,b)].
% 18.64/18.81 3296 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1795,a,1749,b)].
% 18.64/18.81 3297 -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(1796,a,1749,b)].
% 18.64/18.81 3298 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1797,a,1749,b)].
% 18.64/18.81 3299 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1798,a,1749,b)].
% 18.64/18.81 3300 -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(1799,a,1749,b)].
% 18.64/18.81 3301 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1749,b)].
% 18.64/18.81 3302 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1801,a,1749,b)].
% 18.64/18.81 3303 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1802,a,1749,b)].
% 18.64/18.81 3304 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1803,a,1749,b)].
% 18.64/18.81 3305 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1804,a,1749,b)].
% 18.64/18.81 3306 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1805,a,1749,b)].
% 18.64/18.81 3307 -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(1806,a,1749,b)].
% 18.64/18.81 3308 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1807,a,1749,b)].
% 18.64/18.81 3309 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1808,a,1749,b)].
% 19.12/19.26 3310 -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(1809,a,1749,b)].
% 19.12/19.26 3311 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1810,a,1749,b)].
% 19.12/19.26 3312 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1811,a,1749,b)].
% 19.12/19.26 3313 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1812,a,1749,b)].
% 19.12/19.26 3314 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1813,a,1749,b)].
% 19.12/19.26 3315 -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].
% 19.12/19.26 3316 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 19.12/19.26 3317 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 19.12/19.26 3318 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 19.12/19.26 3319 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom). [assumption].
% 19.12/19.26 3320 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom). [assumption].
% 19.12/19.26 3321 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 19.12/19.26 3322 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom). [assumption].
% 19.12/19.26 3323 -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].
% 19.12/19.26 3324 -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].
% 19.12/19.26 3325 -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].
% 19.12/19.26 3326 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(13,b,1,a)].
% 19.12/19.26 3327 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(13,b,3,a)].
% 19.12/19.26 3328 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 19.12/19.26 3329 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 19.12/19.26 3330 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1075,b,1068,a)].
% 19.12/19.26 3331 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1098,b,1091,a)].
% 19.12/19.26 3332 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1318,a,1267,a)].
% 19.12/19.26 3333 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1318,a,1293,b)].
% 19.12/19.26 3334 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1318,a,1294,b)].
% 19.12/19.26 3335 -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)].
% 19.12/19.26 3336 -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)].
% 19.12/19.26 3337 -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)].
% 19.19/19.28 3338 -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)].
% 19.19/19.28 3339 -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)].
% 19.19/19.28 3340 -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)].
% 19.19/19.28 3341 -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)].
% 19.19/19.28 3342 -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)].
% 19.19/19.28 3343 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1488,a,1472,b)].
% 19.19/19.28 3344 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1489,a,1472,b)].
% 19.19/19.28 3345 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1490,b,1472,b)].
% 19.19/19.28 3346 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,b,1472,b)].
% 19.19/19.28 3347 -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)].
% 19.19/19.28 3348 -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)].
% 19.19/19.28 3349 -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)].
% 19.19/19.28 3350 -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)].
% 19.19/19.28 3351 -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)].
% 19.19/19.28 3352 -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)].
% 19.19/19.28 3353 -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)].
% 19.19/19.28 3354 -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)].
% 19.19/19.28 3355 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1532,b,1508,a)].
% 19.19/19.28 3356 -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)].
% 19.19/19.28 3357 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1532,b,1510,a)].
% 19.19/19.28 3358 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1532,b,1511,a)].
% 19.19/19.28 3359 -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)].
% 19.19/19.28 3360 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1532,b,1513,a)].
% 19.19/19.28 3361 -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)].
% 19.19/19.28 3362 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1532,b,1515,a)].
% 19.19/19.28 3363 -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)].
% 19.19/19.28 3364 -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)].
% 19.19/19.28 3365 -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)].
% 19.19/19.28 3366 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1532,b,1519,a)].
% 19.21/19.32 3367 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1532,b,1520,a)].
% 19.21/19.32 3368 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1532,b,1521,a)].
% 19.21/19.32 3369 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1580,b,1566,a)].
% 19.21/19.32 3370 -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)].
% 19.21/19.32 3371 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1580,b,1568,a)].
% 19.21/19.32 3372 -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)].
% 19.21/19.32 3373 -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)].
% 19.21/19.32 3374 -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)].
% 19.21/19.32 3375 -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)].
% 19.21/19.32 3376 -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)].
% 19.21/19.32 3377 -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)].
% 19.21/19.32 3378 -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)].
% 19.21/19.32 3379 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1580,b,1576,a)].
% 19.21/19.32 3380 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1599,a,1580,b)].
% 19.21/19.32 3381 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1600,a,1580,b)].
% 19.21/19.32 3382 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1622,a)].
% 19.21/19.32 3383 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1623,a)].
% 19.21/19.32 3384 -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(1645,b,1624,a)].
% 19.21/19.32 3385 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1625,a)].
% 19.21/19.32 3386 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1626,a)].
% 19.21/19.32 3387 -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(1645,b,1627,a)].
% 19.21/19.32 3388 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1645,b,1628,a)].
