TSTP Solution File: ANA036-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA036-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 19:21:53 EDT 2022
% Result : Timeout 300.03s 300.13s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA036-1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.30 % Computer : n013.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Fri Jul 8 04:37:14 EDT 2022
% 0.09/0.30 % CPUTime :
% 2.07/2.35 ============================== Prover9 ===============================
% 2.07/2.35 Prover9 (32) version 2009-11A, November 2009.
% 2.07/2.35 Process 32343 was started by sandbox on n013.cluster.edu,
% 2.07/2.35 Fri Jul 8 04:37:16 2022
% 2.07/2.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32189_n013.cluster.edu".
% 2.07/2.35 ============================== end of head ===========================
% 2.07/2.35
% 2.07/2.35 ============================== INPUT =================================
% 2.07/2.35
% 2.07/2.35 % Reading from file /tmp/Prover9_32189_n013.cluster.edu
% 2.07/2.35
% 2.07/2.35 set(prolog_style_variables).
% 2.07/2.35 set(auto2).
% 2.07/2.35 % set(auto2) -> set(auto).
% 2.07/2.35 % set(auto) -> set(auto_inference).
% 2.07/2.35 % set(auto) -> set(auto_setup).
% 2.07/2.35 % set(auto_setup) -> set(predicate_elim).
% 2.07/2.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.07/2.35 % set(auto) -> set(auto_limits).
% 2.07/2.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.07/2.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.07/2.35 % set(auto) -> set(auto_denials).
% 2.07/2.35 % set(auto) -> set(auto_process).
% 2.07/2.35 % set(auto2) -> assign(new_constants, 1).
% 2.07/2.35 % set(auto2) -> assign(fold_denial_max, 3).
% 2.07/2.35 % set(auto2) -> assign(max_weight, "200.000").
% 2.07/2.35 % set(auto2) -> assign(max_hours, 1).
% 2.07/2.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.07/2.35 % set(auto2) -> assign(max_seconds, 0).
% 2.07/2.35 % set(auto2) -> assign(max_minutes, 5).
% 2.07/2.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.07/2.35 % set(auto2) -> set(sort_initial_sos).
% 2.07/2.35 % set(auto2) -> assign(sos_limit, -1).
% 2.07/2.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.07/2.35 % set(auto2) -> assign(max_megs, 400).
% 2.07/2.35 % set(auto2) -> assign(stats, some).
% 2.07/2.35 % set(auto2) -> clear(echo_input).
% 2.07/2.35 % set(auto2) -> set(quiet).
% 2.07/2.35 % set(auto2) -> clear(print_initial_clauses).
% 2.07/2.35 % set(auto2) -> clear(print_given).
% 2.07/2.35 assign(lrs_ticks,-1).
% 2.07/2.35 assign(sos_limit,10000).
% 2.07/2.35 assign(order,kbo).
% 2.07/2.35 set(lex_order_vars).
% 2.07/2.35 clear(print_given).
% 2.07/2.35
% 2.07/2.35 % formulas(sos). % not echoed (2800 formulas)
% 2.07/2.35
% 2.07/2.35 ============================== end of input ==========================
% 2.07/2.35
% 2.07/2.35 % From the command line: assign(max_seconds, 300).
% 2.07/2.35
% 2.07/2.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.07/2.35
% 2.07/2.35 % Formulas that are not ordinary clauses:
% 2.07/2.35
% 2.07/2.35 ============================== end of process non-clausal formulas ===
% 2.07/2.35
% 2.07/2.35 ============================== PROCESS INITIAL CLAUSES ===============
% 2.07/2.35
% 2.07/2.35 ============================== PREDICATE ELIMINATION =================
% 2.07/2.35 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].
% 2.07/2.35 2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom). [assumption].
% 2.07/2.35 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)].
% 2.07/2.35 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].
% 2.07/2.35 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)].
% 2.07/2.35 4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 2.07/2.35 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4,a,1,a)].
% 2.07/2.35 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4,a,3,a)].
% 2.07/2.35 5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 2.07/2.35 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(5,a,1,a)].
% 2.07/2.35 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(5,a,3,a)].
% 2.07/2.35 6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 2.07/2.35 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 2.07/2.35 Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 2.07/2.35 7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 2.07/2.37 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(7,b,1,a)].
% 2.07/2.37 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(7,b,3,a)].
% 2.07/2.37 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].
% 2.07/2.37 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)].
% 2.07/2.37 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)].
% 2.07/2.37 9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(9,a,2,a)].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(9,a,4,a)].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(9,a,5,a)].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(9,a,7,b)].
% 2.07/2.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 2.07/2.37 10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 2.07/2.37 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(10,a,2,a)].
% 2.07/2.37 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(10,a,4,a)].
% 2.07/2.37 Derived: class_HOL_Oplus(tc_nat). [resolve(10,a,5,a)].
% 2.07/2.37 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 2.07/2.37 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(10,a,7,b)].
% 2.07/2.37 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 2.07/2.37 11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 2.07/2.37 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 2.07/2.37 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 2.07/2.37 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].
% 2.07/2.37 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)].
% 2.07/2.37 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)].
% 2.07/2.37 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].
% 2.07/2.37 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)].
% 2.07/2.37 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)].
% 2.07/2.37 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].
% 2.07/2.37 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)].
% 2.07/2.37 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)].
% 2.07/2.37 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 2.16/2.40 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 2.16/2.40 19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 2.16/2.40 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(19,b,1,a)].
% 2.16/2.40 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(19,b,3,a)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.16/2.40 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 2.16/2.40 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].
% 2.16/2.40 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)].
% 2.16/2.40 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)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 2.18/2.46 24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 2.18/2.46 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(24,b,1,a)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(24,b,3,a)].
% 2.18/2.46 25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 2.18/2.46 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 2.18/2.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 2.18/2.46 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].
% 2.18/2.46 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)].
% 2.18/2.46 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)].
% 2.18/2.46 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 2.18/2.49 37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 2.18/2.49 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 2.18/2.49 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 2.18/2.49 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].
% 2.18/2.49 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)].
% 2.18/2.49 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)].
% 2.18/2.49 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].
% 2.36/2.67 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)].
% 2.36/2.67 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)].
% 2.36/2.67 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].
% 2.36/2.67 42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom). [assumption].
% 2.36/2.67 43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 2.36/2.67 44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 2.36/2.67 45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 2.36/2.67 46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 2.36/2.67 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 2.36/2.67 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 2.36/2.67 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 2.36/2.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 2.36/2.67 47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 2.36/2.67 48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 2.36/2.67 49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 2.36/2.67 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].
% 2.36/2.67 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 2.36/2.67 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 2.36/2.67 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].
% 2.36/2.67 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].
% 2.36/2.67 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].
% 2.36/2.67 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].
% 2.36/2.67 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].
% 2.36/2.67 56 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 2.47/2.73 57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 2.47/2.73 58 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_14) # label(axiom). [assumption].
% 2.47/2.73 59 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_15) # label(axiom). [assumption].
% 2.47/2.73 60 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) # label(axiom). [assumption].
% 2.47/2.73 61 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 2.47/2.73 62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 2.47/2.73 63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 2.47/2.73 64 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_19) # label(axiom). [assumption].
% 2.47/2.73 65 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) # label(axiom). [assumption].
% 2.47/2.73 66 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_26) # label(axiom). [assumption].
% 2.47/2.73 67 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_25) # label(axiom). [assumption].
% 2.47/2.73 68 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_4) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 2.47/2.73 69 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_19) # label(axiom). [assumption].
% 2.47/2.73 70 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_19) # label(axiom). [assumption].
% 2.47/2.73 71 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 2.47/2.73 72 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_13) # label(axiom). [assumption].
% 2.47/2.73 73 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_15) # label(axiom). [assumption].
% 2.47/2.73 74 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_4) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 2.47/2.73 75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 2.47/2.75 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 2.47/2.75 76 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_4) # label(axiom). [assumption].
% 2.47/2.75 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 2.47/2.75 77 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_9) # label(axiom). [assumption].
% 2.47/2.75 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 2.47/2.75 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 2.47/2.75 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 2.47/2.75 78 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_13) # label(axiom). [assumption].
% 2.47/2.75 79 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(8,b,1,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_OrderedGroup_Oab__group__add(D). [resolve(79,a,42,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(79,a,43,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(79,a,44,a)].
% 2.47/2.75 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 2.47/2.75 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(79,a,46,b)].
% 2.47/2.75 80 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(8,b,3,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_OrderedGroup_Oab__group__add(D). [resolve(80,a,42,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(80,a,43,a)].
% 2.47/2.75 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(80,a,44,a)].
% 2.47/2.75 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 2.47/2.75 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(80,a,46,b)].
% 2.47/2.75 81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(9,a,8,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(81,b,42,a)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(81,b,43,a)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(81,b,44,a)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(81,b,46,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(81,b,54,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(81,b,57,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(81,b,59,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(81,b,62,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(81,b,66,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(81,b,67,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(81,b,73,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 2.67/2.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 2.67/2.95 82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(10,a,8,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(82,b,42,a)].
% 2.67/2.95 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(82,b,43,a)].
% 2.67/2.95 Derived: class_HOL_Oplus(tc_nat). [resolve(82,b,44,a)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(82,b,46,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(82,b,54,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(82,b,57,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(82,b,59,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(82,b,62,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(82,b,66,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(82,b,67,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(82,b,73,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 2.67/2.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 2.67/2.95 83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom). [assumption].
% 2.67/2.99 84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom). [assumption].
% 2.67/2.99 85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom). [assumption].
% 2.67/2.99 86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom). [assumption].
% 2.67/2.99 87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom). [assumption].
% 2.67/2.99 88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 2.67/2.99 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(83,a,84,a)].
% 2.67/2.99 Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(83,a,85,a)].
% 2.67/2.99 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(83,a,86,a)].
% 2.67/2.99 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(83,a,87,a)].
% 2.67/2.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 2.67/2.99 89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom). [assumption].
% 2.67/2.99 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(89,a,84,a)].
% 2.67/2.99 Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(89,a,85,a)].
% 2.67/2.99 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(89,a,86,a)].
% 2.67/2.99 Derived: class_HOL_Otimes(tc_nat). [resolve(89,a,87,a)].
% 2.67/2.99 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 2.67/2.99 90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 2.67/2.99 91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom). [assumption].
% 2.67/2.99 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(91,b,83,a)].
% 2.67/2.99 Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A). [resolve(91,b,89,a)].
% 2.67/2.99 92 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 2.67/2.99 93 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_7) # label(axiom). [assumption].
% 2.67/2.99 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(93,b,83,a)].
% 2.67/2.99 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A). [resolve(93,b,89,a)].
% 2.67/2.99 94 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 2.67/2.99 95 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_1) # label(axiom). [assumption].
% 2.67/2.99 96 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) # label(axiom). [assumption].
% 2.67/2.99 97 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_5) # label(axiom). [assumption].
% 2.67/2.99 98 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) # label(axiom). [assumption].
% 2.67/2.99 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 2.67/2.99 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 2.67/2.99 99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom). [assumption].
% 2.96/3.24 100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 2.96/3.24 101 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) # label(axiom). [assumption].
% 2.96/3.24 102 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_20) # label(axiom). [assumption].
% 2.96/3.24 103 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 2.96/3.24 104 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 2.96/3.24 105 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) # label(axiom). [assumption].
% 2.96/3.24 106 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_7) # label(axiom). [assumption].
% 2.96/3.24 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(106,b,83,a)].
% 2.96/3.24 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A). [resolve(106,b,89,a)].
% 2.96/3.24 107 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_2) # label(axiom). [assumption].
% 2.96/3.24 108 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 2.96/3.24 109 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom). [assumption].
% 2.96/3.24 110 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom). [assumption].
% 2.96/3.24 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(108,a,109,a)].
% 2.96/3.24 Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(108,a,110,a)].
% 2.96/3.24 111 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 2.96/3.24 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C). [resolve(111,a,109,a)].
% 2.96/3.24 Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(111,a,110,a)].
% 2.96/3.24 112 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 2.96/3.24 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(112,a,108,a)].
% 2.96/3.24 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(112,a,111,a)].
% 2.96/3.25 113 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 2.96/3.25 Derived: c_times(c_1,A,tc_nat) = A. [resolve(113,a,108,a)].
% 2.96/3.25 Derived: c_times(A,c_1,tc_nat) = A. [resolve(113,a,111,a)].
% 2.96/3.25 114 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.96/3.25 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(114,b,108,a)].
% 2.96/3.25 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(114,b,111,a)].
% 2.96/3.25 115 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 2.96/3.25 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(115,b,108,a)].
% 2.96/3.25 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(115,b,111,a)].
% 2.96/3.25 116 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 3.07/3.30 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(116,a,109,a)].
% 3.07/3.30 Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(116,a,110,a)].
% 3.07/3.30 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(116,a,112,a)].
% 3.07/3.30 Derived: class_HOL_Oone(tc_nat). [resolve(116,a,113,a)].
% 3.07/3.30 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(116,a,114,b)].
% 3.07/3.30 Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(116,a,115,b)].
% 3.07/3.30 117 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 3.07/3.30 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(117,a,115,b)].
% 3.07/3.30 118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 3.07/3.30 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(118,a,115,b)].
% 3.07/3.30 119 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B. [resolve(119,b,108,a)].
% 3.07/3.30 Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B. [resolve(119,b,111,a)].
% 3.07/3.30 120 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_24) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B. [resolve(120,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B. [resolve(120,b,111,a)].
% 3.07/3.30 121 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_15) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(121,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(121,b,111,a)].
% 3.07/3.30 122 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(122,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(122,b,111,a)].
% 3.07/3.30 123 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B. [resolve(123,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B. [resolve(123,b,111,a)].
% 3.07/3.30 124 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(124,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(124,b,111,a)].
% 3.07/3.30 125 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B. [resolve(125,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B. [resolve(125,b,111,a)].
% 3.07/3.30 126 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B. [resolve(126,b,108,a)].
% 3.07/3.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B. [resolve(126,b,111,a)].
% 3.07/3.30 127 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(127,b,108,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(127,b,111,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(127,b,117,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(127,b,118,a)].
% 3.26/3.51 128 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(128,b,108,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(128,b,111,a)].
% 3.26/3.51 129 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(129,b,108,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(129,b,111,a)].
% 3.26/3.51 130 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_9) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(130,b,108,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(130,b,111,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(130,b,116,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(130,b,117,a)].
% 3.26/3.51 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(130,b,118,a)].
% 3.26/3.51 131 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__distrib__number__of_0) # label(axiom). [assumption].
% 3.26/3.51 132 class_Ring__and__Field_Osemiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_17) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_plus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(131,b,132,a)].
% 3.26/3.51 133 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__distrib__number__of_0) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_plus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(133,b,132,a)].
% 3.26/3.51 134 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 3.26/3.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(134,a,131,b)].
% 3.26/3.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(134,a,133,b)].
% 3.26/3.55 135 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 3.26/3.55 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(135,a,131,b)].
% 3.26/3.55 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(135,a,133,b)].
% 3.26/3.55 136 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 3.26/3.55 Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(136,b,131,b)].
% 3.26/3.55 Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(136,b,133,b)].
% 3.26/3.55 137 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 3.26/3.55 Derived: -class_Power_Orecpower(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(137,b,131,b)].
% 3.26/3.55 Derived: -class_Power_Orecpower(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(137,b,133,b)].
% 3.26/3.55 138 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 3.26/3.55 Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(138,b,131,b)].
% 3.26/3.55 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(138,b,133,b)].
% 3.26/3.55 139 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_10) # label(axiom). [assumption].
% 3.26/3.55 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(139,b,131,b)].
% 3.26/3.55 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(139,b,133,b)].
% 3.26/3.55 140 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 3.26/3.55 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(140,b,131,b)].
% 3.26/3.55 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(140,b,133,b)].
% 3.26/3.55 141 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_2) # label(axiom). [assumption].
% 3.26/3.55 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(141,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(141,b,133,b)].
% 3.26/3.57 142 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(142,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(142,b,133,b)].
% 3.26/3.57 143 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_7) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(143,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(143,b,133,b)].
% 3.26/3.57 144 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(144,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(144,b,133,b)].
% 3.26/3.57 145 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(145,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(145,b,133,b)].
% 3.26/3.57 146 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(146,b,131,b)].
% 3.26/3.57 Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(146,b,133,b)].
% 3.26/3.57 147 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 3.26/3.57 Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(147,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(147,b,133,b)].
% 3.37/3.60 148 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(148,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(148,b,133,b)].
% 3.37/3.60 149 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(149,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(149,b,133,b)].
% 3.37/3.60 150 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(150,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(150,b,133,b)].
% 3.37/3.60 151 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_7) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(151,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(151,b,133,b)].
% 3.37/3.60 152 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(152,b,131,b)].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(152,b,133,b)].
% 3.37/3.60 153 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_1) # label(axiom). [assumption].
% 3.37/3.60 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(153,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(153,b,133,b)].
% 3.38/3.62 154 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) # label(axiom). [assumption].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(154,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(154,b,133,b)].
% 3.38/3.62 155 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_2) # label(axiom). [assumption].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(155,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(155,b,133,b)].
% 3.38/3.62 156 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_10) # label(axiom). [assumption].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(156,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(156,b,133,b)].
% 3.38/3.62 157 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_4) # label(axiom). [assumption].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(157,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(157,b,133,b)].
% 3.38/3.62 158 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(158,b,131,b)].
% 3.38/3.62 Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(158,b,133,b)].
% 3.38/3.62 159 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 3.38/3.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(159,b,131,b)].
% 3.38/3.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(159,b,133,b)].
% 3.38/3.63 160 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 3.38/3.63 Derived: -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(160,b,131,b)].
% 3.38/3.63 Derived: -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(160,b,133,b)].
% 3.38/3.63 161 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 3.38/3.63 Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(161,b,131,b)].
% 3.38/3.63 Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(161,b,133,b)].
% 3.38/3.63 162 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(162,a,132,a)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(162,a,137,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(162,a,138,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(162,a,139,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(162,a,140,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(162,a,141,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(162,a,142,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(162,a,143,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(162,a,145,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(162,a,146,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(162,a,147,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(162,a,148,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(162,a,149,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(162,a,150,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(162,a,152,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(162,a,153,b)].
% 3.38/3.63 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(162,a,155,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(162,a,156,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(162,a,157,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(162,a,159,b)].
% 3.38/3.64 163 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(163,a,132,a)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(163,a,140,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(163,a,141,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(163,a,143,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(163,a,157,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(163,a,159,b)].
% 3.38/3.64 164 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 3.38/3.64 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(164,a,132,a)].
% 3.38/3.64 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,140,b)].
% 3.38/3.64 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,141,b)].
% 3.38/3.64 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,143,b)].
% 3.38/3.64 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,157,b)].
% 3.38/3.64 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,159,b)].
% 3.38/3.64 165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(165,a,132,a)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(165,a,138,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,140,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,141,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(165,a,142,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,143,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(165,a,145,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(165,a,146,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(165,a,147,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(165,a,148,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(165,a,149,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(165,a,150,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(165,a,151,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(165,a,153,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(165,a,154,b)].
% 3.38/3.64 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(165,a,155,b)].
% 3.38/3.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,157,b)].