% 19.21/19.32 3389 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1645,b,1629,a)].
% 19.21/19.32 3390 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1645,b,1630,a)].
% 19.21/19.32 3391 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1645,b,1631,a)].
% 19.21/19.32 3392 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1632,a)].
% 19.21/19.32 3393 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1645,b,1633,a)].
% 19.23/19.35 3394 -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(1645,b,1634,a)].
% 19.23/19.35 3395 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1645,b,1635,a)].
% 19.23/19.35 3396 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1645,b,1636,a)].
% 19.23/19.35 3397 -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(1645,b,1637,a)].
% 19.23/19.35 3398 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1645,b,1638,a)].
% 19.23/19.35 3399 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1645,b,1639,a)].
% 19.23/19.35 3400 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1645,b,1640,a)].
% 19.23/19.35 3401 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1645,b,1641,a)].
% 19.23/19.35 3402 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1781,a,1748,b)].
% 19.23/19.35 3403 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1782,a,1748,b)].
% 19.23/19.35 3404 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1783,a,1748,b)].
% 19.23/19.35 3405 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1784,a,1748,b)].
% 19.23/19.35 3406 -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(1785,a,1748,b)].
% 19.23/19.35 3407 -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(1786,a,1748,b)].
% 19.23/19.35 3408 -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(1787,a,1748,b)].
% 19.23/19.35 3409 -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(1788,a,1748,b)].
% 19.23/19.35 3410 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1789,a,1748,b)].
% 19.23/19.35 3411 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(1790,a,1748,b)].
% 19.23/19.35 3412 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1791,a,1748,b)].
% 19.23/19.35 3413 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1792,d,1748,b)].
% 19.23/19.35 3414 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1793,c,1748,b)].
% 19.23/19.35 3415 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1794,a,1748,b)].
% 19.23/19.35 3416 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1795,a,1748,b)].
% 19.23/19.35 3417 -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(1796,a,1748,b)].
% 19.23/19.35 3418 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1797,a,1748,b)].
% 19.23/19.35 3419 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1798,a,1748,b)].
% 19.54/19.64 3420 -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(1799,a,1748,b)].
% 19.54/19.64 3421 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1748,b)].
% 19.54/19.64 3422 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1801,a,1748,b)].
% 19.54/19.64 3423 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1802,a,1748,b)].
% 19.54/19.64 3424 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1803,a,1748,b)].
% 19.54/19.64 3425 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1804,a,1748,b)].
% 19.54/19.64 3426 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1805,a,1748,b)].
% 19.54/19.64 3427 -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(1806,a,1748,b)].
% 19.54/19.64 3428 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1807,a,1748,b)].
% 19.54/19.64 3429 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1808,a,1748,b)].
% 19.54/19.64 3430 -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(1809,a,1748,b)].
% 19.54/19.64 3431 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1810,a,1748,b)].
% 19.54/19.64 3432 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1811,a,1748,b)].
% 19.54/19.64 3433 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1812,a,1748,b)].
% 19.54/19.64 3434 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1813,a,1748,b)].
% 19.54/19.64 3435 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 19.54/19.64 3436 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 19.54/19.64 3437 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom). [assumption].
% 19.54/19.64 3438 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 19.54/19.64 3439 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom). [assumption].
% 19.54/19.64 3440 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_2) # label(axiom). [assumption].
% 19.54/19.64 3441 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 19.54/19.64 3442 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom). [assumption].
% 19.54/19.64 3443 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 19.54/19.64 3444 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom). [assumption].
% 19.54/19.64 3445 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_43) # label(axiom). [assumption].
% 19.54/19.66 3446 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_48) # label(axiom). [assumption].
% 19.54/19.66 3447 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(26,b,1,a)].
% 19.54/19.66 3448 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(26,b,3,a)].
% 19.54/19.66 3449 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 19.54/19.66 3450 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 19.54/19.66 3451 -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)].
% 19.54/19.66 3452 -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)].
% 19.54/19.66 3453 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(167,a,149,b)].
% 19.54/19.66 3454 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(168,a,149,b)].
% 19.54/19.66 3455 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 19.54/19.66 3456 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 19.54/19.66 3457 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 19.54/19.66 3458 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 19.54/19.66 3459 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,286,a)].
% 19.54/19.66 3460 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,288,a)].
% 19.54/19.66 3461 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(320,a,299,b)].
% 19.54/19.66 3462 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(321,a,299,b)].
% 19.54/19.66 3463 -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)].
% 19.54/19.66 3464 -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)].
% 19.54/19.66 3465 -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)].
% 19.54/19.66 3466 -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)].
% 19.54/19.66 3467 -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)].
% 19.54/19.66 3468 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(350,a,339,b)].
% 19.54/19.66 3469 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(351,a,339,b)].
% 19.54/19.66 3470 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(358,b,339,b)].
% 19.54/19.66 3471 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(359,b,339,b)].
% 19.54/19.66 3472 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,339,b)].
% 19.54/19.66 3473 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,339,b)].
% 19.54/19.66 3474 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(364,b,339,b)].
% 19.65/19.79 3475 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(365,b,339,b)].
% 19.65/19.79 3476 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 19.65/19.79 3477 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 19.65/19.79 3478 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(368,a,339,b)].
% 19.65/19.79 3479 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(369,a,339,b)].
% 19.65/19.79 3480 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(370,c,339,b)].
% 19.65/19.79 3481 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(371,c,339,b)].
% 19.65/19.79 3482 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(799,a,724,a)].
% 19.65/19.79 3483 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(799,a,731,a)].
% 19.65/19.79 3484 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1078,b,1068,a)].
% 19.65/19.79 3485 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1091,a)].
% 19.65/19.79 3486 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1314,a,1267,a)].
% 19.65/19.79 3487 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1314,a,1293,b)].
% 19.65/19.79 3488 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1314,a,1294,b)].
% 19.65/19.79 3489 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1449,b,1420,a)].
% 19.65/19.79 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3489,a,3436,a)].
% 19.65/19.79 3490 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1449,b,1421,a)].
% 19.65/19.79 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3490,a,3436,a)].
% 19.65/19.79 3491 -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)].
% 19.65/19.79 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(3491,a,3436,a)].
% 19.65/19.79 3492 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1449,b,1423,a)].
% 19.65/19.79 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3492,a,3436,a)].
% 19.65/19.79 3493 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1449,b,1424,a)].
% 19.65/19.79 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3493,a,3436,a)].
% 19.65/19.79 3494 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1449,b,1425,a)].
% 19.65/19.79 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3494,a,3436,a)].
% 19.65/19.79 3495 -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)].
% 19.65/19.79 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3495,a,3436,a)].
% 19.65/19.79 3496 -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)].
% 19.65/19.79 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3496,a,3436,a)].
% 19.65/19.79 3497 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1449,b,1428,a)].
% 19.65/19.79 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3497,a,3436,a)].
% 19.65/19.79 3498 -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)].
% 19.65/19.79 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3498,a,3436,a)].
% 19.65/19.79 3499 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1449,b,1430,a)].
% 19.73/19.82 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3499,a,3436,a)].
% 19.73/19.82 3500 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1449,b,1431,a)].
% 19.73/19.82 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3500,a,3436,a)].
% 19.73/19.82 3501 -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)].
% 19.73/19.82 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3501,a,3436,a)].
% 19.73/19.82 3502 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1449,b,1433,a)].
% 19.73/19.82 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3502,a,3436,a)].
% 19.73/19.82 3503 -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)].
% 19.73/19.82 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3503,a,3436,a)].
% 19.73/19.82 3504 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1449,b,1436,a)].
% 19.73/19.82 3505 -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)].
% 19.73/19.82 3506 -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)].
% 19.73/19.82 3507 -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)].
% 19.73/19.82 3508 -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)].
% 19.73/19.82 3509 -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)].
% 19.73/19.82 3510 -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)].
% 19.73/19.82 3511 -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)].
% 19.73/19.82 3512 -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)].
% 19.73/19.82 3513 -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)].
% 19.73/19.82 3514 -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)].
% 19.73/19.82 3515 -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)].
% 19.73/19.82 3516 -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)].
% 19.73/19.82 3517 -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)].
% 19.73/19.82 3518 -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)].
% 19.73/19.82 3519 -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)].
% 19.73/19.82 3520 -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)].
% 19.73/19.82 3521 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1534,b,1508,a)].
% 19.73/19.82 3522 -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)].
% 19.73/19.82 3523 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1534,b,1510,a)].
% 19.73/19.82 3524 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1534,b,1511,a)].
% 19.73/19.82 3525 -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)].
% 19.73/19.85 3526 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1534,b,1513,a)].
% 19.73/19.85 3527 -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)].
% 19.73/19.85 3528 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1534,b,1515,a)].
% 19.73/19.85 3529 -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)].
% 19.73/19.85 3530 -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)].
% 19.73/19.85 3531 -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)].
% 19.73/19.85 3532 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1534,b,1519,a)].
% 19.73/19.85 3533 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1561,c,1534,b)].
% 19.73/19.85 3534 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1562,c,1534,b)].
% 19.73/19.85 3535 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1563,b,1534,b)].
% 19.73/19.85 3536 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1564,b,1534,b)].
% 19.73/19.85 3537 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1587,b,1566,a)].
% 19.73/19.85 3538 -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)].
% 19.73/19.85 3539 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1587,b,1568,a)].
% 19.73/19.85 3540 -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)].
% 19.73/19.85 3541 -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)].
% 19.73/19.85 3542 -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)].
% 19.73/19.85 3543 -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)].
% 19.73/19.85 3544 -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)].
% 19.73/19.85 3545 -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)].
% 19.73/19.85 3546 -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)].
% 19.73/19.85 3547 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1587,b,1576,a)].
% 19.73/19.85 3548 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1599,a,1587,b)].
% 19.73/19.85 3549 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1600,a,1587,b)].
% 19.73/19.85 3550 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1622,a)].
% 19.73/19.85 3551 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1623,a)].
% 19.73/19.85 3552 -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(1652,b,1624,a)].