% 3.38/3.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(165,a,158,b)].
% 3.38/3.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,159,b)].
% 3.38/3.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(165,a,160,b)].
% 3.38/3.65 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(165,a,161,b)].
% 3.38/3.65 166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 3.38/3.65 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(166,a,132,a)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(166,a,138,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,140,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,141,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(166,a,142,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,143,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(166,a,145,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(166,a,146,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(166,a,147,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(166,a,148,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(166,a,149,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(166,a,150,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(166,a,151,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(166,a,153,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(166,a,154,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(166,a,155,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,157,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(166,a,158,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,159,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(166,a,160,b)].
% 3.38/3.65 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(166,a,161,b)].
% 3.38/3.65 167 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 3.38/3.65 Derived: -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(167,b,131,b)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(167,b,133,b)].
% 3.38/3.65 168 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_1) # label(axiom). [assumption].
% 3.38/3.65 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(168,b,131,b)].
% 3.38/3.65 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(168,b,133,b)].
% 3.38/3.66 169 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 3.38/3.66 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(169,b,131,b)].
% 3.38/3.66 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(169,b,133,b)].
% 3.38/3.66 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(169,b,164,a)].
% 3.38/3.66 170 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_3) # label(axiom). [assumption].
% 3.38/3.66 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(170,b,131,b)].
% 3.38/3.66 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(170,b,133,b)].
% 3.38/3.66 171 -class_Ring__and__Field_Osemiring(A) | c_times(B,c_plus(C,D,A),A) = c_plus(c_times(B,C,A),c_times(B,D,A),A) # label(cls_Ring__and__Field_Oring__distrib__1_0) # label(axiom). [assumption].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(171,a,132,a)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(171,a,134,a)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(171,a,135,a)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(171,a,136,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(171,a,137,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(171,a,138,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(171,a,139,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(171,a,140,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(171,a,141,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(171,a,142,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(171,a,143,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(171,a,144,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(171,a,145,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(171,a,146,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(171,a,147,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(171,a,148,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(171,a,149,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(171,a,150,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(171,a,151,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(171,a,152,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(171,a,153,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(171,a,154,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(171,a,155,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(171,a,156,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(171,a,157,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(171,a,158,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(171,a,159,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(171,a,160,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(171,a,161,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0(D). [resolve(171,a,167,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0__cancel(D). [resolve(171,a,168,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1(D). [resolve(171,a,169,b)].
% 3.38/3.66 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1__cancel(D). [resolve(171,a,170,b)].
% 3.38/3.66 172 -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),D,A) = c_plus(c_times(B,D,A),c_times(C,D,A),A) # label(cls_Ring__and__Field_Oring__distrib__2_0) # label(axiom). [assumption].
% 3.38/3.66 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(172,a,132,a)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(172,a,134,a)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(172,a,135,a)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(172,a,136,b)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(172,a,137,b)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(172,a,138,b)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(172,a,139,b)].
% 3.38/3.66 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(172,a,140,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(172,a,141,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(172,a,142,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(172,a,143,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(172,a,144,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(172,a,145,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(172,a,146,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(172,a,147,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(172,a,148,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(172,a,149,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(172,a,150,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(172,a,151,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(172,a,152,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(172,a,153,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(172,a,154,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(172,a,155,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(172,a,156,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(172,a,157,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(172,a,158,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(172,a,159,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(172,a,160,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(172,a,161,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0(C). [resolve(172,a,167,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(172,a,168,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1(C). [resolve(172,a,169,b)].
% 3.65/3.90 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(172,a,170,b)].
% 3.65/3.90 173 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 3.65/3.90 174 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].
% 3.68/3.99 175 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 3.68/3.99 176 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 3.68/3.99 177 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 3.68/3.99 178 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 3.68/3.99 179 -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].
% 3.68/3.99 180 -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].
% 3.68/3.99 181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 3.68/3.99 182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 3.68/3.99 183 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 3.68/3.99 184 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 3.68/3.99 185 -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].
% 3.68/3.99 186 -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].
% 3.68/3.99 187 -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].
% 3.68/3.99 188 -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].
% 3.68/3.99 189 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 3.68/3.99 190 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 3.68/3.99 191 -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].
% 3.68/3.99 192 -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].
% 3.68/3.99 193 -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].
% 3.68/3.99 194 -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].
% 3.68/3.99 195 -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].
% 3.68/3.99 196 -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].
% 3.68/3.99 197 -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].
% 3.68/3.99 198 -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(140,b,131,b)].
% 3.68/4.00 199 -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(140,b,133,b)].
% 3.68/4.00 200 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(162,a,140,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(200,b,174,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(200,b,175,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(200,b,176,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(200,b,177,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(200,b,178,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,b,179,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(200,b,180,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(200,b,188,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(200,b,195,b)].
% 3.68/4.00 201 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(163,a,140,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(201,b,174,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(201,b,175,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(201,b,176,a)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(201,b,177,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(201,b,178,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,b,179,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(201,b,180,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(201,b,186,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(201,b,188,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(201,b,189,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(201,b,190,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(201,b,191,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(201,b,192,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(201,b,193,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(201,b,194,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(201,b,195,b)].
% 3.68/4.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(201,b,196,b)].
% 3.68/4.00 202 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(164,a,140,b)].
% 3.68/4.00 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(202,b,174,a)].
% 3.68/4.00 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(202,b,175,a)].
% 3.68/4.00 Derived: class_HOL_Oplus(tc_nat). [resolve(202,b,176,a)].
% 3.68/4.00 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 3.68/4.00 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(202,b,178,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(202,b,180,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(202,b,186,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(202,b,189,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(202,b,190,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(202,b,191,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(202,b,192,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(202,b,193,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(202,b,194,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 3.77/4.01 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(202,b,196,b)].
% 3.77/4.01 203 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(165,a,140,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(203,b,174,a)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(203,b,175,a)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(203,b,176,a)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(203,b,178,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(203,b,180,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 3.77/4.01 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(203,b,196,b)].
% 3.77/4.01 204 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(166,a,140,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(204,b,174,a)].
% 3.77/4.01 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(204,b,175,a)].
% 3.77/4.01 Derived: class_HOL_Otimes(tc_nat). [resolve(204,b,176,a)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(204,b,178,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(204,b,180,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 3.77/4.01 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(204,b,196,b)].
% 3.77/4.01 205 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring(D). [resolve(171,a,140,b)].
% 3.77/4.01 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(205,b,174,a)].
% 3.77/4.01 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(205,b,175,a)].
% 3.77/4.01 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(205,b,176,a)].
% 3.98/4.29 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(205,b,177,b)].
% 3.98/4.29 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(205,b,178,b)].
% 3.98/4.29 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(205,b,179,b)].
% 3.98/4.29 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(205,b,180,b)].
% 3.98/4.29 206 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring(C). [resolve(172,a,140,b)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(206,b,174,a)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(206,b,175,a)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(206,b,176,a)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(206,b,177,b)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(206,b,178,b)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(206,b,179,b)].
% 3.98/4.29 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(206,b,180,b)].
% 3.98/4.29 207 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 3.98/4.29 208 class_Ring__and__Field_Osemiring__0(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_19) # label(axiom). [assumption].
% 3.98/4.29 209 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 3.98/4.29 210 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 3.98/4.29 211 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 3.98/4.29 212 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 3.98/4.29 213 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_3) # label(axiom). [assumption].
% 3.98/4.29 214 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_9) # label(axiom). [assumption].
% 3.98/4.29 215 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_10) # label(axiom). [assumption].
% 3.98/4.29 216 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) # label(axiom). [assumption].
% 3.98/4.29 217 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_6) # label(axiom). [assumption].
% 3.98/4.29 218 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) # label(axiom). [assumption].
% 3.98/4.29 219 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 3.98/4.29 220 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 3.98/4.29 221 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Olordered__ring_13) # label(axiom). [assumption].
% 3.98/4.30 222 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) # label(axiom). [assumption].
% 3.98/4.30 223 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_22) # label(axiom). [assumption].
% 3.98/4.30 224 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_19) # label(axiom). [assumption].
% 3.98/4.30 225 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_6) # label(axiom). [assumption].
% 3.98/4.30 226 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_13) # label(axiom). [assumption].
% 3.98/4.30 227 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_0) # label(axiom). [assumption].
% 3.98/4.30 228 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) # label(axiom). [assumption].
% 3.98/4.30 229 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_1) # label(axiom). [assumption].
% 3.98/4.30 230 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_9) # label(axiom). [assumption].
% 3.98/4.30 231 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_3) # label(axiom). [assumption].
% 3.98/4.30 232 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__ring_6) # label(axiom). [assumption].
% 3.98/4.30 233 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__semiring_0) # label(axiom). [assumption].
% 3.98/4.30 234 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 3.98/4.30 235 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring__1_6) # label(axiom). [assumption].
% 3.98/4.30 236 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 3.98/4.30 237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 3.98/4.30 238 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 3.98/4.30 239 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 3.98/4.30 240 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(240,a,208,a)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(240,a,209,a)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(240,a,210,a)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(240,a,212,b)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 3.98/4.30 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(240,a,214,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(240,a,219,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(240,a,223,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(240,a,224,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(240,a,230,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 3.98/4.31 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 3.98/4.31 241 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 3.98/4.31 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(241,a,208,a)].
% 3.98/4.31 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(241,a,209,a)].
% 3.98/4.31 Derived: class_HOL_Ozero(tc_nat). [resolve(241,a,210,a)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(241,a,212,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(241,a,214,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(241,a,219,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 3.98/4.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(241,a,223,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(241,a,224,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(241,a,230,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 4.08/4.38 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 4.08/4.38 242 -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].
% 4.08/4.38 243 -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].
% 4.08/4.38 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 4.08/4.38 244 -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].
% 4.08/4.38 245 -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(167,b,131,b)].
% 4.08/4.38 246 -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(167,b,133,b)].
% 4.08/4.38 247 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0(D). [resolve(171,a,167,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(247,b,215,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(247,b,216,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(247,b,217,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(247,b,218,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(247,b,219,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(247,b,220,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(247,b,221,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(247,b,222,b)].
% 4.08/4.38 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(247,b,223,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(247,b,224,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(247,b,225,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(247,b,226,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(247,b,227,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(247,b,228,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(247,b,229,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(247,b,230,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(247,b,231,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(247,b,232,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(247,b,233,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(247,b,234,b)].
% 4.08/4.39 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(247,b,235,b)].
% 4.08/4.39 248 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0(C). [resolve(172,a,167,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(248,b,215,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(248,b,216,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(248,b,217,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(248,b,218,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(248,b,219,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(248,b,220,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(248,b,221,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(248,b,222,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(248,b,223,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(248,b,224,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(248,b,225,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(248,b,226,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(248,b,227,b)].
% 4.08/4.39 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(248,b,228,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(248,b,229,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(248,b,230,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(248,b,231,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(248,b,232,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(248,b,233,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(248,b,234,b)].
% 4.28/4.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(248,b,235,b)].
% 4.28/4.59 249 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_3) # label(axiom). [assumption].
% 4.28/4.59 250 class_Ring__and__Field_Ocomm__semiring__0(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_20) # label(axiom). [assumption].
% 4.28/4.59 251 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 4.28/4.59 252 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 4.28/4.59 253 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 4.28/4.59 254 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 4.28/4.59 255 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_0) # label(axiom). [assumption].
% 4.28/4.59 256 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_5) # label(axiom). [assumption].
% 4.28/4.59 257 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_4) # label(axiom). [assumption].
% 4.28/4.59 258 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 4.28/4.59 259 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_6) # label(axiom). [assumption].
% 4.28/4.59 260 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 4.28/4.59 261 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_8) # label(axiom). [assumption].
% 4.28/4.59 262 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 4.28/4.59 263 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) # label(axiom). [assumption].
% 4.28/4.59 264 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_3) # label(axiom). [assumption].
% 4.28/4.59 265 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) # label(axiom). [assumption].
% 4.28/4.59 266 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 4.28/4.59 267 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 4.45/4.70 268 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) # label(axiom). [assumption].
% 4.45/4.70 269 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_18) # label(axiom). [assumption].
% 4.45/4.70 270 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_15) # label(axiom). [assumption].
% 4.45/4.70 271 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_9) # label(axiom). [assumption].
% 4.45/4.70 272 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) # label(axiom). [assumption].
% 4.45/4.70 273 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_5) # label(axiom). [assumption].
% 4.45/4.70 274 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_0) # label(axiom). [assumption].
% 4.45/4.70 275 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(141,b,131,b)].
% 4.45/4.70 276 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(141,b,133,b)].
% 4.45/4.70 277 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(162,a,141,b)].
% 4.45/4.70 278 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(163,a,141,b)].
% 4.45/4.70 279 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(164,a,141,b)].
% 4.45/4.70 280 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(165,a,141,b)].
% 4.45/4.70 281 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(166,a,141,b)].
% 4.45/4.70 282 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(171,a,141,b)].
% 4.45/4.70 283 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(172,a,141,b)].
% 4.45/4.70 284 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(240,a,215,b)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(284,b,250,a)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(284,b,251,a)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(284,b,252,a)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(284,b,253,b)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(284,b,254,b)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,b,255,b)].
% 4.45/4.70 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(284,b,256,b)].
% 4.45/4.70 285 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(241,a,215,b)].
% 4.45/4.70 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(285,b,250,a)].
% 4.45/4.70 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(285,b,251,a)].
% 4.45/4.70 Derived: class_HOL_Ozero(tc_nat). [resolve(285,b,252,a)].
% 4.45/4.70 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(285,b,253,b)].
% 4.45/4.70 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(285,b,254,b)].
% 4.58/4.89 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,b,255,b)].
% 4.58/4.89 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(285,b,256,b)].
% 4.58/4.89 286 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0(D). [resolve(247,b,215,b)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(286,b,250,a)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(286,b,251,a)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(286,b,252,a)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(286,b,253,b)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Power_Orecpower(D). [resolve(286,b,254,b)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(286,b,255,b)].
% 4.58/4.89 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(286,b,256,b)].
% 4.58/4.89 287 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0(C). [resolve(248,b,215,b)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(287,b,250,a)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(287,b,251,a)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(287,b,252,a)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(287,b,253,b)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Power_Orecpower(C). [resolve(287,b,254,b)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(287,b,255,b)].
% 4.58/4.89 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(287,b,256,b)].
% 4.58/4.89 288 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(c_0,B,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__left_0) # label(axiom). [assumption].
% 4.58/4.89 289 class_Ring__and__Field_Osemiring__0__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_21) # label(axiom). [assumption].
% 4.58/4.89 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(288,a,289,a)].
% 4.58/4.89 290 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(B,c_0,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__right_0) # label(axiom). [assumption].
% 4.58/4.89 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(290,a,289,a)].
% 4.58/4.89 291 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 4.58/4.89 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(291,a,288,a)].
% 4.58/4.89 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(291,a,290,a)].
% 4.58/4.89 292 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 4.58/4.89 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(292,a,288,a)].
% 4.58/4.89 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(292,a,290,a)].
% 4.58/4.89 293 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 4.58/4.89 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,288,a)].
% 4.66/4.94 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,290,a)].
% 4.66/4.94 294 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0. [resolve(294,b,288,a)].
% 4.66/4.94 Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0. [resolve(294,b,290,a)].
% 4.66/4.94 295 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring_17) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,290,a)].
% 4.66/4.94 296 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_8) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0. [resolve(296,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0. [resolve(296,b,290,a)].
% 4.66/4.94 297 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,290,a)].
% 4.66/4.94 298 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,290,a)].
% 4.66/4.94 299 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0. [resolve(299,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0. [resolve(299,b,290,a)].
% 4.66/4.94 300 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,290,a)].
% 4.66/4.94 301 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Olordered__ring_12) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,290,a)].
% 4.66/4.94 302 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,290,a)].
% 4.66/4.94 303 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_21) # label(axiom). [assumption].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(303,b,288,a)].
% 4.66/4.94 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(303,b,290,a)].
% 4.66/4.94 304 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_18) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(304,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(304,b,290,a)].
% 4.74/4.98 305 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_3) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,290,a)].
% 4.74/4.98 306 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_12) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,290,a)].
% 4.74/4.98 307 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_21) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,290,a)].
% 4.74/4.98 308 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,290,a)].
% 4.74/4.98 309 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_15) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,290,a)].
% 4.74/4.98 310 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_8) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(310,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(310,b,290,a)].
% 4.74/4.98 311 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__ring_3) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,290,a)].
% 4.74/4.98 312 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(312,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(312,b,290,a)].
% 4.74/4.98 313 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring__1_3) # label(axiom). [assumption].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(313,b,288,a)].
% 4.74/4.98 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(313,b,290,a)].
% 4.74/4.98 314 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_2) # label(axiom). [assumption].
% 4.74/4.98 315 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 4.74/5.02 316 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_4) # label(axiom). [assumption].
% 4.74/5.02 317 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_5) # label(axiom). [assumption].
% 4.74/5.02 318 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_6) # label(axiom). [assumption].
% 4.74/5.02 319 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 4.74/5.02 320 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 4.74/5.02 321 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_15) # label(axiom). [assumption].
% 4.74/5.02 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(321,b,288,a)].
% 4.74/5.02 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(321,b,290,a)].
% 4.74/5.02 322 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(39,b,1,a)].
% 4.74/5.02 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(322,a,289,a)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(322,a,294,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(322,a,295,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(322,a,296,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(322,a,297,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(322,a,298,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(322,a,299,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(322,a,300,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(322,a,301,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(322,a,302,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(322,a,303,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(322,a,304,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(322,a,305,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(322,a,306,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(322,a,307,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(322,a,308,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(322,a,309,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(322,a,310,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(322,a,311,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(322,a,312,b)].
% 4.74/5.02 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(322,a,313,b)].
% 4.74/5.02 323 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(39,b,3,a)].
% 4.74/5.03 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(323,a,289,a)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(323,a,294,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(323,a,295,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(323,a,296,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(323,a,297,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(323,a,298,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(323,a,299,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(323,a,300,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(323,a,301,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(323,a,302,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(323,a,303,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(323,a,304,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(323,a,305,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(323,a,306,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(323,a,307,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(323,a,308,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(323,a,309,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(323,a,310,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(323,a,311,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(323,a,312,b)].
% 4.74/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(323,a,313,b)].
% 4.74/5.03 324 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(77,b,41,a)].
% 4.74/5.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,305,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,311,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(324,a,312,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,313,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(324,a,321,b)].
% 4.74/5.03 325 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(77,b,47,a)].
% 4.74/5.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(325,a,305,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(325,a,311,b)].
% 4.74/5.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(325,a,313,b)].
% 4.74/5.03 326 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(77,b,48,a)].
% 4.74/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(326,a,305,b)].
% 4.74/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(326,a,309,b)].
% 4.96/5.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(326,a,311,b)].
% 4.96/5.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(326,a,313,b)].
% 4.96/5.27 327 -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(168,b,131,b)].
% 4.96/5.27 328 -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(168,b,133,b)].
% 4.96/5.27 329 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__0__cancel(D). [resolve(171,a,168,b)].
% 4.96/5.27 330 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(172,a,168,b)].
% 4.96/5.27 331 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__diff__distrib__number__of_0) # label(axiom). [assumption].