% 19.73/19.85 3553 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1625,a)].
% 19.73/19.85 3554 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1626,a)].
% 19.81/19.91 3555 -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(1652,b,1627,a)].
% 19.81/19.91 3556 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1652,b,1628,a)].
% 19.81/19.91 3557 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1652,b,1629,a)].
% 19.81/19.91 3558 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1652,b,1630,a)].
% 19.81/19.91 3559 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1652,b,1631,a)].
% 19.81/19.91 3560 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1632,a)].
% 19.81/19.91 3561 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1652,b,1633,a)].
% 19.81/19.91 3562 -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(1652,b,1634,a)].
% 19.81/19.91 3563 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1652,b,1635,a)].
% 19.81/19.91 3564 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1652,b,1636,a)].
% 19.81/19.91 3565 -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(1652,b,1637,a)].
% 19.81/19.91 3566 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1652,b,1638,a)].
% 19.81/19.91 3567 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1652,b,1639,a)].
% 19.81/19.91 3568 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1652,b,1640,a)].
% 19.81/19.91 3569 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1652,b,1641,a)].
% 19.81/19.91 3570 -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(2054,a,2039,b)].
% 19.81/19.91 3571 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2069,a,2039,b)].
% 19.81/19.91 3572 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2070,a,2039,b)].
% 19.81/19.91 3573 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2071,a,2039,b)].
% 19.81/19.91 3574 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2072,a,2039,b)].
% 19.81/19.91 3575 -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(2073,a,2039,b)].
% 19.81/19.91 3576 -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(2074,a,2039,b)].
% 19.81/19.91 3577 -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(2075,a,2039,b)].
% 19.81/19.91 3578 -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(2076,a,2039,b)].
% 19.81/19.91 3579 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2039,b)].
% 19.81/19.91 3580 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(2078,a,2039,b)].
% 19.81/19.91 3581 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2079,a,2039,b)].
% 19.81/19.91 3582 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2080,d,2039,b)].
% 19.81/19.92 3583 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2081,c,2039,b)].
% 19.81/19.92 3584 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2082,a,2039,b)].
% 19.81/19.92 3585 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2083,a,2039,b)].
% 19.81/19.92 3586 -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(2084,a,2039,b)].
% 19.81/19.92 3587 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2085,a,2039,b)].
% 19.81/19.92 3588 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2086,a,2039,b)].
% 19.81/19.92 3589 -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(2087,a,2039,b)].
% 19.81/19.92 3590 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2088,a,2039,b)].
% 19.81/19.92 3591 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2089,a,2039,b)].
% 19.81/19.92 3592 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2090,a,2039,b)].
% 19.81/19.92 3593 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2091,a,2039,b)].
% 19.81/19.92 3594 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2092,a,2039,b)].
% 19.81/19.92 3595 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2093,a,2039,b)].
% 19.81/19.92 3596 -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(2094,a,2039,b)].
% 19.81/19.92 3597 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2095,a,2039,b)].
% 19.81/19.92 3598 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2096,a,2039,b)].
% 19.81/19.92 3599 -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(2097,a,2039,b)].
% 19.81/19.92 3600 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2098,a,2039,b)].
% 19.81/19.92 3601 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2099,a,2039,b)].
% 19.81/19.92 3602 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2100,a,2039,b)].
% 19.81/19.92 3603 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2101,a,2039,b)].
% 19.81/19.92 3604 -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(2172,d,2105,b)].
% 19.81/19.92 3605 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2173,b,2105,b)].
% 19.81/19.92 3606 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2174,b,2105,b)].
% 19.81/19.92 3607 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2175,b,2105,b)].
% 19.81/19.92 3608 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2176,b,2105,b)].
% 19.81/19.92 3609 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2177,c,2105,b)].
% 19.81/19.92 3610 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2178,c,2105,b)].
% 19.81/19.94 3611 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2179,b,2105,b)].
% 19.81/19.94 3612 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2180,c,2105,b)].
% 19.81/19.94 3613 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2181,b,2105,b)].
% 19.81/19.94 3614 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2182,c,2105,b)].
% 19.81/19.94 3615 -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(2183,c,2105,b)].
% 19.81/19.94 3616 -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(2184,c,2105,b)].
% 19.81/19.94 3617 -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(2185,c,2105,b)].
% 19.81/19.94 3618 -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(2186,c,2105,b)].
% 19.81/19.94 3619 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2187,c,2105,b)].
% 19.81/19.94 3620 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(2188,b,2105,b)].
% 19.81/19.94 3621 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2189,b,2105,b)].
% 19.81/19.94 3622 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2190,d,2105,b)].
% 19.81/19.94 3623 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2191,c,2105,b)].
% 19.81/19.94 3624 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2192,c,2105,b)].
% 19.81/19.94 3625 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2193,c,2105,b)].
% 19.81/19.94 3626 -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(2194,d,2105,b)].
% 19.81/19.94 3627 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2195,c,2105,b)].
% 19.81/19.94 3628 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2196,c,2105,b)].
% 19.81/19.94 3629 -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(2197,d,2105,b)].
% 19.81/19.94 3630 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2198,c,2105,b)].