% 4.96/5.27 332 class_Ring__and__Field_Oring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_22) # label(axiom). [assumption].
% 4.96/5.27 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_minus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(331,b,332,a)].
% 4.96/5.27 333 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__diff__distrib__number__of_0) # label(axiom). [assumption].
% 4.96/5.27 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_minus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(333,b,332,a)].
% 4.96/5.27 334 -class_Ring__and__Field_Oring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A) # label(cls_Ring__and__Field_Ominus__mult__minus_0) # label(axiom). [assumption].
% 4.96/5.27 Derived: c_times(c_uminus(A,tc_fun(B,C)),c_uminus(D,tc_fun(B,C)),tc_fun(B,C)) = c_times(A,D,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(334,a,332,a)].
% 4.96/5.27 335 -class_Ring__and__Field_Oring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A) # label(cls_Ring__and__Field_Omult__minus__left_0) # label(axiom). [assumption].
% 4.96/5.27 Derived: c_times(c_uminus(A,tc_fun(B,C)),D,tc_fun(B,C)) = c_uminus(c_times(A,D,tc_fun(B,C)),tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(335,a,332,a)].
% 4.96/5.27 336 -class_Ring__and__Field_Oring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A) # label(cls_Ring__and__Field_Omult__minus__right_0) # label(axiom). [assumption].
% 4.96/5.27 Derived: c_times(A,c_uminus(B,tc_fun(C,D)),tc_fun(C,D)) = c_uminus(c_times(A,B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(336,a,332,a)].
% 4.96/5.27 337 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 4.96/5.27 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(337,a,331,b)].
% 4.96/5.27 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(337,a,333,b)].
% 5.06/5.31 Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint). [resolve(337,a,334,a)].
% 5.06/5.31 Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(337,a,335,a)].
% 5.06/5.31 Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(337,a,336,a)].
% 5.06/5.31 338 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 5.06/5.31 Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(338,b,331,b)].
% 5.06/5.31 Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(338,b,333,b)].
% 5.06/5.31 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,334,a)].
% 5.06/5.31 Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,335,a)].
% 5.06/5.31 Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,336,a)].
% 5.06/5.31 339 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(339,b,331,b)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(339,b,333,b)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(339,b,334,a)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,335,a)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,336,a)].
% 5.06/5.31 340 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_1) # label(axiom). [assumption].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(340,b,331,b)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(340,b,333,b)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(340,b,334,a)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(340,b,335,a)].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(340,b,336,a)].
% 5.06/5.31 341 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 5.06/5.31 Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(341,b,331,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(341,b,333,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(341,b,334,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(341,b,335,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(341,b,336,a)].
% 5.06/5.33 342 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(342,b,331,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(342,b,333,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(342,b,334,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,335,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,336,a)].
% 5.06/5.33 343 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 5.06/5.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(343,b,331,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(343,b,333,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(343,b,334,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,335,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,336,a)].
% 5.06/5.33 344 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(344,b,331,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(344,b,333,b)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(344,b,334,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(344,b,335,a)].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(344,b,336,a)].
% 5.06/5.33 345 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 5.06/5.33 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(345,b,331,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(345,b,333,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(345,b,334,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(345,b,335,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(345,b,336,a)].
% 5.06/5.35 346 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_0) # label(axiom). [assumption].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(346,b,331,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(346,b,333,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(346,b,334,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(346,b,335,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(346,b,336,a)].
% 5.06/5.35 347 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_1) # label(axiom). [assumption].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(347,b,331,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(347,b,333,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(347,b,334,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(347,b,335,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(347,b,336,a)].
% 5.06/5.35 348 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(348,b,331,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(348,b,333,b)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(348,b,334,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,335,a)].
% 5.06/5.35 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,336,a)].
% 5.06/5.37 349 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 5.06/5.37 350 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 5.06/5.37 351 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 5.06/5.37 352 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 5.06/5.37 353 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 5.06/5.37 354 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(354,a,332,a)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(354,a,337,a)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(354,a,338,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(354,a,339,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(354,a,340,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(354,a,341,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,a,342,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,a,343,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(354,a,344,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(354,a,345,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,a,346,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(354,a,347,b)].
% 5.06/5.37 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,a,348,b)].
% 5.06/5.37 355 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom). [assumption].
% 5.06/5.37 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(355,a,332,a)].
% 5.06/5.37 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(355,a,337,a)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(355,a,338,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(355,a,339,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(355,a,340,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(355,a,341,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(355,a,342,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(355,a,343,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(355,a,344,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(355,a,345,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(355,a,346,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(355,a,347,b)].
% 5.06/5.37 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(355,a,348,b)].
% 5.06/5.37 356 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 5.06/5.37 357 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 5.06/5.37 358 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 5.17/5.44 Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(358,b,331,b)].
% 5.17/5.44 Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(358,b,333,b)].
% 5.17/5.44 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(358,b,334,a)].
% 5.17/5.44 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,335,a)].
% 5.17/5.44 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,336,a)].
% 5.17/5.44 359 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(37,b,1,a)].
% 5.17/5.44 360 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(37,b,3,a)].
% 5.17/5.44 361 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(75,b,41,a)].
% 5.17/5.44 362 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(81,b,75,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,343,b)].
% 5.17/5.44 363 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(82,b,75,b)].
% 5.17/5.44 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,343,b)].
% 5.17/5.44 364 -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(160,b,131,b)].
% 5.17/5.44 365 -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(160,b,133,b)].
% 5.17/5.44 366 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(165,a,160,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(366,b,341,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(366,b,342,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,b,343,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(366,b,344,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(366,b,345,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,b,346,b)].
% 5.17/5.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,b,348,b)].
% 5.17/5.44 367 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(166,a,160,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(367,b,341,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(367,b,342,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,b,343,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(367,b,344,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(367,b,345,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,b,346,b)].
% 5.17/5.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,b,348,b)].
% 5.17/5.44 368 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(171,a,160,b)].
% 5.17/5.44 369 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(172,a,160,b)].
% 5.17/5.46 370 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A). [resolve(240,a,234,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(370,b,341,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(370,b,342,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(370,b,343,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(370,b,344,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(370,b,345,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(370,b,346,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(370,b,347,b)].
% 5.17/5.46 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(370,b,348,b)].
% 5.17/5.46 371 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(241,a,234,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(371,b,341,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(371,b,342,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(371,b,343,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(371,b,344,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(371,b,345,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(371,b,346,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(371,b,347,b)].
% 5.17/5.46 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(371,b,348,b)].
% 5.17/5.46 372 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring(D). [resolve(247,b,234,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(372,b,341,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(372,b,342,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(372,b,343,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(372,b,344,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(372,b,345,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(372,b,346,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(372,b,347,b)].
% 5.17/5.46 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(372,b,348,b)].
% 5.17/5.46 373 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring(C). [resolve(248,b,234,b)].
% 5.17/5.46 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(373,b,341,b)].
% 5.17/5.46 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(373,b,342,b)].
% 5.17/5.46 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(373,b,343,b)].
% 5.17/5.46 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(373,b,344,b)].
% 5.17/5.46 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(373,b,345,b)].
% 5.17/5.48 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(373,b,346,b)].
% 5.17/5.48 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(373,b,347,b)].
% 5.17/5.48 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(373,b,348,b)].
% 5.17/5.48 374 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(312,b,288,a)].
% 5.17/5.48 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(374,a,332,a)].
% 5.17/5.48 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(374,a,337,a)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(374,a,338,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(374,a,339,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(374,a,340,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(374,a,341,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(374,a,342,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(374,a,343,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(374,a,344,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(374,a,345,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(374,a,346,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(374,a,347,b)].
% 5.17/5.48 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(374,a,348,b)].
% 5.17/5.48 375 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(312,b,290,a)].
% 5.17/5.48 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(375,a,332,a)].
% 5.17/5.48 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(375,a,337,a)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(375,a,338,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(375,a,339,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(375,a,340,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(375,a,341,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(375,a,342,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(375,a,343,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(375,a,344,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(375,a,345,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(375,a,346,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(375,a,347,b)].
% 5.17/5.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(375,a,348,b)].
% 5.17/5.48 376 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(322,a,312,b)].
% 5.17/5.48 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(376,c,332,a)].
% 5.17/5.48 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(376,c,337,a)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(376,c,338,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(376,c,339,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(376,c,340,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(376,c,341,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(376,c,342,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(376,c,343,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(376,c,344,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(376,c,345,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(376,c,346,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(376,c,347,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(376,c,348,b)].
% 5.17/5.48 377 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(323,a,312,b)].
% 5.17/5.48 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(377,c,332,a)].
% 5.17/5.48 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(377,c,337,a)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(377,c,338,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(377,c,339,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(377,c,340,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(377,c,341,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(377,c,342,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(377,c,343,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(377,c,344,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(377,c,345,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(377,c,346,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(377,c,347,b)].
% 5.17/5.48 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(377,c,348,b)].
% 5.17/5.48 378 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(324,a,312,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(378,b,332,a)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(378,b,337,a)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(378,b,338,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(378,b,339,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(378,b,340,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(378,b,341,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(378,b,342,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(378,b,343,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(378,b,344,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(378,b,345,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(378,b,346,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(378,b,347,b)].
% 5.17/5.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(378,b,348,b)].
% 5.47/5.78 379 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) # label(axiom). [assumption].
% 5.47/5.78 380 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_23) # label(axiom). [assumption].
% 5.47/5.78 381 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 5.47/5.78 382 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 5.47/5.78 383 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 5.47/5.78 384 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 5.47/5.78 385 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring_18) # label(axiom). [assumption].
% 5.47/5.78 386 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_4) # label(axiom). [assumption].
% 5.47/5.78 387 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) # label(axiom). [assumption].
% 5.47/5.78 388 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) # label(axiom). [assumption].
% 5.47/5.78 389 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) # label(axiom). [assumption].
% 5.47/5.78 390 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) # label(axiom). [assumption].
% 5.47/5.78 391 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) # label(axiom). [assumption].
% 5.47/5.78 392 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) # label(axiom). [assumption].
% 5.47/5.78 393 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) # label(axiom). [assumption].
% 5.47/5.78 394 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_14) # label(axiom). [assumption].
% 5.47/5.78 395 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_14) # label(axiom). [assumption].
% 5.47/5.78 396 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_17) # label(axiom). [assumption].
% 5.47/5.78 397 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_14) # label(axiom). [assumption].
% 5.47/5.78 398 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_8) # label(axiom). [assumption].
% 5.47/5.78 399 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_4) # label(axiom). [assumption].
% 5.47/5.78 400 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(22,b,1,a)].
% 5.47/5.78 401 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(22,b,3,a)].
% 5.47/5.78 402 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(22,b,10,a)].
% 5.47/5.78 403 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(81,b,60,b)].
% 5.56/5.85 404 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(142,b,131,b)].
% 5.56/5.85 405 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(142,b,133,b)].
% 5.56/5.85 406 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(162,a,142,b)].
% 5.56/5.85 407 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(165,a,142,b)].
% 5.56/5.85 408 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(166,a,142,b)].
% 5.56/5.85 409 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(171,a,142,b)].
% 5.56/5.85 410 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(172,a,142,b)].
% 5.56/5.85 411 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(201,b,186,b)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(411,b,380,a)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(411,b,381,a)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(411,b,382,a)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(411,b,383,b)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(411,b,384,b)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(411,b,385,b)].
% 5.56/5.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(411,b,386,b)].
% 5.56/5.85 412 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(202,b,186,b)].
% 5.56/5.85 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(412,b,380,a)].
% 5.56/5.85 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(412,b,381,a)].
% 5.56/5.85 Derived: class_HOL_Oplus(tc_nat). [resolve(412,b,382,a)].
% 5.56/5.85 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(412,b,383,b)].
% 5.56/5.85 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(412,b,384,b)].
% 5.56/5.85 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(412,b,385,b)].
% 5.56/5.85 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(412,b,386,b)].
% 5.56/5.85 413 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(240,a,216,b)].
% 5.56/5.85 414 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(241,a,216,b)].
% 5.56/5.85 415 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(D). [resolve(247,b,216,b)].
% 5.56/5.85 416 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(248,b,216,b)].
% 5.56/5.85 417 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(297,b,288,a)].
% 5.56/5.85 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(417,a,382,a)].
% 5.56/5.85 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(417,a,384,b)].
% 5.56/5.85 418 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(297,b,290,a)].
% 5.56/5.85 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(418,a,382,a)].
% 5.56/5.85 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(418,a,384,b)].
% 5.56/5.85 419 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(322,a,297,b)].
% 5.56/5.85 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(419,c,382,a)].
% 5.56/5.85 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(419,c,384,b)].
% 5.87/6.14 420 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(323,a,297,b)].
% 5.87/6.14 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(420,c,382,a)].
% 5.87/6.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(420,c,384,b)].
% 5.87/6.14 421 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom). [assumption].
% 5.87/6.14 422 class_Ring__and__Field_Ocomm__ring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_24) # label(axiom). [assumption].
% 5.87/6.14 423 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 5.87/6.14 424 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 5.87/6.14 425 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 5.87/6.14 426 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 5.87/6.14 427 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom). [assumption].
% 5.87/6.14 428 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 5.87/6.14 429 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 5.87/6.14 430 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 5.87/6.14 431 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 5.87/6.14 432 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 5.87/6.14 433 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_0) # label(axiom). [assumption].
% 5.87/6.14 434 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 5.87/6.14 435 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 5.87/6.14 436 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_4) # label(axiom). [assumption].
% 5.87/6.14 437 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_1) # label(axiom). [assumption].
% 5.87/6.14 438 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_0) # label(axiom). [assumption].
% 5.87/6.14 439 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(20,b,1,a)].
% 5.87/6.14 440 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(20,b,3,a)].
% 5.87/6.14 441 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(20,b,10,a)].
% 5.87/6.14 442 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(81,b,58,b)].
% 5.87/6.14 443 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(138,b,131,b)].
% 5.87/6.14 444 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(138,b,133,b)].
% 5.87/6.14 445 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(162,a,138,b)].
% 5.87/6.18 446 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(165,a,138,b)].
% 5.87/6.18 447 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(166,a,138,b)].
% 5.87/6.18 448 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(171,a,138,b)].
% 5.87/6.18 449 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(172,a,138,b)].
% 5.87/6.18 450 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(200,b,179,b)].
% 5.87/6.18 451 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(201,b,179,b)].
% 5.87/6.18 452 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(202,b,179,b)].
% 5.87/6.18 453 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(203,b,179,b)].
% 5.87/6.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(453,b,422,a)].
% 5.87/6.18 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(453,b,423,a)].
% 5.87/6.18 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 5.87/6.18 454 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(204,b,179,b)].
% 5.87/6.18 Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(454,b,422,a)].
% 5.87/6.18 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(454,b,423,a)].
% 5.87/6.18 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(454,b,424,b)].
% 5.87/6.18 455 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(205,b,179,b)].
% 5.87/6.18 456 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(206,b,179,b)].
% 5.87/6.18 457 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(240,a,213,b)].
% 5.87/6.18 458 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(241,a,213,b)].
% 5.87/6.18 459 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(284,b,255,b)].
% 5.87/6.18 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(459,b,422,a)].
% 5.87/6.18 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(459,b,423,a)].
% 5.87/6.18 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(459,b,424,b)].
% 5.87/6.18 460 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(285,b,255,b)].
% 5.87/6.18 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(460,b,422,a)].
% 5.87/6.18 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(460,b,423,a)].
% 5.87/6.18 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(460,b,424,b)].
% 5.87/6.18 461 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__ring(D). [resolve(286,b,255,b)].
% 5.87/6.18 Derived: c_times(A,c_plus(B,C,tc_fun(D,E)),tc_fun(D,E)) = c_plus(c_times(A,B,tc_fun(D,E)),c_times(A,C,tc_fun(D,E)),tc_fun(D,E)) | -class_Ring__and__Field_Ocomm__ring__1(E). [resolve(461,b,422,a)].
% 5.87/6.18 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(461,b,423,a)].
% 5.87/6.18 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(461,b,424,b)].
% 5.87/6.18 462 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(287,b,255,b)].
% 5.87/6.18 Derived: c_times(c_plus(A,B,tc_fun(C,D)),E,tc_fun(C,D)) = c_plus(c_times(A,E,tc_fun(C,D)),c_times(B,E,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(462,b,422,a)].
% 5.87/6.18 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(462,b,423,a)].
% 5.87/6.18 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(462,b,424,b)].
% 5.97/6.20 463 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(295,b,288,a)].
% 5.97/6.20 464 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(295,b,290,a)].
% 5.97/6.20 465 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(322,a,295,b)].
% 5.97/6.20 466 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(323,a,295,b)].
% 5.97/6.20 467 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(339,b,331,b)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_minus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(467,a,422,a)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(467,a,423,a)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(467,a,424,b)].
% 5.97/6.20 468 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(339,b,333,b)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_minus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(468,a,422,a)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(468,a,423,a)].
% 5.97/6.20 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(468,a,424,b)].
% 5.97/6.20 469 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(339,b,334,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,tc_fun(B,C)),c_uminus(D,tc_fun(B,C)),tc_fun(B,C)) = c_times(A,D,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(469,a,422,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint). [resolve(469,a,423,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(469,a,424,b)].
% 5.97/6.20 470 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,335,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,tc_fun(B,C)),D,tc_fun(B,C)) = c_uminus(c_times(A,D,tc_fun(B,C)),tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(470,a,422,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(470,a,423,a)].
% 5.97/6.20 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(470,a,424,b)].
% 5.97/6.20 471 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(339,b,336,a)].
% 5.97/6.23 Derived: c_times(A,c_uminus(B,tc_fun(C,D)),tc_fun(C,D)) = c_uminus(c_times(A,B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(471,a,422,a)].
% 5.97/6.23 Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(471,a,423,a)].
% 5.97/6.23 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(471,a,424,b)].
% 5.97/6.23 472 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(354,a,339,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(472,b,422,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(472,b,423,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(472,b,424,b)].
% 5.97/6.23 473 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(355,a,339,b)].
% 5.97/6.23 Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(473,b,422,a)].
% 5.97/6.23 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(473,b,423,a)].
% 5.97/6.23 Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(473,b,424,b)].
% 5.97/6.23 474 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(374,a,339,b)].
% 5.97/6.23 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(474,b,422,a)].
% 5.97/6.23 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(474,b,423,a)].
% 5.97/6.23 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(474,b,424,b)].
% 5.97/6.23 475 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(375,a,339,b)].
% 5.97/6.23 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(475,b,422,a)].
% 5.97/6.23 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(475,b,423,a)].
% 5.97/6.23 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(475,b,424,b)].
% 5.97/6.23 476 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(376,c,339,b)].
% 5.97/6.23 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(476,c,422,a)].
% 5.97/6.23 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(476,c,423,a)].
% 5.97/6.23 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(476,c,424,b)].
% 5.97/6.23 477 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(377,c,339,b)].
% 5.97/6.23 Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(477,c,422,a)].
% 5.97/6.23 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(477,c,423,a)].
% 5.97/6.23 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(477,c,424,b)].
% 5.97/6.23 478 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(378,b,339,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(478,b,422,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(478,b,423,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(478,b,424,b)].
% 5.97/6.23 479 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(411,b,385,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(479,b,422,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(479,b,423,a)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(479,b,424,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(479,b,434,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(479,b,435,b)].
% 5.97/6.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(479,b,436,b)].
% 6.18/6.45 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(479,b,437,b)].
% 6.18/6.45 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(479,b,438,b)].
% 6.18/6.45 480 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(412,b,385,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(480,b,422,a)].
% 6.18/6.45 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(480,b,423,a)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,424,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(480,b,434,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(480,b,435,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(480,b,436,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(480,b,437,b)].
% 6.18/6.45 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(480,b,438,b)].
% 6.18/6.45 481 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_0 != c_1 # label(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) # label(axiom). [assumption].
% 6.18/6.45 482 class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_25) # label(axiom). [assumption].
% 6.18/6.45 Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(481,a,482,a)].
% 6.18/6.45 483 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_1 != c_0 # label(cls_Ring__and__Field_Oone__neq__zero_0) # label(axiom). [assumption].
% 6.18/6.45 Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(483,a,482,a)].
% 6.18/6.45 484 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 6.18/6.45 Derived: c_0 != c_1. [resolve(484,a,481,a)].
% 6.18/6.45 Derived: c_1 != c_0. [resolve(484,a,483,a)].
% 6.18/6.45 485 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 6.18/6.45 486 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 6.18/6.45 487 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 6.18/6.45 488 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) # label(axiom). [assumption].
% 6.18/6.45 489 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) # label(axiom). [assumption].
% 6.18/6.45 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(489,a,482,a)].
% 6.18/6.45 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(489,a,487,b)].
% 6.18/6.45 490 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_23) # label(axiom). [assumption].
% 6.18/6.45 491 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_0) # label(axiom). [assumption].
% 6.18/6.45 492 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) # label(axiom). [assumption].
% 6.18/6.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(492,b,489,a)].
% 6.18/6.45 493 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ofield_11) # label(axiom). [assumption].
% 6.18/6.45 494 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oidom_11) # label(axiom). [assumption].
% 6.18/6.45 495 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__field_14) # label(axiom). [assumption].
% 6.18/6.45 496 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_11) # label(axiom). [assumption].
% 6.58/6.83 497 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_5) # label(axiom). [assumption].
% 6.58/6.83 498 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oring__1_16) # label(axiom). [assumption].
% 6.58/6.83 499 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Osemiring__1_0) # label(axiom). [assumption].
% 6.58/6.83 500 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_1) # label(axiom). [assumption].
% 6.58/6.83 501 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 6.58/6.83 502 class_Ring__and__Field_Osemiring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_26) # label(axiom). [assumption].
% 6.58/6.83 503 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 6.58/6.83 504 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 6.58/6.83 505 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 6.58/6.83 506 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 6.58/6.83 507 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_22) # label(axiom). [assumption].
% 6.58/6.83 508 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_16) # label(axiom). [assumption].
% 6.58/6.83 509 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) # label(axiom). [assumption].
% 6.58/6.83 510 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 6.58/6.83 511 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 6.58/6.83 512 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_13) # label(axiom). [assumption].
% 6.58/6.83 513 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_10) # label(axiom). [assumption].
% 6.58/6.83 514 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_4) # label(axiom). [assumption].
% 6.58/6.83 515 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oring__1_15) # label(axiom). [assumption].
% 6.58/6.83 516 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom). [assumption].
% 6.58/6.83 517 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(517,a,507,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(517,a,508,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(517,a,510,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(517,a,511,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(517,a,512,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(517,a,513,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(517,a,514,b)].
% 6.58/6.83 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(517,a,515,b)].
% 6.58/6.89 518 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 6.58/6.89 519 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 6.58/6.89 520 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 6.58/6.89 521 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 6.58/6.89 522 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 6.58/6.89 523 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_0) # label(axiom). [assumption].
% 6.58/6.89 524 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(129,b,108,a)].
% 6.58/6.89 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(524,a,502,a)].
% 6.58/6.89 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(524,a,503,a)].
% 6.58/6.89 Derived: c_times(c_1,A,tc_nat) = A. [resolve(524,a,504,a)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(524,a,505,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(524,a,506,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(524,a,507,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(524,a,508,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(524,a,509,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(524,a,510,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(524,a,511,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(524,a,512,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(524,a,513,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(524,a,514,b)].
% 6.58/6.89 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(524,a,515,b)].
% 6.58/6.89 525 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(129,b,111,a)].
% 6.58/6.89 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(525,a,502,a)].
% 6.58/6.89 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(525,a,503,a)].
% 6.58/6.89 Derived: c_times(A,c_1,tc_nat) = A. [resolve(525,a,504,a)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(525,a,505,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(525,a,506,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(525,a,507,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(525,a,508,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(525,a,509,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(525,a,510,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(525,a,511,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(525,a,512,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(525,a,513,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(525,a,514,b)].
% 6.58/6.89 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(525,a,515,b)].
% 6.58/6.89 526 -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(169,b,131,b)].
% 6.88/7.16 527 -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(169,b,133,b)].
% 6.88/7.16 528 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(169,b,164,a)].
% 6.88/7.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,a,508,b)].
% 6.88/7.16 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(528,a,523,b)].
% 6.88/7.16 529 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1(D). [resolve(171,a,169,b)].
% 6.88/7.16 530 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1(C). [resolve(172,a,169,b)].
% 6.88/7.16 531 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(243,b,241,a)].
% 6.88/7.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(531,a,508,b)].
% 6.88/7.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(531,a,509,b)].
% 6.88/7.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(531,a,514,b)].
% 6.88/7.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(531,a,515,b)].
% 6.88/7.16 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(531,a,523,b)].
% 6.88/7.16 532 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 6.88/7.16 533 class_Ring__and__Field_Ocomm__semiring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_27) # label(axiom). [assumption].
% 6.88/7.16 534 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 6.88/7.16 535 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 6.88/7.16 536 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 6.88/7.16 537 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 6.88/7.16 538 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_20) # label(axiom). [assumption].
% 6.88/7.16 539 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_10) # label(axiom). [assumption].
% 6.88/7.16 540 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_11) # label(axiom). [assumption].
% 6.88/7.16 541 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_12) # label(axiom). [assumption].
% 6.88/7.16 542 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_13) # label(axiom). [assumption].
% 6.88/7.16 543 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_14) # label(axiom). [assumption].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(543,a,533,a)].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(543,a,534,a)].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(543,a,535,a)].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(543,a,536,b)].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(543,a,537,b)].
% 6.88/7.16 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(543,a,538,b)].
% 6.88/7.16 544 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 7.06/7.35 545 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_8) # label(axiom). [assumption].
% 7.06/7.35 546 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 7.06/7.35 547 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) # label(axiom). [assumption].
% 7.06/7.35 548 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 7.06/7.35 549 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 7.06/7.35 550 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_10) # label(axiom). [assumption].
% 7.06/7.35 551 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_7) # label(axiom). [assumption].
% 7.06/7.35 552 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_1) # label(axiom). [assumption].
% 7.06/7.35 553 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(121,b,108,a)].
% 7.06/7.35 554 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(121,b,111,a)].
% 7.06/7.35 555 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(143,b,131,b)].
% 7.06/7.35 556 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(143,b,133,b)].
% 7.06/7.35 557 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(162,a,143,b)].
% 7.06/7.35 558 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(163,a,143,b)].
% 7.06/7.35 559 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(164,a,143,b)].
% 7.06/7.35 560 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(165,a,143,b)].
% 7.06/7.35 561 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(166,a,143,b)].
% 7.06/7.35 562 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(171,a,143,b)].
% 7.06/7.35 563 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(172,a,143,b)].
% 7.06/7.35 564 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(240,a,217,b)].
% 7.06/7.35 565 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(241,a,217,b)].
% 7.06/7.35 566 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1(D). [resolve(247,b,217,b)].
% 7.06/7.35 567 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1(C). [resolve(248,b,217,b)].
% 7.06/7.35 568 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(517,a,508,b)].
% 7.06/7.35 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(568,b,533,a)].
% 7.06/7.35 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(568,b,534,a)].
% 7.06/7.35 Derived: class_HOL_Oone(tc_nat). [resolve(568,b,535,a)].
% 7.06/7.35 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(568,b,536,b)].
% 7.06/7.35 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(568,b,537,b)].
% 7.06/7.35 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(568,b,538,b)].
% 7.06/7.35 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(568,b,547,b)].
% 7.28/7.56 569 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(524,a,508,b)].
% 7.28/7.56 Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(569,b,533,a)].
% 7.28/7.56 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(569,b,534,a)].
% 7.28/7.56 Derived: c_times(c_1,A,tc_nat) = A. [resolve(569,b,535,a)].
% 7.28/7.56 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(569,b,536,b)].
% 7.28/7.56 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(569,b,537,b)].
% 7.28/7.56 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(569,b,538,b)].
% 7.28/7.56 570 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(525,a,508,b)].
% 7.28/7.56 Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(570,b,533,a)].
% 7.28/7.56 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(570,b,534,a)].
% 7.28/7.56 Derived: c_times(A,c_1,tc_nat) = A. [resolve(570,b,535,a)].
% 7.28/7.56 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(570,b,536,b)].
% 7.28/7.56 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(570,b,537,b)].
% 7.28/7.56 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(570,b,538,b)].
% 7.28/7.56 571 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,a,508,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(571,b,533,a)].
% 7.28/7.56 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(571,b,534,a)].
% 7.28/7.56 Derived: class_HOL_Oplus(tc_nat). [resolve(571,b,535,a)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(571,b,536,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(571,b,537,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(571,b,538,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(571,b,547,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(571,b,548,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(571,b,549,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(571,b,550,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(571,b,551,b)].
% 7.28/7.56 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(571,b,552,b)].
% 7.28/7.56 572 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(531,a,508,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(572,b,533,a)].
% 7.28/7.56 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(572,b,534,a)].
% 7.28/7.56 Derived: class_HOL_Ozero(tc_nat). [resolve(572,b,535,a)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(572,b,536,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(572,b,537,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(572,b,538,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(572,b,548,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(572,b,549,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(572,b,550,b)].
% 7.28/7.56 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(572,b,551,b)].
% 7.28/7.56 573 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 7.28/7.56 574 class_Ring__and__Field_Osemiring__1__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_28) # label(axiom). [assumption].
% 7.28/7.56 575 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 7.28/7.56 576 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 7.28/7.56 577 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 7.36/7.62 578 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 7.36/7.62 579 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_27) # label(axiom). [assumption].
% 7.36/7.62 580 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) # label(axiom). [assumption].
% 7.36/7.62 581 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 7.36/7.62 582 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 7.36/7.62 583 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_12) # label(axiom). [assumption].
% 7.36/7.62 584 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_9) # label(axiom). [assumption].
% 7.36/7.62 585 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_3) # label(axiom). [assumption].
% 7.36/7.62 586 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oring__1_19) # label(axiom). [assumption].
% 7.36/7.62 587 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_11) # label(axiom). [assumption].
% 7.36/7.62 588 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 7.36/7.62 589 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_4) # label(axiom). [assumption].
% 7.36/7.62 590 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 7.36/7.62 591 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_6) # label(axiom). [assumption].
% 7.36/7.62 592 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_7) # label(axiom). [assumption].
% 7.36/7.62 593 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_8) # label(axiom). [assumption].
% 7.36/7.62 594 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(40,b,1,a)].
% 7.36/7.62 595 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(40,b,3,a)].
% 7.36/7.62 596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(81,b,78,b)].
% 7.36/7.62 597 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(82,b,78,b)].
% 7.36/7.62 598 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(130,b,108,a)].
% 7.36/7.62 599 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(130,b,111,a)].
% 7.36/7.62 600 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A). [resolve(130,b,116,a)].
% 7.36/7.62 601 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(130,b,117,a)].
% 7.36/7.62 602 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(130,b,118,a)].
% 7.36/7.62 603 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(170,b,131,b)].
% 7.36/7.62 604 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(170,b,133,b)].
% 7.66/7.93 605 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Osemiring__1__cancel(D). [resolve(171,a,170,b)].
% 7.66/7.93 606 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(172,a,170,b)].
% 7.66/7.93 607 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(321,b,288,a)].
% 7.66/7.93 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(607,a,580,b)].
% 7.66/7.93 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(607,a,585,b)].
% 7.66/7.93 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(607,a,586,b)].
% 7.66/7.93 608 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(321,b,290,a)].
% 7.66/7.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(608,a,580,b)].
% 7.66/7.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(608,a,585,b)].
% 7.66/7.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(608,a,586,b)].
% 7.66/7.93 609 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(324,a,321,b)].
% 7.66/7.93 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(609,b,576,a)].
% 7.66/7.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(609,b,578,b)].
% 7.66/7.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(609,b,580,b)].
% 7.66/7.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(609,b,585,b)].
% 7.66/7.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(609,b,586,b)].
% 7.66/7.93 610 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(528,a,523,b)].
% 7.66/7.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(610,b,586,b)].
% 7.66/7.93 611 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(531,a,523,b)].
% 7.66/7.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(611,b,580,b)].
% 7.66/7.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(611,b,585,b)].
% 7.66/7.93 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(611,b,586,b)].
% 7.66/7.93 612 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 7.66/7.93 613 class_Ring__and__Field_Oring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_29) # label(axiom). [assumption].
% 7.66/7.93 614 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 7.66/7.93 615 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 7.66/7.93 616 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_26) # label(axiom). [assumption].
% 7.66/7.93 617 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 7.66/7.93 618 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 7.66/7.93 619 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_5) # label(axiom). [assumption].
% 7.66/7.93 620 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_2) # label(axiom). [assumption].
% 7.66/7.93 621 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 7.78/8.05 622 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 7.78/8.05 623 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 7.78/8.05 624 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom). [assumption].
% 7.78/8.05 625 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 7.78/8.05 626 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 7.78/8.05 627 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom). [assumption].
% 7.78/8.05 628 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 7.78/8.05 629 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 7.78/8.05 630 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(38,b,1,a)].
% 7.78/8.05 631 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(38,b,3,a)].
% 7.78/8.05 632 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(38,b,9,a)].
% 7.78/8.05 633 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(38,b,10,a)].
% 7.78/8.05 634 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(76,b,41,a)].
% 7.78/8.05 635 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(128,b,108,a)].
% 7.78/8.05 636 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(128,b,111,a)].
% 7.78/8.05 637 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(161,b,131,b)].
% 7.78/8.05 638 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(161,b,133,b)].
% 7.78/8.05 639 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(165,a,161,b)].
% 7.78/8.05 640 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(166,a,161,b)].
% 7.78/8.05 641 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(171,a,161,b)].
% 7.78/8.05 642 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(172,a,161,b)].
% 7.78/8.05 643 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(240,a,235,b)].
% 7.78/8.05 644 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(241,a,235,b)].
% 7.78/8.05 645 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oring__1(D). [resolve(247,b,235,b)].
% 7.78/8.05 646 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(248,b,235,b)].
% 7.78/8.05 647 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(313,b,288,a)].
% 7.78/8.05 648 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(313,b,290,a)].
% 7.78/8.05 649 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(322,a,313,b)].
% 7.78/8.05 650 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(323,a,313,b)].
% 7.78/8.05 651 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(324,a,313,b)].
% 7.78/8.05 652 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(325,a,313,b)].
% 7.78/8.05 653 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(326,a,313,b)].
% 7.78/8.05 654 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(358,b,331,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(654,a,616,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(654,a,617,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(654,a,618,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(654,a,619,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(654,a,620,b)].
% 7.78/8.06 655 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(358,b,333,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(655,a,616,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(655,a,617,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(655,a,618,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(655,a,619,b)].
% 7.78/8.06 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(655,a,620,b)].
% 7.78/8.06 656 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(358,b,334,a)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(656,a,616,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(656,a,617,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(656,a,618,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(656,a,619,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(656,a,620,b)].
% 7.78/8.06 657 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,335,a)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(657,a,616,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(657,a,617,b)].
% 7.78/8.06 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(657,a,618,b)].
% 7.78/8.10 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(657,a,619,b)].
% 7.78/8.10 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(657,a,620,b)].
% 7.78/8.10 658 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(358,b,336,a)].
% 7.78/8.10 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(658,a,616,b)].
% 7.78/8.10 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(658,a,617,b)].
% 7.78/8.10 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(658,a,618,b)].
% 7.78/8.10 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(658,a,619,b)].
% 7.78/8.10 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(658,a,620,b)].
% 7.78/8.11 659 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A). [resolve(517,a,515,b)].
% 7.78/8.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(659,b,617,b)].
% 7.78/8.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(659,b,618,b)].
% 7.78/8.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(659,b,619,b)].
% 7.78/8.11 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(659,b,620,b)].
% 7.78/8.11 660 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(524,a,515,b)].
% 7.78/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(660,b,617,b)].
% 7.78/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(660,b,618,b)].
% 7.78/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(660,b,619,b)].
% 7.78/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(660,b,620,b)].
% 7.78/8.11 661 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(525,a,515,b)].
% 7.78/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(661,b,617,b)].
% 7.78/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(661,b,618,b)].
% 7.78/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(661,b,619,b)].
% 7.78/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(661,b,620,b)].
% 7.78/8.11 662 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(531,a,515,b)].
% 7.78/8.11 663 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(607,a,586,b)].
% 7.78/8.11 Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(663,b,613,a)].
% 7.78/8.11 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(663,b,614,a)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(663,b,615,b)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(663,b,616,b)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(663,b,617,b)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(663,b,618,b)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(663,b,619,b)].
% 7.78/8.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(663,b,620,b)].
% 7.78/8.11 664 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(608,a,586,b)].
% 7.78/8.11 Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(664,b,613,a)].
% 7.78/8.11 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(664,b,614,a)].
% 7.78/8.11 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(664,b,615,b)].
% 7.78/8.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(664,b,616,b)].
% 7.78/8.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(664,b,617,b)].
% 7.78/8.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(664,b,618,b)].
% 7.88/8.19 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(664,b,619,b)].
% 7.88/8.19 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(664,b,620,b)].
% 7.88/8.19 665 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(609,b,586,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(665,b,613,a)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(665,b,614,a)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(665,b,615,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(665,b,616,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(665,b,617,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(665,b,618,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(665,b,619,b)].
% 7.88/8.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(665,b,620,b)].
% 7.88/8.19 666 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(610,b,586,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(666,b,613,a)].
% 7.88/8.19 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(666,b,614,a)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(666,b,615,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(666,b,616,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(666,b,617,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(666,b,618,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(666,b,619,b)].
% 7.88/8.19 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(666,b,620,b)].
% 7.88/8.19 667 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(611,b,586,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(667,b,613,a)].
% 7.88/8.19 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(667,b,614,a)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(667,b,615,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(667,b,616,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(667,b,617,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(667,b,618,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(667,b,619,b)].
% 7.88/8.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(667,b,620,b)].
% 7.88/8.19 668 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_0,c_IntDef_ONats,A) # label(cls_IntDef_ONats__0_0) # label(axiom). [assumption].
% 7.88/8.19 669 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_30) # label(axiom). [assumption].
% 7.88/8.19 Derived: c_in(c_0,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(668,a,669,a)].