% 19.81/19.94 3631 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2199,c,2105,b)].
% 19.81/19.94 3632 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2200,c,2105,b)].
% 19.81/19.94 3633 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,c,2105,b)].
% 19.81/19.94 3634 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2202,c,2105,b)].
% 19.81/19.94 3635 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2203,c,2105,b)].
% 19.81/19.94 3636 -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(2204,d,2105,b)].
% 19.81/19.94 3637 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2205,c,2105,b)].
% 19.94/20.05 3638 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,c,2105,b)].
% 19.94/20.05 3639 -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(2207,d,2105,b)].
% 19.94/20.05 3640 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2208,c,2105,b)].
% 19.94/20.05 3641 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2105,b)].
% 19.94/20.05 3642 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2210,c,2105,b)].
% 19.94/20.05 3643 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2105,b)].
% 19.94/20.05 3644 -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(3090,a,3061,b)].
% 19.94/20.05 3645 -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(3091,a,3061,b)].
% 19.94/20.05 3646 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3092,a,3061,b)].
% 19.94/20.05 3647 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3093,a,3061,b)].
% 19.94/20.05 3648 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3094,a,3061,b)].
% 19.94/20.05 3649 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3095,b,3061,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3649,b,3445,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3649,b,3446,b)].
% 19.94/20.05 3650 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3096,b,3061,b)].
% 19.94/20.05 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(3650,b,3436,a)].
% 19.94/20.05 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3650,b,3445,b)].
% 19.94/20.05 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3650,b,3446,b)].
% 19.94/20.05 3651 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3103,b,3061,b)].
% 19.94/20.05 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3651,b,3436,a)].
% 19.94/20.05 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3651,b,3445,b)].
% 19.94/20.05 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3651,b,3446,b)].
% 19.94/20.05 3652 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3104,b,3061,b)].
% 19.94/20.05 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3652,b,3436,a)].
% 19.94/20.05 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3652,b,3445,b)].
% 19.94/20.05 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3652,b,3446,b)].
% 19.94/20.05 3653 -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(3112,a,3061,b)].
% 19.94/20.05 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(3653,c,3436,a)].
% 19.94/20.05 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(3653,c,3445,b)].
% 19.94/20.05 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(3653,c,3446,b)].
% 19.94/20.05 3654 -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(3113,a,3061,b)].
% 19.94/20.05 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(3654,c,3436,a)].
% 19.94/20.05 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(3654,c,3445,b)].
% 19.94/20.05 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(3654,c,3446,b)].
% 19.94/20.05 3655 -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(3114,a,3061,b)].
% 19.94/20.05 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(3655,c,3436,a)].
% 19.94/20.05 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(3655,c,3445,b)].
% 19.94/20.05 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(3655,c,3446,b)].
% 19.94/20.05 3656 -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(3115,a,3061,b)].
% 19.94/20.05 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(3656,c,3436,a)].
% 19.94/20.05 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(3656,c,3445,b)].
% 19.94/20.05 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(3656,c,3446,b)].
% 19.94/20.05 3657 -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(3116,a,3061,b)].
% 19.94/20.05 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(3657,c,3436,a)].
% 19.94/20.05 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(3657,c,3445,b)].
% 19.94/20.05 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(3657,c,3446,b)].
% 19.94/20.05 3658 -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(3117,a,3061,b)].
% 19.94/20.05 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(3658,c,3436,a)].
% 19.94/20.05 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(3658,c,3445,b)].
% 19.94/20.05 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(3658,c,3446,b)].
% 19.94/20.05 3659 -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(3118,a,3061,b)].
% 19.94/20.05 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(3659,c,3436,a)].
% 19.94/20.05 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(3659,c,3445,b)].
% 19.94/20.05 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(3659,c,3446,b)].
% 19.94/20.05 3660 -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(3119,a,3061,b)].
% 19.94/20.05 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(3660,c,3436,a)].
% 19.94/20.05 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(3660,c,3445,b)].
% 19.94/20.05 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(3660,c,3446,b)].
% 19.94/20.05 3661 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3153,a,3061,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3661,b,3436,a)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3661,b,3445,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3661,b,3446,b)].
% 19.94/20.05 3662 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3154,a,3061,b)].
% 19.94/20.05 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3662,b,3436,a)].
% 19.94/20.05 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3662,b,3445,b)].
% 19.94/20.05 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3662,b,3446,b)].
% 19.94/20.05 3663 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3189,b,3061,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3663,b,3436,a)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3663,b,3445,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3663,b,3446,b)].
% 19.94/20.05 3664 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3190,b,3061,b)].
% 19.94/20.05 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3664,b,3436,a)].
% 19.94/20.05 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3664,b,3445,b)].
% 19.94/20.05 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3664,b,3446,b)].
% 19.94/20.05 3665 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3191,b,3061,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3665,b,3436,a)].
% 19.94/20.05 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3665,b,3445,b)].
% 19.94/20.05 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3665,b,3446,b)].
% 19.94/20.05 3666 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3192,b,3061,b)].
% 19.94/20.05 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3666,b,3436,a)].