% 7.88/8.19 670 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_1,c_IntDef_ONats,A) # label(cls_IntDef_ONats__1_0) # label(axiom). [assumption].
% 7.88/8.19 Derived: c_in(c_1,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(670,a,669,a)].
% 7.88/8.19 671 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__add_0) # label(axiom). [assumption].
% 7.88/8.19 Derived: -c_in(A,c_IntDef_ONats,tc_fun(B,C)) | -c_in(D,c_IntDef_ONats,tc_fun(B,C)) | c_in(c_plus(D,A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(671,a,669,a)].
% 7.88/8.19 672 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__mult_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: -c_in(A,c_IntDef_ONats,tc_fun(B,C)) | -c_in(D,c_IntDef_ONats,tc_fun(B,C)) | c_in(c_times(D,A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(672,a,669,a)].
% 7.96/8.27 673 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A) # label(cls_IntDef_Oof__nat__in__Nats_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_in(c_NatArith_Oof__nat(A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(673,a,669,a)].
% 7.96/8.27 674 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A) # label(cls_NatArith_Oof__nat_Oof__nat__Suc_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_fun(B,C)) = c_plus(c_NatArith_Oof__nat(A,tc_fun(B,C)),c_1,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(674,a,669,a)].
% 7.96/8.27 675 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_1,A) = c_1 # label(cls_NatArith_Oof__nat__1_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_1,tc_fun(A,B)) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(675,a,669,a)].
% 7.96/8.27 676 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__add_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_fun(C,D)) = c_plus(c_NatArith_Oof__nat(A,tc_fun(C,D)),c_NatArith_Oof__nat(B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(676,a,669,a)].
% 7.96/8.27 677 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__mult_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_fun(C,D)) = c_times(c_NatArith_Oof__nat(A,tc_fun(C,D)),c_NatArith_Oof__nat(B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D). [resolve(677,a,669,a)].
% 7.96/8.27 678 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_IntDef_Oiszero(c_1,A) # label(cls_Numeral_Obin__rel__simps__10_0) # label(axiom). [assumption].
% 7.96/8.27 Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(678,a,669,a)].
% 7.96/8.27 679 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 7.96/8.27 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,668,a)].
% 7.96/8.27 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,670,a)].
% 7.96/8.27 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,671,a)].
% 7.96/8.27 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,672,a)].
% 7.96/8.27 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(679,a,673,a)].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(679,a,674,a)].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(679,a,675,a)].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(679,a,676,a)].
% 7.96/8.27 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(679,a,677,a)].
% 7.96/8.27 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(679,a,678,a)].
% 7.96/8.27 680 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 8.05/8.30 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(680,a,668,a)].
% 8.05/8.30 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(680,a,670,a)].
% 8.05/8.30 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(680,a,671,a)].
% 8.05/8.30 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(680,a,672,a)].
% 8.05/8.30 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(680,a,673,a)].
% 8.05/8.30 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(680,a,674,a)].
% 8.05/8.30 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(680,a,675,a)].
% 8.05/8.30 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(680,a,676,a)].
% 8.05/8.30 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(680,a,677,a)].
% 8.05/8.30 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(680,a,678,a)].
% 8.05/8.30 681 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(681,b,668,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(681,b,670,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(681,b,671,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(681,b,672,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(681,b,673,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(681,b,674,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(681,b,675,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(681,b,676,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(681,b,677,a)].
% 8.05/8.30 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(681,b,678,a)].
% 8.05/8.30 682 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(682,b,668,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(682,b,670,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(682,b,671,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(682,b,672,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(682,b,673,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(682,b,674,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(682,b,675,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(682,b,676,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(682,b,677,a)].
% 8.05/8.30 Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A). [resolve(682,b,678,a)].
% 8.05/8.30 683 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_28) # label(axiom). [assumption].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(683,b,668,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(683,b,670,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(683,b,671,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(683,b,672,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(683,b,673,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(683,b,674,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(683,b,675,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(683,b,676,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(683,b,677,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A). [resolve(683,b,678,a)].
% 8.05/8.31 684 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) # label(axiom). [assumption].
% 8.05/8.31 685 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) # label(axiom). [assumption].
% 8.05/8.31 686 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) # label(axiom). [assumption].
% 8.05/8.31 687 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) # label(axiom). [assumption].
% 8.05/8.31 688 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) # label(axiom). [assumption].
% 8.05/8.31 689 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) # label(axiom). [assumption].
% 8.05/8.31 690 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) # label(axiom). [assumption].
% 8.05/8.31 691 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) # label(axiom). [assumption].
% 8.05/8.31 692 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) # label(axiom). [assumption].
% 8.05/8.31 693 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_6) # label(axiom). [assumption].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(693,b,668,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(693,b,670,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(693,b,671,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(693,b,672,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(693,b,673,a)].
% 8.05/8.31 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(693,b,674,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(693,b,675,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(693,b,676,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(693,b,677,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A). [resolve(693,b,678,a)].
% 8.05/8.32 694 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_6) # label(axiom). [assumption].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(694,b,668,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(694,b,670,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(694,b,671,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(694,b,672,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(694,b,673,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(694,b,674,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(694,b,675,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(694,b,676,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(694,b,677,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(694,b,678,a)].
% 8.05/8.32 695 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_9) # label(axiom). [assumption].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(695,b,668,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(695,b,670,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(695,b,671,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(695,b,672,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(695,b,673,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(695,b,674,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(695,b,675,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(695,b,676,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(695,b,677,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A). [resolve(695,b,678,a)].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(695,b,691,a)].
% 8.05/8.32 696 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_6) # label(axiom). [assumption].
% 8.05/8.32 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(696,b,668,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(696,b,670,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(696,b,671,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(696,b,672,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(696,b,673,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(696,b,674,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(696,b,675,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(696,b,676,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(696,b,677,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(696,b,678,a)].
% 8.05/8.36 697 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_0) # label(axiom). [assumption].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(697,b,668,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(697,b,670,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(697,b,671,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(697,b,672,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(697,b,673,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(697,b,674,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(697,b,675,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(697,b,676,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(697,b,677,a)].
% 8.05/8.36 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(697,b,678,a)].
% 8.05/8.36 698 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(23,b,1,a)].
% 8.05/8.36 699 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(23,b,3,a)].
% 8.05/8.36 700 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(23,b,9,a)].
% 8.05/8.36 701 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A). [resolve(23,b,10,a)].
% 8.05/8.36 702 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(61,b,41,a)].
% 8.05/8.36 703 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(98,b,83,a)].
% 8.05/8.36 704 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(98,b,89,a)].
% 8.05/8.36 705 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(122,b,108,a)].
% 8.05/8.36 706 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(122,b,111,a)].
% 8.05/8.36 707 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(144,b,131,b)].
% 8.18/8.42 708 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(144,b,133,b)].
% 8.18/8.42 709 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(171,a,144,b)].
% 8.18/8.42 710 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(172,a,144,b)].
% 8.18/8.42 711 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(200,b,188,b)].
% 8.18/8.42 712 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(201,b,188,b)].
% 8.18/8.42 713 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(202,b,188,b)].
% 8.18/8.42 714 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(203,b,188,b)].
% 8.18/8.42 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(714,b,680,a)].
% 8.18/8.42 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(714,b,682,b)].
% 8.18/8.42 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(714,b,683,b)].
% 8.18/8.42 715 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(204,b,188,b)].
% 8.18/8.42 Derived: class_HOL_Otimes(tc_nat). [resolve(715,b,680,a)].
% 8.18/8.42 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(715,b,682,b)].
% 8.18/8.42 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(715,b,683,b)].
% 8.18/8.42 716 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(240,a,218,b)].
% 8.18/8.42 717 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(241,a,218,b)].
% 8.18/8.42 718 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(D). [resolve(247,b,218,b)].
% 8.18/8.42 719 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(248,b,218,b)].
% 8.18/8.42 720 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(298,b,288,a)].
% 8.18/8.42 721 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(298,b,290,a)].
% 8.18/8.42 722 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(322,a,298,b)].
% 8.18/8.42 723 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(323,a,298,b)].
% 8.18/8.42 724 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A). [resolve(492,b,489,a)].
% 8.18/8.42 725 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(524,a,509,b)].
% 8.18/8.42 726 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(525,a,509,b)].
% 8.18/8.42 727 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(531,a,509,b)].
% 8.18/8.42 728 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(568,b,547,b)].
% 8.18/8.42 Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(728,b,669,a)].
% 8.18/8.42 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(728,b,679,a)].
% 8.18/8.42 Derived: class_HOL_Oone(tc_nat). [resolve(728,b,680,a)].
% 8.18/8.42 Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,681,b)].
% 8.18/8.42 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(728,b,682,b)].
% 8.18/8.42 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(728,b,683,b)].
% 8.18/8.42 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(728,b,697,b)].
% 8.18/8.42 729 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(571,b,547,b)].
% 8.26/8.55 Derived: class_HOL_Oplus(tc_nat). [resolve(729,b,680,a)].
% 8.26/8.55 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(729,b,682,b)].
% 8.26/8.55 730 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(607,a,580,b)].
% 8.26/8.55 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(730,b,680,a)].
% 8.26/8.55 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(730,b,682,b)].
% 8.26/8.55 731 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(608,a,580,b)].
% 8.26/8.55 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(731,b,680,a)].
% 8.26/8.55 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(731,b,682,b)].
% 8.26/8.55 732 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(609,b,580,b)].
% 8.26/8.55 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(732,b,680,a)].
% 8.26/8.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(732,b,682,b)].
% 8.26/8.55 733 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(611,b,580,b)].
% 8.26/8.55 Derived: class_HOL_Ozero(tc_nat). [resolve(733,b,680,a)].
% 8.26/8.55 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(733,b,682,b)].
% 8.26/8.55 734 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom). [assumption].
% 8.26/8.55 735 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom). [assumption].
% 8.26/8.55 736 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom). [assumption].
% 8.26/8.55 737 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom). [assumption].
% 8.26/8.55 738 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom). [assumption].
% 8.26/8.55 739 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 8.26/8.55 740 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom). [assumption].
% 8.26/8.55 Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(734,a,735,a)].
% 8.26/8.55 Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(734,a,736,a)].
% 8.26/8.55 741 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom). [assumption].
% 8.26/8.55 Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B). [resolve(741,a,735,a)].
% 8.26/8.55 Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A). [resolve(741,a,736,a)].
% 8.26/8.55 742 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 8.26/8.55 743 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 8.26/8.55 744 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 8.26/8.55 745 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 8.26/8.55 746 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 8.26/8.55 747 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) # label(axiom). [assumption].
% 8.26/8.55 748 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom). [assumption].
% 8.26/8.58 749 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 8.26/8.58 750 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) # label(axiom). [assumption].
% 8.26/8.58 751 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 8.26/8.58 752 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom). [assumption].
% 8.26/8.58 753 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_16) # label(axiom). [assumption].
% 8.26/8.58 754 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom). [assumption].
% 8.26/8.58 755 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 8.26/8.58 756 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 8.26/8.58 757 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) # label(axiom). [assumption].
% 8.26/8.58 758 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_27) # label(axiom). [assumption].
% 8.26/8.58 759 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 8.26/8.58 760 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_11) # label(axiom). [assumption].
% 8.26/8.58 761 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 8.26/8.58 762 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_5) # label(axiom). [assumption].
% 8.26/8.58 763 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) # label(axiom). [assumption].
% 8.26/8.58 764 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_8) # label(axiom). [assumption].
% 8.26/8.58 765 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_16) # label(axiom). [assumption].
% 8.26/8.58 766 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_8) # label(axiom). [assumption].
% 8.26/8.58 767 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 8.26/8.58 768 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 8.26/8.58 769 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B). [resolve(41,a,42,a)].
% 8.26/8.58 770 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(41,a,43,a)].
% 8.26/8.58 771 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(41,a,44,a)].
% 8.26/8.58 772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(41,a,45,b)].
% 8.36/8.62 773 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(41,a,46,b)].
% 8.36/8.62 774 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(50,b,41,a)].
% 8.36/8.62 775 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(56,b,41,a)].
% 8.36/8.62 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(775,b,734,a)].
% 8.36/8.62 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(775,b,741,a)].
% 8.36/8.62 776 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(68,b,41,a)].
% 8.36/8.62 777 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(71,b,41,a)].
% 8.36/8.62 778 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(74,b,41,a)].
% 8.36/8.62 779 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(162,a,132,a)].
% 8.36/8.62 780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(162,a,137,b)].
% 8.36/8.62 781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(162,a,139,b)].
% 8.36/8.62 782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(162,a,145,b)].
% 8.36/8.62 783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(162,a,146,b)].
% 8.36/8.62 784 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(162,a,147,b)].
% 8.36/8.62 785 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(162,a,148,b)].
% 8.36/8.62 786 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(162,a,149,b)].
% 8.36/8.62 787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(162,a,150,b)].
% 8.36/8.62 788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(162,a,152,b)].
% 8.36/8.62 789 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(162,a,153,b)].
% 8.36/8.62 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(789,a,734,a)].
% 8.36/8.62 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(789,a,741,a)].
% 8.36/8.62 790 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(162,a,155,b)].
% 8.36/8.62 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(790,a,734,a)].
% 8.36/8.62 791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(162,a,156,b)].
% 8.36/8.62 792 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(162,a,157,b)].
% 8.36/8.62 793 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(162,a,159,b)].
% 8.36/8.62 794 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(200,b,174,a)].
% 8.36/8.62 795 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(200,b,175,a)].
% 8.36/8.62 796 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(200,b,176,a)].
% 8.36/8.62 797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(200,b,177,b)].
% 8.36/8.62 798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(200,b,178,b)].
% 8.36/8.62 799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(200,b,180,b)].
% 8.36/8.62 800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(200,b,195,b)].
% 8.36/8.62 801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(324,a,305,b)].
% 8.36/8.62 802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(324,a,311,b)].
% 8.36/8.66 803 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(378,b,332,a)].
% 8.36/8.66 804 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(378,b,337,a)].
% 8.36/8.66 805 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(378,b,338,b)].
% 8.36/8.66 806 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(378,b,340,b)].
% 8.36/8.66 807 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(378,b,341,b)].
% 8.36/8.66 808 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(378,b,342,b)].
% 8.36/8.66 809 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(378,b,343,b)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,734,a)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(809,a,741,a)].
% 8.36/8.66 810 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(378,b,344,b)].
% 8.36/8.66 811 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(378,b,345,b)].
% 8.36/8.66 812 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(378,b,346,b)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(812,a,734,a)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(812,a,741,a)].
% 8.36/8.66 813 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(378,b,347,b)].
% 8.36/8.66 814 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(378,b,348,b)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,734,a)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(814,a,741,a)].
% 8.36/8.66 815 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(478,b,422,a)].
% 8.36/8.66 816 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(478,b,423,a)].
% 8.36/8.66 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(478,b,424,b)].
% 8.36/8.66 818 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(609,b,576,a)].
% 8.36/8.66 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(818,a,734,a)].
% 8.36/8.66 819 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(609,b,578,b)].
% 8.36/8.66 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(819,a,734,a)].
% 8.36/8.66 820 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(609,b,585,b)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(820,a,734,a)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(820,a,741,a)].
% 8.36/8.66 821 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(665,b,613,a)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)). [resolve(821,a,734,a)].
% 8.36/8.66 822 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(665,b,614,a)].
% 8.36/8.66 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(822,a,734,a)].
% 8.36/8.66 823 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(665,b,615,b)].
% 8.36/8.66 Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(823,a,734,a)].
% 8.36/8.66 824 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(665,b,616,b)].
% 8.36/8.66 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(824,a,734,a)].
% 8.36/8.66 825 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(665,b,617,b)].
% 8.48/8.77 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(825,a,734,a)].
% 8.48/8.77 826 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(665,b,618,b)].
% 8.48/8.77 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(826,a,734,a)].
% 8.48/8.77 827 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(665,b,619,b)].
% 8.48/8.77 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(827,a,734,a)].
% 8.48/8.77 828 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(665,b,620,b)].
% 8.48/8.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(828,a,734,a)].
% 8.48/8.77 829 class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(732,b,680,a)].
% 8.48/8.77 Derived: class_HOL_Oplus(tc_nat). [resolve(829,a,741,a)].
% 8.48/8.77 830 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(732,b,682,b)].
% 8.48/8.77 Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A). [resolve(830,a,741,a)].
% 8.48/8.77 831 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 8.48/8.77 832 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset # label(cls_Finite__Set_OMax__ge_0) # label(axiom). [assumption].
% 8.48/8.77 833 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMax__in_0) # label(axiom). [assumption].
% 8.48/8.77 834 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A) # label(cls_Finite__Set_OMax__insert_0) # label(axiom). [assumption].
% 8.48/8.77 835 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__le__iff_0) # label(axiom). [assumption].
% 8.48/8.77 836 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_1) # label(axiom). [assumption].
% 8.48/8.77 837 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_2) # label(axiom). [assumption].
% 8.48/8.77 838 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__less__iff_0) # label(axiom). [assumption].
% 8.48/8.77 839 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_1) # label(axiom). [assumption].
% 8.48/8.77 840 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_2) # label(axiom). [assumption].
% 8.48/8.77 841 -class_Orderings_Olinorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMax__singleton_0) # label(axiom). [assumption].
% 8.48/8.77 842 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_0) # label(axiom). [assumption].
% 8.48/8.77 843 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_1) # label(axiom). [assumption].
% 8.48/8.77 844 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_2) # label(axiom). [assumption].
% 8.48/8.77 845 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_0) # label(axiom). [assumption].
% 8.48/8.77 846 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_1) # label(axiom). [assumption].
% 8.48/8.77 847 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_2) # label(axiom). [assumption].
% 8.48/8.77 848 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMin__in_0) # label(axiom). [assumption].
% 8.48/8.77 849 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A) # label(cls_Finite__Set_OMin__insert_0) # label(axiom). [assumption].
% 8.48/8.77 850 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__le_0) # label(axiom). [assumption].
% 8.48/8.77 851 -class_Orderings_Olinorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMin__singleton_0) # label(axiom). [assumption].
% 8.48/8.77 852 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) # label(axiom). [assumption].
% 8.48/8.77 853 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) # label(axiom). [assumption].
% 8.48/8.77 854 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) # label(axiom). [assumption].
% 8.48/8.77 855 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 8.48/8.77 856 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 8.48/8.77 857 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A) # label(cls_Orderings_Omax__less__iff__conj_0) # label(axiom). [assumption].
% 8.48/8.77 858 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A) # label(cls_Orderings_Omax__less__iff__conj_1) # label(axiom). [assumption].
% 8.48/8.77 859 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omax__less__iff__conj_2) # label(axiom). [assumption].
% 8.48/8.77 860 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A) # label(cls_Orderings_Omin__less__iff__conj_0) # label(axiom). [assumption].
% 8.48/8.77 861 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A) # label(cls_Orderings_Omin__less__iff__conj_1) # label(axiom). [assumption].
% 8.48/8.77 862 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__less__iff__conj_2) # label(axiom). [assumption].
% 8.48/8.77 863 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) # label(axiom). [assumption].
% 8.48/8.77 864 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) # label(axiom). [assumption].
% 8.48/8.77 865 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) # label(axiom). [assumption].