% 19.94/20.05 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3666,b,3445,b)].
% 19.94/20.05 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3666,b,3446,b)].
% 19.94/20.05 3667 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(3193,c,3061,b)].
% 19.94/20.05 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(3667,c,3436,a)].
% 19.94/20.05 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(3667,c,3445,b)].
% 19.94/20.05 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(3667,c,3446,b)].
% 19.94/20.05 3668 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(3194,c,3061,b)].
% 19.94/20.05 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(3668,c,3436,a)].
% 19.94/20.05 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(3668,c,3445,b)].
% 20.55/20.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3668,c,3446,b)].
% 20.55/20.64 3669 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3247,a,3203,b)].
% 20.55/20.64 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3669,b,3436,a)].
% 20.55/20.64 3670 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) # label(axiom). [assumption].
% 20.55/20.64 3671 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom). [assumption].
% 20.55/20.64 3672 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) # label(axiom). [assumption].
% 20.55/20.64 3673 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Ofield_32) # label(axiom). [assumption].
% 20.55/20.64 3674 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oidom_30) # label(axiom). [assumption].
% 20.55/20.64 3675 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__field_31) # label(axiom). [assumption].
% 20.55/20.64 3676 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__idom_56) # label(axiom). [assumption].
% 20.55/20.64 3677 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1319,a,1267,a)].
% 20.55/20.64 3678 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1319,a,1293,b)].
% 20.55/20.64 3679 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1319,a,1294,b)].
% 20.55/20.64 3680 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 20.55/20.64 3681 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 20.55/20.64 3682 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 20.55/20.64 Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A). [resolve(3680,a,3682,b)].
% 20.55/20.64 3683 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 20.55/20.64 3684 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 20.55/20.64 3685 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom). [assumption].
% 20.55/20.64 3686 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 20.55/20.64 3687 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom). [assumption].
% 20.55/20.64 3688 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 20.55/20.64 3689 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom). [assumption].
% 20.55/20.64 3690 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 20.55/20.64 3691 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom). [assumption].
% 20.55/20.64 3692 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 20.55/20.64 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3692,a,3682,b)].
% 20.55/20.67 3693 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 20.55/20.67 3694 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 20.55/20.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A). [resolve(3694,b,3680,a)].
% 20.55/20.67 3695 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 20.55/20.67 3696 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 20.55/20.67 3697 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 20.55/20.67 3698 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 20.55/20.67 3699 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(108,a,100,b)].
% 20.55/20.67 3700 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)].
% 20.55/20.67 3701 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(126,b,110,a)].
% 20.55/20.67 3702 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(126,b,113,a)].
% 20.55/20.67 3703 -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)].
% 20.55/20.67 3704 -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)].
% 20.55/20.67 3705 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(167,a,148,b)].
% 20.55/20.67 3706 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(168,a,148,b)].
% 20.55/20.67 3707 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(203,b,190,b)].
% 20.55/20.67 3708 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(204,b,190,b)].
% 20.55/20.67 3709 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 20.55/20.67 3710 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 20.55/20.67 3711 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 20.55/20.67 3712 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 20.55/20.67 3713 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,286,a)].
% 20.55/20.67 3714 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,288,a)].
% 20.55/20.67 3715 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(320,a,298,b)].
% 20.55/20.67 3716 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(321,a,298,b)].
% 20.55/20.67 3717 -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)].
% 20.55/20.67 3718 -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)].
% 20.55/20.67 3719 -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)].
% 20.55/20.67 3720 -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)].
% 20.55/20.67 3721 -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)].
% 20.55/20.67 3722 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(350,a,338,b)].
% 20.55/20.68 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3722,b,3682,b)].
% 20.55/20.68 3723 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(351,a,338,b)].
% 20.55/20.68 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3723,b,3682,b)].
% 20.55/20.68 3724 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(362,b,338,b)].
% 20.55/20.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3724,b,3682,b)].
% 20.55/20.68 3725 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(363,b,338,b)].
% 20.55/20.68 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(3725,b,3682,b)].
% 20.55/20.68 3726 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(364,b,338,b)].
% 20.55/20.68 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3726,b,3682,b)].
% 20.55/20.68 3727 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(365,b,338,b)].
% 20.55/20.68 3728 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 20.55/20.68 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(3728,c,3682,b)].
% 20.55/20.68 3729 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 20.55/20.68 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(3729,c,3682,b)].
% 20.55/20.68 3730 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(368,a,338,b)].
% 20.55/20.68 3731 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(369,a,338,b)].
% 20.55/20.68 3732 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(370,c,338,b)].
% 20.55/20.68 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3732,c,3682,b)].
% 20.55/20.68 3733 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(371,c,338,b)].
% 20.55/20.68 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3733,c,3682,b)].
% 20.55/20.68 3734 c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Oidom(C). [resolve(444,b,429,b)].
% 20.55/20.68 Derived: c_times(A,B,C) = c_times(B,A,C) | -class_Ring__and__Field_Ofield(C). [resolve(3734,b,3682,b)].
% 20.55/20.68 3735 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)].
% 20.55/20.68 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(3735,b,3682,b)].
% 20.55/20.68 3736 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(475,b,429,b)].
% 20.55/20.68 3737 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(476,b,429,b)].
% 20.55/20.68 3738 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(513,a,507,b)].
% 20.55/20.68 3739 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(520,a,507,b)].
% 20.55/20.68 3740 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(521,a,507,b)].
% 20.55/20.68 3741 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(565,b,543,b)].
% 20.55/20.68 3742 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(566,b,543,b)].
% 20.55/20.68 3743 -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)].
% 20.55/20.68 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3743,c,3682,b)].
% 20.55/20.70 3744 -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)].
% 20.55/20.70 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(3744,c,3682,b)].
% 20.55/20.70 3745 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)].
% 20.55/20.70 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3745,b,3682,b)].
% 20.55/20.70 3746 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)].
% 20.55/20.70 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3746,b,3682,b)].
% 20.55/20.70 3747 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)].
% 20.55/20.70 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3747,b,3682,b)].
% 20.55/20.70 3748 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(649,b,610,b)].
% 20.55/20.70 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(3748,b,3682,b)].
% 20.55/20.70 3749 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(650,b,610,b)].
% 20.55/20.70 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3749,b,3682,b)].
% 20.55/20.70 3750 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(651,b,610,b)].
% 20.55/20.70 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3750,b,3682,b)].
% 20.55/20.70 3751 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(653,b,610,b)].
% 20.55/20.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3751,b,3682,b)].
% 20.55/20.70 3752 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(654,b,610,b)].
% 20.55/20.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3752,b,3682,b)].
% 20.55/20.70 3753 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(656,b,610,b)].
% 20.55/20.70 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3753,b,3682,b)].
% 20.55/20.70 3754 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(657,b,610,b)].
% 20.55/20.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(3754,b,3682,b)].
% 20.55/20.70 3755 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(684,b,658,a)].
% 20.55/20.70 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3755,a,3682,b)].
% 20.55/20.70 3756 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(684,b,660,a)].
% 20.55/20.70 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3756,a,3682,b)].
% 20.55/20.70 3757 -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)].
% 20.55/20.70 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(3757,a,3682,b)].
% 20.55/20.70 3758 -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)].
% 20.55/20.70 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(3758,a,3682,b)].
% 20.55/20.70 3759 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(684,b,663,a)].
% 20.55/20.70 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3759,a,3682,b)].
% 20.55/20.70 3760 -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)].
% 20.55/20.70 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(3760,a,3682,b)].
% 22.53/22.63 3761 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(684,b,665,a)].
% 22.53/22.63 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3761,a,3682,b)].
% 22.53/22.63 3762 -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)].
% 22.53/22.63 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(3762,a,3682,b)].
% 22.53/22.63 3763 -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)].
% 22.53/22.63 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(3763,a,3682,b)].
% 22.53/22.63 3764 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(684,b,668,a)].
% 22.53/22.63 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3764,a,3682,b)].
% 22.53/22.63 3765 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(816,a,724,a)].
% 22.53/22.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3765,a,3682,b)].
% 22.53/22.63 3766 -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)].
% 22.53/22.63 3767 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 22.53/22.63 3768 -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)].
% 22.53/22.63 3769 -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)].
% 22.53/22.63 3770 -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)].
% 22.53/22.63 3771 -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)].
% 22.53/22.63 3772 -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)].
% 22.53/22.63 3773 -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)].
% 22.53/22.63 3774 -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)].
% 22.53/22.63 3775 -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)].
% 22.53/22.63 3776 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,831,a)].
% 22.53/22.63 3777 -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)].
% 22.53/22.63 3778 -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)].
% 22.53/22.63 3779 -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)].
% 22.53/22.63 3780 -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)].
% 22.53/22.63 3781 -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)].
% 22.53/22.63 3782 -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)].
% 22.53/22.63 3783 -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)].
% 22.53/22.63 3784 -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)].
% 22.53/22.63 3785 -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)].
% 22.53/22.63 3786 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(893,b,841,a)].
% 22.53/22.63 3787 -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)].
% 22.53/22.63 3788 -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)].
% 22.53/22.63 3789 -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)].
% 22.53/22.63 3790 -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)].
% 22.53/22.63 3791 -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)].
% 22.53/22.63 3792 -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)].
% 22.53/22.63 3793 -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)].
% 22.53/22.63 3794 -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)].
% 22.53/22.63 3795 -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)].
% 22.53/22.63 3796 -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)].
% 22.53/22.63 3797 -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)].
% 22.53/22.63 3798 -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)].
% 22.53/22.63 3799 -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)].
% 22.53/22.63 3800 -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)].
% 22.53/22.63 3801 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(893,b,856,a)].
% 22.53/22.63 3802 -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)].
% 22.53/22.63 3803 -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)].
% 22.53/22.63 3804 -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)].
% 22.64/22.73 3805 -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)].
% 22.64/22.73 3806 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(893,b,861,a)].
% 22.64/22.73 3807 -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)].
% 22.64/22.73 3808 -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)].
% 22.64/22.73 3809 -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)].
% 22.64/22.73 3810 -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)].