% 8.48/8.77 866 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 8.48/8.77 867 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) # label(axiom). [assumption].
% 8.48/8.77 868 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) # label(axiom). [assumption].
% 8.48/8.77 869 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) # label(axiom). [assumption].
% 8.48/8.77 870 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) # label(axiom). [assumption].
% 8.48/8.77 871 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 8.48/8.77 872 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) # label(axiom). [assumption].
% 8.48/8.77 873 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A) # label(cls_SetInterval_OCompl__atLeast_0) # label(axiom). [assumption].
% 8.48/8.77 874 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A) # label(cls_SetInterval_OCompl__atMost_0) # label(axiom). [assumption].
% 8.48/8.77 875 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A) # label(cls_SetInterval_OCompl__greaterThan_0) # label(axiom). [assumption].
% 8.48/8.77 876 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A) # label(cls_SetInterval_OCompl__lessThan_0) # label(axiom). [assumption].
% 8.48/8.77 877 -class_Orderings_Olinorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C # label(cls_SetInterval_OatLeast__eq__iff_0) # label(axiom). [assumption].
% 8.48/8.77 878 -class_Orderings_Olinorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C # label(cls_SetInterval_OatMost__eq__iff_0) # label(axiom). [assumption].
% 8.48/8.77 879 -class_Orderings_Olinorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C # label(cls_SetInterval_OgreaterThan__eq__iff_0) # label(axiom). [assumption].
% 8.48/8.77 880 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OgreaterThan__subset__iff_0) # label(axiom). [assumption].
% 8.48/8.77 881 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)) # label(cls_SetInterval_OgreaterThan__subset__iff_1) # label(axiom). [assumption].
% 8.48/8.77 882 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A) # label(cls_SetInterval_Oivl__diff_0) # label(axiom). [assumption].
% 8.48/8.77 883 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_0) # label(axiom). [assumption].
% 8.48/8.77 884 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_1) # label(axiom). [assumption].
% 8.48/8.77 885 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_2) # label(axiom). [assumption].
% 8.48/8.77 886 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_3) # label(axiom). [assumption].
% 8.48/8.77 887 -class_Orderings_Olinorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C # label(cls_SetInterval_OlessThan__eq__iff_0) # label(axiom). [assumption].
% 8.48/8.77 888 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OlessThan__subset__iff_0) # label(axiom). [assumption].
% 8.48/8.77 889 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) # label(cls_SetInterval_OlessThan__subset__iff_1) # label(axiom). [assumption].
% 8.48/8.77 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,832,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,833,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(831,a,834,a)].
% 8.48/8.77 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,835,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,836,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,837,a)].
% 8.48/8.77 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,838,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,839,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,840,a)].
% 8.48/8.77 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,841,a)].
% 8.48/8.77 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,842,a)].
% 8.48/8.77 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,843,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,844,a)].
% 8.48/8.78 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,845,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,846,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,847,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,848,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(831,a,849,a)].
% 8.48/8.78 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(831,a,850,a)].
% 8.48/8.78 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,851,a)].
% 8.48/8.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(831,a,852,a)].
% 8.48/8.78 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,853,a)].
% 8.48/8.78 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(831,a,854,a)].
% 8.48/8.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(831,a,855,b)].
% 8.48/8.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(831,a,856,b)].
% 8.48/8.78 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(831,a,857,a)].
% 8.48/8.78 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(831,a,858,a)].
% 8.48/8.78 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(831,a,859,a)].
% 8.48/8.78 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(831,a,860,a)].
% 8.48/8.78 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(831,a,861,a)].
% 8.48/8.78 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(831,a,862,a)].
% 8.48/8.78 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(831,a,863,a)].
% 8.48/8.78 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(831,a,864,a)].
% 8.48/8.78 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(831,a,865,a)].
% 8.48/8.79 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(831,a,866,a)].
% 8.48/8.79 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(831,a,867,a)].
% 8.48/8.79 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(831,a,868,a)].
% 8.48/8.79 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(831,a,869,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(831,a,870,a)].
% 8.48/8.79 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(831,a,871,a)].
% 8.48/8.79 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(831,a,872,a)].
% 8.48/8.79 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(831,a,873,a)].
% 8.48/8.79 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(831,a,874,a)].
% 8.48/8.79 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(831,a,875,a)].
% 8.48/8.79 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(831,a,876,a)].
% 8.48/8.79 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(831,a,877,a)].
% 8.48/8.79 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(831,a,878,a)].
% 8.48/8.79 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(831,a,879,a)].
% 8.48/8.79 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(831,a,880,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(831,a,881,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(831,a,882,a)].
% 8.48/8.79 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(831,a,883,a)].
% 8.48/8.79 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(831,a,884,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(831,a,885,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(831,a,886,a)].
% 8.48/8.79 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(831,a,887,a)].
% 8.48/8.79 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(831,a,888,a)].
% 8.48/8.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(831,a,889,a)].
% 8.48/8.79 890 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(890,a,832,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(890,a,833,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(890,a,834,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(890,a,835,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(890,a,836,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(890,a,837,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(890,a,838,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(890,a,839,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(890,a,840,a)].
% 8.48/8.79 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(890,a,841,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(890,a,842,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(890,a,843,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(890,a,844,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(890,a,845,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(890,a,846,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(890,a,847,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(890,a,848,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(890,a,849,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(890,a,850,a)].
% 8.48/8.79 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(890,a,851,a)].
% 8.48/8.79 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(890,a,852,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(890,a,853,a)].
% 8.48/8.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(890,a,854,a)].
% 8.57/8.80 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(890,a,855,b)].
% 8.57/8.80 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(890,a,856,b)].
% 8.57/8.80 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(890,a,857,a)].
% 8.57/8.80 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(890,a,858,a)].
% 8.57/8.80 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(890,a,859,a)].
% 8.57/8.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(890,a,860,a)].
% 8.57/8.80 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(890,a,861,a)].
% 8.57/8.80 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(890,a,862,a)].
% 8.57/8.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(890,a,863,a)].
% 8.57/8.80 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(890,a,864,a)].
% 8.57/8.80 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(890,a,865,a)].
% 8.57/8.80 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(890,a,866,a)].
% 8.57/8.80 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(890,a,867,a)].
% 8.57/8.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(890,a,868,a)].
% 8.57/8.80 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(890,a,869,a)].
% 8.57/8.80 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(890,a,870,a)].
% 8.57/8.80 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(890,a,871,a)].
% 8.57/8.80 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(890,a,872,a)].
% 8.57/8.80 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(890,a,873,a)].
% 8.57/8.80 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(890,a,874,a)].
% 8.57/8.80 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(890,a,875,a)].
% 8.57/8.80 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(890,a,876,a)].
% 8.57/8.80 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(890,a,877,a)].
% 8.57/8.80 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(890,a,878,a)].
% 8.57/8.80 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(890,a,879,a)].
% 8.57/8.80 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(890,a,880,a)].
% 8.57/8.80 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(890,a,881,a)].
% 8.57/8.80 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(890,a,882,a)].
% 8.57/8.80 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(890,a,883,a)].
% 8.57/8.80 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(890,a,884,a)].
% 8.57/8.80 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(890,a,885,a)].
% 8.57/8.81 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(890,a,886,a)].
% 8.57/8.81 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(890,a,887,a)].
% 8.57/8.81 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(890,a,888,a)].
% 8.57/8.81 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)). [resolve(890,a,889,a)].
% 8.57/8.81 891 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(891,b,832,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(891,b,833,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(891,b,834,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(891,b,835,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,836,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,837,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(891,b,838,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,839,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,840,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(891,b,842,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,843,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,844,a)].
% 8.57/8.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(891,b,845,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,846,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,847,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(891,b,848,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(891,b,849,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(891,b,850,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,851,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(891,b,852,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(891,b,853,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(891,b,854,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(891,b,855,b)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(891,b,856,b)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(891,b,857,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(891,b,858,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(891,b,859,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(891,b,860,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(891,b,861,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(891,b,862,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(891,b,863,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(891,b,864,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(891,b,865,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,866,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(891,b,867,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(891,b,868,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(891,b,869,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(891,b,870,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,871,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(891,b,872,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(891,b,873,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(891,b,874,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(891,b,875,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(891,b,876,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,877,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,878,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,879,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(891,b,880,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(891,b,881,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(891,b,882,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(891,b,883,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(891,b,884,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(891,b,885,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(891,b,886,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,887,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(891,b,888,a)].
% 8.57/8.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(891,b,889,a)].
% 8.57/8.83 892 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 8.57/8.83 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(892,a,831,a)].
% 8.57/8.83 Derived: class_LOrder_Olorder(tc_nat). [resolve(892,a,890,a)].
% 8.57/8.83 Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(892,a,891,b)].
% 8.57/8.83 893 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 8.57/8.83 Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(893,a,831,a)].
% 8.57/8.83 Derived: class_LOrder_Ojoin__semilorder(tc_nat). [resolve(893,a,890,a)].
% 8.57/8.83 Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(893,a,891,b)].
% 8.57/8.83 894 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 8.57/8.83 Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(894,a,831,a)].
% 8.57/8.83 Derived: class_LOrder_Omeet__semilorder(tc_nat). [resolve(894,a,890,a)].
% 8.57/8.83 Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(894,a,891,b)].
% 8.57/8.83 895 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 8.57/8.83 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(895,a,831,a)].
% 8.57/8.83 Derived: class_Orderings_Oord(tc_nat). [resolve(895,a,890,a)].
% 8.57/8.83 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(895,a,891,b)].
% 8.57/8.83 896 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 8.57/8.83 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(896,a,831,a)].
% 8.57/8.83 Derived: class_Orderings_Oorder(tc_nat). [resolve(896,a,890,a)].
% 8.57/8.83 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(896,a,891,b)].
% 8.57/8.83 897 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) # label(axiom). [assumption].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(897,b,832,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(897,b,833,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(897,b,834,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(897,b,835,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,836,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,837,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(897,b,838,a)].
% 8.57/8.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,839,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,840,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,841,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(897,b,842,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,843,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,844,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(897,b,845,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,846,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,847,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(897,b,848,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(897,b,849,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(897,b,850,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,851,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(897,b,852,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(897,b,853,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(897,b,854,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(897,b,855,b)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(897,b,856,b)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(897,b,857,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(897,b,858,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(897,b,859,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(897,b,860,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(897,b,861,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(897,b,862,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(897,b,863,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(897,b,864,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(897,b,865,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(897,b,866,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(897,b,867,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(897,b,868,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(897,b,869,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(897,b,870,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(897,b,871,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(897,b,872,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(897,b,873,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(897,b,874,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(897,b,875,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(897,b,876,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(897,b,877,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(897,b,878,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(897,b,879,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(897,b,880,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(897,b,881,a)].
% 8.57/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(897,b,882,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(897,b,883,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(897,b,884,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(897,b,885,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(897,b,886,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(897,b,887,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(897,b,888,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(897,b,889,a)].
% 8.57/8.85 898 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(898,b,832,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(898,b,833,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(898,b,834,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(898,b,835,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(898,b,836,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(898,b,837,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(898,b,838,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(898,b,839,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(898,b,840,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(898,b,841,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(898,b,842,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(898,b,843,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(898,b,844,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(898,b,845,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(898,b,846,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(898,b,847,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(898,b,848,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(898,b,849,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(898,b,850,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(898,b,851,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(898,b,852,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(898,b,853,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(898,b,854,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(898,b,855,b)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(898,b,856,b)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(898,b,857,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(898,b,858,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(898,b,859,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(898,b,860,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(898,b,861,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(898,b,862,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(898,b,863,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(898,b,864,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(898,b,865,a)].
% 8.57/8.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B. [resolve(898,b,866,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(898,b,867,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(898,b,868,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(898,b,869,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(898,b,870,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B. [resolve(898,b,871,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(898,b,872,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(898,b,873,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(898,b,874,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(898,b,875,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(898,b,876,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(898,b,877,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(898,b,878,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(898,b,879,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(898,b,880,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(898,b,881,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(898,b,882,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(898,b,883,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(898,b,884,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(898,b,885,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(898,b,886,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(898,b,887,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(898,b,888,a)].
% 8.57/8.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(898,b,889,a)].
% 8.57/8.86 899 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(899,b,832,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(899,b,833,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(899,b,834,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(899,b,835,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(899,b,836,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(899,b,837,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(899,b,838,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(899,b,839,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(899,b,840,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(899,b,841,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(899,b,842,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(899,b,843,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(899,b,844,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(899,b,845,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(899,b,846,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(899,b,847,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(899,b,848,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(899,b,849,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(899,b,850,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(899,b,851,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(899,b,852,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(899,b,853,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(899,b,854,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(899,b,855,b)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(899,b,856,b)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(899,b,857,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(899,b,858,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(899,b,859,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(899,b,860,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(899,b,861,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(899,b,862,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(899,b,863,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(899,b,864,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(899,b,865,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(899,b,866,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(899,b,867,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(899,b,868,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(899,b,869,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(899,b,870,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(899,b,871,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(899,b,872,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(899,b,873,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(899,b,874,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(899,b,875,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(899,b,876,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(899,b,877,a)].
% 8.57/8.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(899,b,878,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(899,b,879,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(899,b,880,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(899,b,881,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(899,b,882,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(899,b,883,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(899,b,884,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(899,b,885,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(899,b,886,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(899,b,887,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(899,b,888,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(899,b,889,a)].
% 8.57/8.88 900 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(900,b,832,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(900,b,833,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(900,b,834,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(900,b,835,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,836,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,837,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(900,b,838,a)].
% 8.57/8.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,839,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,840,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,841,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(900,b,842,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,843,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,844,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(900,b,845,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,846,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,847,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(900,b,848,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(900,b,849,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(900,b,850,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,851,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(900,b,852,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(900,b,853,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(900,b,854,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(900,b,855,b)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(900,b,856,b)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(900,b,857,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(900,b,858,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(900,b,859,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(900,b,860,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(900,b,861,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(900,b,862,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(900,b,863,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(900,b,864,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(900,b,865,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(900,b,866,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(900,b,867,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(900,b,868,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(900,b,869,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(900,b,870,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(900,b,871,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(900,b,872,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(900,b,873,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(900,b,874,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(900,b,875,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(900,b,876,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(900,b,877,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(900,b,878,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(900,b,879,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(900,b,880,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(900,b,881,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(900,b,882,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(900,b,883,a)].
% 8.66/8.89 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(900,b,884,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(900,b,885,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(900,b,886,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(900,b,887,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(900,b,888,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(900,b,889,a)].
% 8.66/8.90 901 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(901,b,832,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(901,b,833,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(901,b,834,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(901,b,835,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,836,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,837,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(901,b,838,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,839,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,840,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,841,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(901,b,842,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,843,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,844,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(901,b,845,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,846,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,847,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(901,b,848,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(901,b,849,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(901,b,850,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,851,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(901,b,852,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(901,b,853,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(901,b,854,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(901,b,855,b)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(901,b,856,b)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(901,b,857,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(901,b,858,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(901,b,859,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(901,b,860,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(901,b,861,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(901,b,862,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(901,b,863,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(901,b,864,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(901,b,865,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(901,b,866,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(901,b,867,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(901,b,868,a)].
% 8.66/8.90 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(901,b,869,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(901,b,870,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(901,b,871,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(901,b,872,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(901,b,873,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(901,b,874,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(901,b,875,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(901,b,876,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(901,b,877,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(901,b,878,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(901,b,879,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(901,b,880,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(901,b,881,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(901,b,882,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(901,b,883,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(901,b,884,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(901,b,885,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(901,b,886,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(901,b,887,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(901,b,888,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(901,b,889,a)].
% 8.66/8.91 902 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(902,b,832,a)].
% 8.66/8.91 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(902,b,833,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(902,b,834,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(902,b,835,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,836,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,837,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(902,b,838,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,839,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,840,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,841,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(902,b,842,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,843,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,844,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(902,b,845,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,846,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,847,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(902,b,848,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(902,b,849,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(902,b,850,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,851,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(902,b,852,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(902,b,853,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(902,b,854,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(902,b,855,b)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(902,b,856,b)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(902,b,857,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(902,b,858,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(902,b,859,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(902,b,860,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(902,b,861,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(902,b,862,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(902,b,863,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(902,b,864,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(902,b,865,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(902,b,866,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(902,b,867,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(902,b,868,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(902,b,869,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(902,b,870,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(902,b,871,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(902,b,872,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(902,b,873,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(902,b,874,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(902,b,875,a)].
% 8.66/8.92 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(902,b,876,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(902,b,877,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(902,b,878,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(902,b,879,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(902,b,880,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(902,b,881,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(902,b,882,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(902,b,883,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(902,b,884,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(902,b,885,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(902,b,886,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(902,b,887,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(902,b,888,a)].
% 8.66/8.93 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(902,b,889,a)].
% 8.66/8.93 903 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(903,b,832,a)].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(903,b,833,a)].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(903,b,834,a)].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(903,b,835,a)].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,836,a)].
% 8.66/8.93 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,837,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(903,b,838,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,839,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,840,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,841,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(903,b,842,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,843,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,844,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(903,b,845,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,846,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,847,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(903,b,848,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(903,b,849,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(903,b,850,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,851,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(903,b,852,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(903,b,853,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(903,b,854,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(903,b,855,b)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(903,b,856,b)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(903,b,857,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(903,b,858,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(903,b,859,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(903,b,860,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(903,b,861,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(903,b,862,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(903,b,863,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(903,b,864,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(903,b,865,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(903,b,866,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(903,b,867,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(903,b,868,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(903,b,869,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(903,b,870,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(903,b,871,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(903,b,872,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(903,b,873,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(903,b,874,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(903,b,875,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(903,b,876,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(903,b,877,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(903,b,878,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(903,b,879,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(903,b,880,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(903,b,881,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(903,b,882,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(903,b,883,a)].
% 8.66/8.94 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(903,b,884,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(903,b,885,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(903,b,886,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(903,b,887,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(903,b,888,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(903,b,889,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(903,b,892,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(903,b,893,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(903,b,894,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(903,b,895,a)].
% 8.66/8.95 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(903,b,896,a)].
% 8.66/8.95 904 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Omax(B,C,A),A) # label(cls_Orderings_Ole__maxI1_0) # label(axiom). [assumption].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(904,a,831,a)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(904,a,890,a)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(904,a,891,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(904,a,897,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(904,a,898,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(904,a,899,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(904,a,900,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(904,a,901,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(904,a,902,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(904,a,903,b)].
% 8.66/8.95 905 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Omax(C,B,A),A) # label(cls_Orderings_Ole__maxI2_0) # label(axiom). [assumption].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(905,a,831,a)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(905,a,890,a)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(905,a,891,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(905,a,897,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(905,a,898,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(905,a,899,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(905,a,900,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(905,a,901,b)].
% 8.66/8.95 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(905,a,902,b)].
% 8.97/9.21 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(905,a,903,b)].
% 8.97/9.21 906 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 8.97/9.21 907 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_1 # label(cls_IntArith_Oabs__minus__one_0) # label(axiom). [assumption].
% 8.97/9.21 908 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A),A) = c_1 # label(cls_IntArith_Oabs__power__minus__one_0) # label(axiom). [assumption].