% 22.64/22.73 3811 -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)].
% 22.64/22.73 3812 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(893,b,867,a)].
% 22.64/22.73 3813 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(893,b,868,a)].
% 22.64/22.73 3814 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(893,b,869,a)].
% 22.64/22.73 3815 -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)].
% 22.64/22.73 3816 -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)].
% 22.64/22.73 3817 -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)].
% 22.64/22.73 3818 -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)].
% 22.64/22.73 3819 -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)].
% 22.64/22.73 3820 -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)].
% 22.64/22.73 3821 -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)].
% 22.64/22.73 3822 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(893,b,877,a)].
% 22.64/22.73 3823 -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)].
% 22.64/22.73 3824 -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)].
% 22.64/22.73 3825 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1068,a)].
% 22.64/22.73 3826 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1091,a)].
% 22.64/22.73 3827 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1598,b,1566,a)].
% 22.64/22.73 3828 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1567,a)].
% 22.64/22.73 3829 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1568,a)].
% 22.64/22.75 3830 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1569,a)].
% 22.64/22.75 3831 -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)].
% 22.64/22.75 3832 -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)].
% 22.64/22.75 3833 -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)].
% 22.64/22.75 3834 -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)].
% 22.64/22.75 3835 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1574,a)].
% 22.64/22.75 3836 -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)].
% 22.64/22.75 3837 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1598,b,1576,a)].
% 22.64/22.75 3838 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1599,a,1598,b)].
% 22.64/22.75 3839 -c_less(A,B,C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1600,a,1598,b)].
% 22.64/22.75 3840 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1622,a)].
% 22.64/22.75 3841 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1623,a)].
% 22.64/22.75 3842 -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(1663,b,1624,a)].
% 22.64/22.75 3843 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1625,a)].
% 22.64/22.75 3844 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1626,a)].
% 22.64/22.75 3845 -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(1663,b,1627,a)].
% 22.64/22.75 3846 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1628,a)].
% 22.64/22.75 3847 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1663,b,1629,a)].
% 22.64/22.75 3848 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1663,b,1630,a)].
% 22.64/22.75 3849 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1663,b,1631,a)].
% 22.64/22.75 3850 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1632,a)].
% 22.64/22.75 3851 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1633,a)].
% 22.64/22.75 3852 -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(1663,b,1634,a)].
% 22.64/22.75 3853 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1635,a)].
% 22.64/22.75 3854 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1636,a)].
% 22.64/22.75 3855 -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(1663,b,1637,a)].
% 22.64/22.75 3856 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1663,b,1638,a)].
% 24.55/24.63 3857 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1663,b,1639,a)].
% 24.55/24.63 3858 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1663,b,1640,a)].
% 24.55/24.63 3859 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1663,b,1641,a)].
% 24.55/24.63
% 24.55/24.63 ============================== end predicate elimination =============
% 24.55/24.63
% 24.55/24.63 Auto_denials: (non-Horn, no changes).
% 24.55/24.63
% 24.55/24.63 Term ordering decisions:
% 24.55/24.63 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. t_b=1. c_IntDef_Ointrel=1. c_Datatype_Ooption_ONone=1. c_IntDef_OInteg=1. c_Wellfounded__Relations_Oless__than=1. c_Extraction_Osumbool_OLeft=1. c_Extraction_Osumbool_ORight=1. c_List_Onibble_ONibble0=1. c_List_Onibble_ONibble1=1. c_List_Onibble_ONibble2=1. c_List_Onibble_ONibble3=1. c_List_Onibble_ONibble4=1. c_List_Onibble_ONibble5=1. c_List_Onibble_ONibble6=1. c_List_Onibble_ONibble7=1. c_List_Onibble_ONibble8=1. c_List_Onibble_ONibble9=1. c_List_Onibble_ONibbleA=1. c_List_Onibble_ONibbleB=1. c_List_Onibble_ONibbleC=1. c_List_Onibble_ONibbleD=1. c_List_Onibble_ONibbleE=1. c_List_Onibble_ONibbleF=1. c_Product__Type_OUnity=1. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. tc_Product__Type_Ounit=1. v_c=1. v_ca=1. tc_List_Ochar=1. tc_bool=1. v_xa=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. v_f=1. c_IntDef_ORep__Integ=1. v_g=1. v_x=1. c_times=1. c_plus=1. c_SetInterval_OatLeastLessThan=1. c_minus=1. c_insert=1. c_divide=1. c_Orderings_Omin=1. c_Orderings_Omax=1. c_Nat_Opower=1. c_SetInterval_OatLeastAtMost=1. c_List_Olist_OCons=1. c_SetInterval_OgreaterThanAtMost=1. c_Divides_Oop_Amod=1. c_append=1. c_SetInterval_OgreaterThanLessThan=1. c_div=1. c_inter=1. c_union=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=1. c_Main_OMax__le__iff__1=1. c_Main_OMax__less__iff__1=1. c_Main_OMin__ge__iff__1=1. c_Main_OMin__gr__iff__1=1. c_List_Onth=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_Datatype__Universe_OIn0=1. c_Datatype__UnivCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------