% 8.97/9.21 909 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__10_0) # label(axiom). [assumption].
% 8.97/9.21 910 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__10_1) # label(axiom). [assumption].
% 8.97/9.21 911 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__11_0) # label(axiom). [assumption].
% 8.97/9.21 912 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_less(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__11_1) # label(axiom). [assumption].
% 8.97/9.21 913 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__12_0) # label(axiom). [assumption].
% 8.97/9.21 914 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__12_1) # label(axiom). [assumption].
% 8.97/9.21 915 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_1,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__13_0) # label(axiom). [assumption].
% 8.97/9.21 916 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__13_1) # label(axiom). [assumption].
% 8.97/9.21 917 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_0) # label(axiom). [assumption].
% 8.97/9.21 918 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_1) # label(axiom). [assumption].
% 8.97/9.21 919 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | -c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_0) # label(axiom). [assumption].
% 8.97/9.21 920 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_1) # label(axiom). [assumption].
% 8.97/9.21 921 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_0) # label(axiom). [assumption].
% 8.97/9.21 922 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_1) # label(axiom). [assumption].
% 8.97/9.21 923 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_0) # label(axiom). [assumption].
% 8.97/9.21 924 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_1) # label(axiom). [assumption].
% 8.97/9.21 925 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_1,A) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A) # label(cls_IntArith_Oarith__special__1_0) # label(axiom). [assumption].
% 8.97/9.21 926 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),B),A) # label(cls_IntArith_Oarith__special__2_0) # label(axiom). [assumption].
% 8.97/9.21 927 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),A) # label(cls_IntArith_Oarith__special__3_0) # label(axiom). [assumption].
% 8.97/9.21 928 -class_Numeral_Onumber__ring(A) | c_minus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A) # label(cls_IntArith_Oarith__special__4_0) # label(axiom). [assumption].
% 8.97/9.21 929 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A) # label(cls_IntArith_Oarith__special__5_0) # label(axiom). [assumption].
% 8.97/9.21 930 -class_Numeral_Onumber__ring(A) | c_0 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__6_0) # label(axiom). [assumption].
% 8.97/9.21 931 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_0 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__6_1) # label(axiom). [assumption].
% 8.97/9.21 932 -class_Numeral_Onumber__ring(A) | c_1 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__7_0) # label(axiom). [assumption].
% 8.97/9.21 933 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_1 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__7_1) # label(axiom). [assumption].
% 8.97/9.21 934 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__8_0) # label(axiom). [assumption].
% 8.97/9.21 935 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_Numeral_Onumber__of(B,A) = c_0 # label(cls_IntArith_Oarith__special__8_1) # label(axiom). [assumption].
% 8.97/9.21 936 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__9_0) # label(axiom). [assumption].
% 8.97/9.21 937 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_Numeral_Onumber__of(B,A) = c_1 # label(cls_IntArith_Oarith__special__9_1) # label(axiom). [assumption].
% 8.97/9.21 938 -class_Numeral_Onumber__ring(A) | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_IntArith_Oof__int__m1_0) # label(axiom). [assumption].
% 8.97/9.21 939 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_0 # label(cls_NatBin_Oof__nat__number__of__eq_0) # label(axiom). [assumption].
% 8.97/9.21 940 -class_Numeral_Onumber__ring(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_Numeral_Onumber__of(B,A) # label(cls_NatBin_Oof__nat__number__of__eq_1) # label(axiom). [assumption].
% 8.97/9.21 941 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_NatSimprocs_Odivide__minus1_0) # label(axiom). [assumption].
% 8.97/9.21 942 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | c_less(c_0,c_divide(B,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A),A),A) # label(cls_NatSimprocs_Ohalf__gt__zero_0) # label(axiom). [assumption].
% 8.97/9.21 943 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(c_divide(c_1,B,A),A) # label(cls_NatSimprocs_Ominus1__divide_0) # label(axiom). [assumption].
% 8.97/9.21 944 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_minus(C,c_Numeral_Onumber__of(D,A),A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(D)),A),C,A) # label(cls_Numeral_Oadd__number__of__diff2_0) # label(axiom). [assumption].
% 8.97/9.21 945 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_plus(c_Numeral_Onumber__of(C,A),D,A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A),D,A) # label(cls_Numeral_Oadd__number__of__left_0) # label(axiom). [assumption].
% 8.97/9.21 946 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__1_0) # label(axiom). [assumption].
% 8.97/9.21 947 -class_Numeral_Onumber__ring(A) | c_uminus(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A) # label(cls_Numeral_Obin__arith__extra__simps__2_0) # label(axiom). [assumption].
% 8.97/9.21 948 -class_Numeral_Onumber__ring(A) | c_uminus(c_1,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Numeral_Obin__arith__extra__simps__3_0) # label(axiom). [assumption].
% 8.97/9.21 949 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__4_0) # label(axiom). [assumption].
% 8.97/9.21 950 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A) # label(cls_Numeral_Obin__arith__extra__simps__5_0) # label(axiom). [assumption].
% 8.97/9.21 951 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_uminus(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__arith__extra__simps__6_0) # label(axiom). [assumption].
% 8.97/9.21 952 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(B,A) # label(cls_Numeral_Obin__arith__extra__simps__6_1) # label(axiom). [assumption].
% 8.97/9.21 953 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__11_0) # label(axiom). [assumption].
% 8.97/9.21 954 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__12_0) # label(axiom). [assumption].
% 8.97/9.21 955 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) # label(cls_Numeral_Obin__rel__simps__12_1) # label(axiom). [assumption].
% 8.97/9.21 956 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_0) # label(axiom). [assumption].
% 8.97/9.21 957 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_1) # label(axiom). [assumption].
% 8.97/9.21 958 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_Numeral_Onumber__of(C,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__1_0) # label(axiom). [assumption].
% 8.97/9.21 959 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_Numeral_Onumber__of(B,A) = c_Numeral_Onumber__of(C,A) # label(cls_Numeral_Obin__rel__simps__1_1) # label(axiom). [assumption].
% 8.97/9.21 960 -class_Numeral_Onumber__ring(A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__2_0) # label(axiom). [assumption].
% 8.97/9.21 961 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__3_0) # label(axiom). [assumption].
% 8.97/9.21 962 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__4_0) # label(axiom). [assumption].
% 8.97/9.21 963 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) # label(cls_Numeral_Obin__rel__simps__4_1) # label(axiom). [assumption].
% 8.97/9.21 964 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB1),A),A) # label(cls_Numeral_Obin__rel__simps__5_0) # label(axiom). [assumption].
% 8.97/9.21 965 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__6_0) # label(axiom). [assumption].
% 8.97/9.21 966 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) # label(cls_Numeral_Obin__rel__simps__6_1) # label(axiom). [assumption].
% 8.97/9.21 967 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__7_0) # label(axiom). [assumption].
% 8.97/9.21 968 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(c_Numeral_Onumber__of(B,A),A),C,A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A),C,A) # label(cls_Numeral_Ominus__number__of__mult_0) # label(axiom). [assumption].
% 8.97/9.21 969 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1_0) # label(axiom). [assumption].
% 8.97/9.21 970 -class_Numeral_Onumber__ring(A) | c_times(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1__right_0) # label(axiom). [assumption].
% 8.97/9.21 971 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_times(c_Numeral_Onumber__of(C,A),D,A),A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A),D,A) # label(cls_Numeral_Omult__number__of__left_0) # label(axiom). [assumption].
% 8.97/9.21 972 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OPls,A) = c_0 # label(cls_Numeral_Onumeral__0__eq__0_0) # label(axiom). [assumption].
% 8.97/9.21 973 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A) = c_1 # label(cls_Numeral_Onumeral__1__eq__1_0) # label(axiom). [assumption].
% 8.97/9.21 974 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_1 # label(cls_Parity_Oneg__one__even__power_0) # label(axiom). [assumption].
% 8.97/9.21 975 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Parity_Oneg__one__odd__power_0) # label(axiom). [assumption].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(906,a,907,a)].
% 8.97/9.21 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(906,a,908,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,909,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,910,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,911,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,912,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,913,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(906,a,914,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,915,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(906,a,916,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,917,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,918,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,919,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,920,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(906,a,921,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(906,a,922,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(906,a,923,a)].
% 8.97/9.21 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(906,a,924,a)].
% 8.97/9.21 Derived: c_plus(c_1,c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint). [resolve(906,a,925,a)].
% 8.97/9.22 Derived: c_plus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A),tc_IntDef_Oint). [resolve(906,a,926,a)].
% 8.97/9.22 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint). [resolve(906,a,927,a)].
% 8.97/9.22 Derived: c_minus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint). [resolve(906,a,928,a)].
% 8.97/9.22 Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint). [resolve(906,a,929,a)].
% 8.97/9.22 Derived: c_0 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,930,a)].
% 8.97/9.22 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_0 = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(906,a,931,a)].
% 8.97/9.22 Derived: c_1 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,932,a)].
% 8.97/9.22 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_1 = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(906,a,933,a)].
% 8.97/9.22 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,934,a)].
% 8.97/9.22 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_0. [resolve(906,a,935,a)].
% 8.97/9.22 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,936,a)].
% 8.97/9.22 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_1. [resolve(906,a,937,a)].
% 8.97/9.22 Derived: c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(906,a,938,a)].
% 8.97/9.22 Derived: -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_0. [resolve(906,a,939,a)].
% 8.97/9.22 Derived: c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(906,a,940,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(906,a,941,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_divide(A,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,942,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_divide(c_1,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,943,a)].
% 8.97/9.22 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(C)),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(906,a,944,a)].
% 8.97/9.22 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(906,a,945,a)].
% 8.97/9.22 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint). [resolve(906,a,946,a)].
% 8.97/9.22 Derived: c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint). [resolve(906,a,947,a)].
% 8.97/9.22 Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(906,a,948,a)].
% 8.97/9.22 Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint). [resolve(906,a,949,a)].
% 8.97/9.22 Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint). [resolve(906,a,950,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,951,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(906,a,952,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,953,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,954,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,955,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,956,a)].
% 8.97/9.22 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,957,a)].
% 8.97/9.22 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_Numeral_Onumber__of(B,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,958,a)].
% 8.97/9.22 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_Numeral_Onumber__of(B,tc_IntDef_Oint). [resolve(906,a,959,a)].
% 8.97/9.22 Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,960,a)].
% 8.97/9.23 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,961,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,962,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,963,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB1),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,964,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,965,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,966,a)].
% 8.97/9.23 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(906,a,967,a)].
% 8.97/9.23 Derived: c_times(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(906,a,968,a)].
% 8.97/9.23 Derived: c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(906,a,969,a)].
% 8.97/9.23 Derived: c_times(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(906,a,970,a)].
% 8.97/9.23 Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(906,a,971,a)].
% 8.97/9.23 Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0. [resolve(906,a,972,a)].
% 8.97/9.23 Derived: c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_IntDef_Oint) = c_1. [resolve(906,a,973,a)].
% 8.97/9.23 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(906,a,974,a)].
% 8.97/9.23 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(906,a,975,a)].
% 8.97/9.23 976 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom). [assumption].
% 8.97/9.23 977 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom). [assumption].
% 8.97/9.23 978 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom). [assumption].
% 8.97/9.23 979 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 8.97/9.23 980 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 8.97/9.23 981 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 8.97/9.23 982 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 8.97/9.29 Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(982,a,906,a)].
% 8.97/9.29 983 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom). [assumption].
% 8.97/9.29 984 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom). [assumption].
% 8.97/9.29 Derived: class_Numeral_Onumber(tc_IntDef_Oint). [resolve(984,a,906,a)].
% 8.97/9.29 985 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 8.97/9.29 986 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom). [assumption].
% 8.97/9.29 987 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 8.97/9.29 988 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(6,b,1,a)].
% 8.97/9.29 989 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(6,b,3,a)].
% 8.97/9.29 990 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(9,a,6,b)].
% 8.97/9.29 991 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(10,a,6,b)].
% 8.97/9.29 992 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(79,a,45,b)].
% 8.97/9.29 993 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(80,a,45,b)].
% 8.97/9.29 994 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(81,b,45,b)].
% 8.97/9.29 995 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(82,b,45,b)].
% 8.97/9.29 996 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(83,a,88,b)].
% 8.97/9.29 997 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(89,a,88,b)].
% 8.97/9.29 998 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B. [resolve(114,b,108,a)].
% 8.97/9.29 999 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B. [resolve(114,b,111,a)].
% 8.97/9.29 1000 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(116,a,114,b)].
% 8.97/9.29 1001 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(136,b,131,b)].
% 8.97/9.29 1002 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(136,b,133,b)].
% 8.97/9.29 1003 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(171,a,136,b)].
% 8.97/9.29 1004 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(172,a,136,b)].
% 8.97/9.29 1005 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(201,b,177,b)].
% 8.97/9.29 1006 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(202,b,177,b)].
% 8.97/9.29 1007 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(203,b,177,b)].
% 8.97/9.29 1008 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(204,b,177,b)].
% 8.97/9.29 1009 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(205,b,177,b)].
% 8.97/9.29 1010 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(206,b,177,b)].
% 8.97/9.29 1011 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(240,a,211,b)].
% 8.97/9.29 1012 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(241,a,211,b)].
% 8.97/9.29 1013 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(284,b,253,b)].
% 8.97/9.29 1014 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(285,b,253,b)].
% 8.97/9.29 1015 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(286,b,253,b)].
% 8.97/9.29 1016 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(287,b,253,b)].
% 9.10/9.31 1017 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0. [resolve(293,b,288,a)].
% 9.10/9.31 1018 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0. [resolve(293,b,290,a)].
% 9.10/9.31 1019 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(338,b,331,b)].
% 9.10/9.31 1020 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(338,b,333,b)].
% 9.10/9.31 1021 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(338,b,334,a)].
% 9.10/9.31 1022 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,335,a)].
% 9.10/9.31 1023 -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(338,b,336,a)].
% 9.10/9.31 1024 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(354,a,338,b)].
% 9.10/9.31 1025 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(355,a,338,b)].
% 9.10/9.31 1026 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(374,a,338,b)].
% 9.10/9.31 1027 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(375,a,338,b)].
% 9.10/9.31 1028 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(376,c,338,b)].
% 9.10/9.31 1029 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(377,c,338,b)].
% 9.10/9.31 1030 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(411,b,383,b)].
% 9.10/9.31 1031 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(412,b,383,b)].
% 9.10/9.31 1032 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 9.10/9.31 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1032,b,906,a)].
% 9.10/9.31 1033 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(454,b,424,b)].
% 9.10/9.31 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1033,b,906,a)].
% 9.10/9.31 1034 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A). [resolve(459,b,424,b)].
% 9.10/9.31 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1034,b,906,a)].
% 9.10/9.31 1035 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(460,b,424,b)].
% 9.10/9.31 1036 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Numeral_Onumber__ring(D). [resolve(461,b,424,b)].
% 9.10/9.31 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1036,b,906,a)].
% 9.10/9.31 1037 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Numeral_Onumber__ring(C). [resolve(462,b,424,b)].
% 9.10/9.31 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1037,b,906,a)].
% 9.10/9.31 1038 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(467,a,424,b)].
% 9.10/9.31 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1038,c,906,a)].
% 9.10/9.31 1039 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(468,a,424,b)].
% 9.10/9.31 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1039,c,906,a)].
% 9.10/9.34 1040 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(469,a,424,b)].
% 9.10/9.34 Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint). [resolve(1040,b,906,a)].
% 9.10/9.34 1041 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(470,a,424,b)].
% 9.10/9.34 Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1041,b,906,a)].
% 9.10/9.34 1042 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(471,a,424,b)].
% 9.10/9.34 Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1042,b,906,a)].
% 9.10/9.34 1043 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(472,b,424,b)].
% 9.10/9.34 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1043,b,906,a)].
% 9.10/9.34 1044 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A). [resolve(473,b,424,b)].
% 9.10/9.34 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1044,b,906,a)].
% 9.10/9.34 1045 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(474,b,424,b)].
% 9.10/9.34 1046 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(475,b,424,b)].
% 9.10/9.34 1047 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(476,c,424,b)].
% 9.10/9.34 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1047,c,906,a)].
% 9.10/9.34 1048 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(477,c,424,b)].
% 9.10/9.34 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1048,c,906,a)].
% 9.10/9.34 1049 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(479,b,424,b)].
% 9.10/9.34 1050 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,424,b)].
% 9.10/9.34 1051 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(524,a,505,b)].
% 9.10/9.34 1052 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(525,a,505,b)].
% 9.10/9.34 1053 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(543,a,536,b)].
% 9.10/9.34 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(1053,b,906,a)].
% 9.10/9.34 1054 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(568,b,536,b)].
% 9.10/9.34 1055 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(569,b,536,b)].
% 9.10/9.34 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1055,b,906,a)].
% 9.10/9.34 1056 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(570,b,536,b)].
% 9.10/9.34 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1056,b,906,a)].
% 9.10/9.34 1057 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(571,b,536,b)].
% 9.10/9.34 1058 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(572,b,536,b)].
% 9.10/9.34 1059 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(663,b,615,b)].
% 9.10/9.34 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1059,b,906,a)].
% 9.10/9.34 1060 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(664,b,615,b)].
% 9.10/9.34 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1060,b,906,a)].
% 9.10/9.34 1061 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(666,b,615,b)].
% 9.10/9.34 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1061,b,906,a)].
% 9.10/9.34 1062 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(667,b,615,b)].
% 9.10/9.34 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1062,b,906,a)].
% 9.10/9.34 1063 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(681,b,668,a)].
% 9.10/9.34 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1063,a,906,a)].
% 9.10/9.34 1064 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(681,b,670,a)].
% 9.10/9.34 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1064,a,906,a)].
% 9.10/9.34 1065 -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(681,b,671,a)].
% 9.10/9.34 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1065,a,906,a)].
% 9.27/9.54 1066 -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(681,b,672,a)].
% 9.27/9.54 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1066,a,906,a)].
% 9.27/9.54 1067 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(681,b,673,a)].
% 9.27/9.54 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1067,a,906,a)].
% 9.27/9.54 1068 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(681,b,674,a)].
% 9.27/9.54 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1068,a,906,a)].
% 9.27/9.54 1069 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(681,b,675,a)].
% 9.27/9.54 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1069,a,906,a)].
% 9.27/9.54 1070 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(681,b,676,a)].
% 9.27/9.54 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1070,a,906,a)].
% 9.27/9.54 1071 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(681,b,677,a)].
% 9.27/9.54 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1071,a,906,a)].
% 9.27/9.54 1072 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A). [resolve(681,b,678,a)].
% 9.27/9.54 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1072,a,906,a)].
% 9.27/9.54 1073 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,681,b)].
% 9.27/9.54 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(1073,b,906,a)].
% 9.27/9.54 1074 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(823,a,734,a)].
% 9.27/9.54 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1074,a,906,a)].
% 9.27/9.54 1075 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 9.27/9.54 1076 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 9.27/9.54 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1075,a,1076,a)].
% 9.27/9.54 1077 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 9.27/9.54 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1077,a,1076,a)].
% 9.27/9.54 1078 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 9.27/9.54 1079 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 9.27/9.54 1080 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 9.27/9.54 Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1076,a)].
% 9.27/9.54 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1080,b,1078,a)].
% 9.27/9.54 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1080,b,1079,a)].
% 9.27/9.54 1081 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 9.27/9.54 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1076,a)].
% 9.27/9.54 1082 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 9.27/9.54 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1076,a)].
% 9.58/9.81 1083 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1076,a)].
% 9.58/9.81 1084 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1076,a)].
% 9.58/9.81 1085 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1076,a)].
% 9.58/9.81 1086 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1086,b,1076,a)].
% 9.58/9.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1086,b,1078,a)].
% 9.58/9.81 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1086,b,1079,a)].
% 9.58/9.81 1087 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1087,b,1076,a)].
% 9.58/9.81 1088 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1088,b,1076,a)].
% 9.58/9.81 1089 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1089,b,1076,a)].
% 9.58/9.81 1090 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_19) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1090,b,1076,a)].
% 9.58/9.81 1091 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1091,b,1076,a)].
% 9.58/9.81 1092 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_12) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1092,b,1076,a)].
% 9.58/9.81 1093 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 9.58/9.81 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1093,b,1076,a)].
% 9.58/9.81 1094 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(893,a,831,a)].
% 9.58/9.81 1095 class_LOrder_Ojoin__semilorder(tc_nat). [resolve(893,a,890,a)].
% 9.58/9.81 1096 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(893,a,891,b)].
% 9.58/9.81 1097 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(903,b,893,a)].
% 9.58/9.81 1098 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 9.58/9.81 1099 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 9.58/9.81 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1098,a,1099,a)].
% 9.58/9.83 1100 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 9.58/9.83 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1100,a,1099,a)].
% 9.58/9.83 1101 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1099,a)].
% 9.58/9.83 1102 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 9.58/9.83 1103 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 9.58/9.83 1104 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1099,a)].
% 9.58/9.83 1105 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1099,a)].
% 9.58/9.83 1106 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1099,a)].
% 9.58/9.83 1107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1099,a)].
% 9.58/9.83 1108 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1099,a)].
% 9.58/9.83 1109 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1109,b,1099,a)].
% 9.58/9.83 1110 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1110,b,1099,a)].
% 9.58/9.83 1111 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1111,b,1099,a)].
% 9.58/9.83 1112 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1112,b,1099,a)].
% 9.58/9.83 1113 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_20) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1113,b,1099,a)].
% 9.58/9.83 1114 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 9.58/9.83 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1114,b,1099,a)].
% 9.58/9.83 1115 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_13) # label(axiom). [assumption].
% 9.87/10.09 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1115,b,1099,a)].
% 9.87/10.09 1116 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 9.87/10.09 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1116,b,1099,a)].
% 9.87/10.09 1117 class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(894,a,831,a)].
% 9.87/10.09 1118 class_LOrder_Omeet__semilorder(tc_nat). [resolve(894,a,890,a)].
% 9.87/10.09 1119 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(894,a,891,b)].
% 9.87/10.09 1120 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(903,b,894,a)].
% 9.87/10.09 1121 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 9.87/10.09 1122 -class_Ring__and__Field_Oordered__semidom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B # label(cls_NatArith_Oof__nat__0__eq__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1123 -class_Ring__and__Field_Oordered__semidom(A) | c_0 = c_NatArith_Oof__nat(c_0,A) # label(cls_NatArith_Oof__nat__0__eq__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1124 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__le__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1125 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat) # label(cls_NatArith_Oof__nat__0__less__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1126 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__less__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1127 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1128 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_0,A) = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1129 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C # label(cls_NatArith_Oof__nat__eq__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1130 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0 # label(cls_NatArith_Oof__nat__le__0__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1131 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) # label(cls_NatArith_Oof__nat__le__0__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1132 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat) # label(cls_NatArith_Oof__nat__le__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1133 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__le__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1134 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A) # label(cls_NatArith_Oof__nat__less__0__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1135 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat) # label(cls_NatArith_Oof__nat__less__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1136 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__less__iff_1) # label(axiom). [assumption].
% 9.87/10.09 1137 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat) # label(cls_Power_Opower__increasing__iff_0) # label(axiom). [assumption].
% 9.87/10.09 1138 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) # label(cls_Power_Opower__increasing__iff_1) # label(axiom). [assumption].
% 9.87/10.10 1139 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D # label(cls_Power_Opower__inject__exp_0) # label(axiom). [assumption].
% 9.87/10.10 1140 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat) # label(cls_Power_Opower__strict__increasing__iff_0) # label(axiom). [assumption].
% 9.87/10.10 1141 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A) # label(cls_Power_Opower__strict__increasing__iff_1) # label(axiom). [assumption].
% 9.87/10.10 1142 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__le__zero_0) # label(axiom). [assumption].
% 9.87/10.10 1143 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__less__zero_0) # label(axiom). [assumption].
% 9.87/10.10 1144 -class_Ring__and__Field_Oordered__semidom(A) | c_less(c_0,c_1,A) # label(cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) # label(axiom). [assumption].
% 9.87/10.10 1145 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_1,A) # label(cls_Ring__and__Field_Ozero__le__one_0) # label(axiom). [assumption].
% 9.87/10.10 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(1121,a,1122,a)].
% 9.87/10.10 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(1121,a,1123,a)].
% 9.87/10.10 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1124,a)].
% 9.87/10.10 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(1121,a,1125,a)].
% 9.87/10.10 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1126,a)].
% 9.87/10.10 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1121,a,1127,a)].
% 9.87/10.10 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(1121,a,1128,a)].
% 9.87/10.10 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(1121,a,1129,a)].
% 9.87/10.10 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1121,a,1130,a)].
% 9.87/10.10 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1121,a,1131,a)].
% 9.87/10.10 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_nat). [resolve(1121,a,1132,a)].
% 9.87/10.10 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1133,a)].
% 9.87/10.10 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1121,a,1134,a)].
% 9.87/10.10 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_nat). [resolve(1121,a,1135,a)].
% 9.87/10.10 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1136,a)].
% 9.87/10.10 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_nat). [resolve(1121,a,1137,b)].
% 9.87/10.10 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1138,b)].
% 9.87/10.10 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | c_Nat_Opower(A,B,tc_IntDef_Oint) != c_Nat_Opower(A,C,tc_IntDef_Oint) | B = C. [resolve(1121,a,1139,b)].
% 9.87/10.10 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_less(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_nat). [resolve(1121,a,1140,b)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_IntDef_Oint) | c_less(c_Nat_Opower(C,A,tc_IntDef_Oint),c_Nat_Opower(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1121,a,1141,b)].
% 9.87/10.12 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(1121,a,1142,a)].
% 9.87/10.12 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(1121,a,1143,a)].
% 9.87/10.12 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(1121,a,1144,a)].
% 9.87/10.12 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(1121,a,1145,a)].
% 9.87/10.12 1146 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 9.87/10.12 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(1146,a,1122,a)].
% 9.87/10.12 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(1146,a,1123,a)].
% 9.87/10.12 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1146,a,1124,a)].
% 9.87/10.12 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat). [resolve(1146,a,1125,a)].
% 9.87/10.12 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(1146,a,1126,a)].
% 9.87/10.12 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(1146,a,1127,a)].
% 9.87/10.12 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(1146,a,1128,a)].
% 9.87/10.12 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(1146,a,1129,a)].
% 9.87/10.12 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(1146,a,1130,a)].
% 9.87/10.12 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(1146,a,1131,a)].
% 9.87/10.12 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1146,a,1132,a)].
% 9.87/10.12 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(1146,a,1133,a)].
% 9.87/10.12 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat). [resolve(1146,a,1134,a)].
% 9.87/10.12 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1146,a,1135,a)].
% 9.87/10.12 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(1146,a,1136,a)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1146,a,1137,b)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat). [resolve(1146,a,1138,b)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | c_Nat_Opower(A,B,tc_nat) != c_Nat_Opower(A,C,tc_nat) | B = C. [resolve(1146,a,1139,b)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_less(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1146,a,1140,b)].
% 9.87/10.12 Derived: -class_Power_Orecpower(tc_nat) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_nat) | c_less(c_Nat_Opower(C,A,tc_nat),c_Nat_Opower(C,B,tc_nat),tc_nat). [resolve(1146,a,1141,b)].
% 9.87/10.12 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(1146,a,1142,a)].
% 9.87/10.12 Derived: -c_less(c_1,c_0,tc_nat). [resolve(1146,a,1143,a)].
% 9.87/10.12 Derived: c_less(c_0,c_1,tc_nat). [resolve(1146,a,1144,a)].
% 9.87/10.12 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(1146,a,1145,a)].
% 9.87/10.12 1147 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semidom(A) # label(clsrel_Ring__and__Field_Oordered__field_60) # label(axiom). [assumption].
% 9.87/10.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1147,b,1122,a)].
% 9.87/10.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1147,b,1123,a)].
% 9.87/10.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1147,b,1124,a)].
% 9.87/10.12 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat). [resolve(1147,b,1125,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1147,b,1126,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1147,b,1127,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1147,b,1128,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1147,b,1129,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1147,b,1130,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1147,b,1131,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat). [resolve(1147,b,1132,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(1147,b,1133,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1147,b,1134,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat). [resolve(1147,b,1135,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(1147,b,1136,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat). [resolve(1147,b,1137,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A). [resolve(1147,b,1138,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D. [resolve(1147,b,1139,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat). [resolve(1147,b,1140,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A). [resolve(1147,b,1141,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A). [resolve(1147,b,1142,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A). [resolve(1147,b,1143,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A). [resolve(1147,b,1144,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A). [resolve(1147,b,1145,a)].
% 9.87/10.13 1148 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__semidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_55) # label(axiom). [assumption].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(1148,b,1122,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(1148,b,1123,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1148,b,1124,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat). [resolve(1148,b,1125,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(1148,b,1126,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(1148,b,1127,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(1148,b,1128,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(1148,b,1129,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(1148,b,1130,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(1148,b,1131,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat). [resolve(1148,b,1132,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(1148,b,1133,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(1148,b,1134,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat). [resolve(1148,b,1135,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(1148,b,1136,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat). [resolve(1148,b,1137,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A). [resolve(1148,b,1138,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D. [resolve(1148,b,1139,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat). [resolve(1148,b,1140,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A). [resolve(1148,b,1141,b)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A). [resolve(1148,b,1142,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A). [resolve(1148,b,1143,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A). [resolve(1148,b,1144,a)].
% 9.87/10.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A). [resolve(1148,b,1145,a)].
% 9.87/10.13 1149 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 9.87/10.13 1150 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom). [assumption].
% 9.87/10.13 1151 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 9.87/10.13 1152 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom). [assumption].
% 9.87/10.13 1153 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 9.87/10.13 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1153,a,1148,b)].
% 9.87/10.13 1154 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 9.87/10.13 1155 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom). [assumption].
% 9.87/10.13 1156 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__semidom_24) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1156,a,1121,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1156,a,1146,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1147,b)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1148,b)].
% 9.87/10.14 1157 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__semidom_25) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1157,a,1121,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1157,a,1146,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1147,b)].
% 9.87/10.14 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1148,b)].
% 9.87/10.14 1158 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_26) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1121,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1158,a,1146,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1147,b)].
% 9.87/10.14 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1148,b)].
% 9.87/10.14 1159 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1147,b)].
% 9.87/10.14 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1148,b)].
% 9.87/10.14 1160 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__semidom_31) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1160,a,1121,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1160,a,1146,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1147,b)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1148,b)].
% 9.87/10.14 1161 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_32) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1161,a,1121,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1161,a,1146,a)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1161,a,1147,b)].
% 9.87/10.14 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1161,a,1148,b)].
% 9.87/10.14 1162 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_33) # label(axiom). [assumption].
% 9.87/10.14 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1162,a,1121,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1162,a,1146,a)].
% 9.87/10.14 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1162,a,1147,b)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1162,a,1148,b)].
% 9.87/10.16 1163 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_34) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1163,a,1121,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1163,a,1146,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1163,a,1147,b)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1163,a,1148,b)].
% 9.87/10.16 1164 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_35) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1164,a,1121,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1164,a,1146,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1164,a,1147,b)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1164,a,1148,b)].
% 9.87/10.16 1165 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_36) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1165,a,1121,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1165,a,1146,a)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1165,a,1147,b)].
% 9.87/10.16 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1165,a,1148,b)].
% 9.87/10.16 1166 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_37) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1166,a,1121,a)].
% 9.87/10.16 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1166,a,1146,a)].
% 9.87/10.16 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1166,a,1147,b)].
% 9.87/10.16 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1166,a,1148,b)].
% 9.87/10.16 1167 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1167,a,1147,b)].
% 9.87/10.16 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1167,a,1148,b)].
% 9.87/10.16 1168 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 9.87/10.16 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1168,a,1147,b)].
% 9.87/10.16 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1168,a,1148,b)].
% 9.87/10.16 1169 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 9.87/10.16 1170 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(31,b,1,a)].
% 9.87/10.16 1171 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(31,b,3,a)].
% 9.87/10.16 1172 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(81,b,69,b)].
% 10.00/10.22 1173 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(82,b,69,b)].
% 10.00/10.22 1174 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B. [resolve(127,b,108,a)].
% 10.00/10.22 1175 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B. [resolve(127,b,111,a)].
% 10.00/10.22 1176 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(127,b,117,a)].
% 10.00/10.22 1177 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A). [resolve(127,b,118,a)].
% 10.00/10.22 1178 -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(152,b,131,b)].
% 10.00/10.22 1179 -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(152,b,133,b)].
% 10.00/10.22 1180 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(171,a,152,b)].
% 10.00/10.22 1181 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(172,a,152,b)].
% 10.00/10.22 1182 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(201,b,194,b)].
% 10.00/10.22 1183 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(202,b,194,b)].
% 10.00/10.22 1184 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(203,b,194,b)].
% 10.00/10.22 1185 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(204,b,194,b)].
% 10.00/10.22 1186 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(240,a,226,b)].
% 10.00/10.22 1187 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(241,a,226,b)].
% 10.00/10.22 1188 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(247,b,226,b)].
% 10.00/10.22 1189 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(248,b,226,b)].
% 10.00/10.22 1190 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0. [resolve(306,b,288,a)].
% 10.00/10.22 1191 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0. [resolve(306,b,290,a)].
% 10.00/10.22 1192 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(322,a,306,b)].
% 10.00/10.22 1193 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(323,a,306,b)].
% 10.00/10.22 1194 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(517,a,514,b)].
% 10.00/10.22 1195 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(524,a,514,b)].
% 10.00/10.22 1196 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(525,a,514,b)].
% 10.00/10.22 1197 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(531,a,514,b)].
% 10.00/10.22 1198 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(571,b,552,b)].
% 10.00/10.22 1199 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(607,a,585,b)].
% 10.00/10.22 1200 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(608,a,585,b)].
% 10.00/10.22 1201 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(611,b,585,b)].
% 10.00/10.22 1202 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(697,b,668,a)].
% 10.00/10.22 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(1202,a,1146,a)].
% 10.00/10.22 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1202,a,1147,b)].
% 10.00/10.22 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1202,a,1148,b)].
% 10.00/10.22 1203 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(697,b,670,a)].
% 10.00/10.22 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(1203,a,1146,a)].
% 10.00/10.22 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1203,a,1147,b)].
% 10.00/10.23 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1203,a,1148,b)].
% 10.00/10.23 1204 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(697,b,671,a)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1204,a,1146,a)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1204,a,1147,b)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1204,a,1148,b)].
% 10.00/10.23 1205 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(697,b,672,a)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1205,a,1146,a)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1205,a,1147,b)].
% 10.00/10.23 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1205,a,1148,b)].
% 10.00/10.23 1206 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(697,b,673,a)].
% 10.00/10.23 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(1206,a,1146,a)].
% 10.00/10.23 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1206,a,1147,b)].
% 10.00/10.23 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1206,a,1148,b)].
% 10.00/10.23 1207 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(697,b,674,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(1207,a,1146,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1207,a,1147,b)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1207,a,1148,b)].
% 10.00/10.23 1208 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(697,b,675,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(1208,a,1146,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1208,a,1147,b)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1208,a,1148,b)].
% 10.00/10.23 1209 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(697,b,676,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(1209,a,1146,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1209,a,1147,b)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1209,a,1148,b)].
% 10.00/10.23 1210 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(697,b,677,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(1210,a,1146,a)].
% 10.00/10.23 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1210,a,1147,b)].
% 10.00/10.28 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1210,a,1148,b)].
% 10.00/10.28 1211 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(697,b,678,a)].
% 10.00/10.28 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(1211,a,1146,a)].
% 10.00/10.28 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1211,a,1147,b)].
% 10.00/10.28 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1211,a,1148,b)].
% 10.00/10.28 1212 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(728,b,697,b)].
% 10.00/10.28 Derived: class_HOL_Oone(tc_nat). [resolve(1212,b,1146,a)].
% 10.00/10.28 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1212,b,1147,b)].
% 10.00/10.28 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1212,b,1148,b)].
% 10.00/10.28 1213 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(820,a,734,a)].
% 10.00/10.28 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1213,a,1146,a)].
% 10.00/10.28 1214 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A). [resolve(820,a,741,a)].
% 10.00/10.28 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1214,a,1147,b)].
% 10.00/10.28 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1214,a,1148,b)].
% 10.00/10.28 1215 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(901,b,832,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(1215,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(1215,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1215,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1215,a,1148,b)].
% 10.00/10.28 1216 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(901,b,833,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(1216,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(1216,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1216,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1216,a,1148,b)].
% 10.00/10.28 1217 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(901,b,834,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1217,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(1217,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1217,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1217,a,1148,b)].
% 10.00/10.28 1218 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(901,b,835,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1218,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(1218,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1218,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1218,a,1148,b)].
% 10.00/10.28 1219 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,836,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1219,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1219,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1219,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1148,b)].
% 10.00/10.28 1220 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,837,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1220,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1220,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1220,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1220,a,1148,b)].
% 10.00/10.28 1221 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(901,b,838,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1221,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(1221,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1221,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1221,a,1148,b)].
% 10.00/10.28 1222 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,839,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1222,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1222,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1222,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1222,a,1148,b)].
% 10.00/10.28 1223 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(901,b,840,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1223,a,1121,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1223,a,1146,a)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1223,a,1147,b)].
% 10.00/10.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1223,a,1148,b)].
% 10.00/10.28 1224 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,841,a)].
% 10.00/10.28 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1224,a,1121,a)].
% 10.00/10.28 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1224,a,1146,a)].
% 10.00/10.28 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1224,a,1147,b)].
% 10.00/10.28 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1148,b)].
% 10.00/10.28 1225 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(901,b,842,a)].
% 10.00/10.28 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1225,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(1225,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1225,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1225,a,1148,b)].
% 10.00/10.29 1226 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,843,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1226,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1226,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1226,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1148,b)].
% 10.00/10.29 1227 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,844,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1227,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1227,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1227,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1227,a,1148,b)].
% 10.00/10.29 1228 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(901,b,845,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1228,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(1228,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1228,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1228,a,1148,b)].
% 10.00/10.29 1229 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,846,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1229,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1229,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1229,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1229,a,1148,b)].
% 10.00/10.29 1230 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(901,b,847,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1230,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1230,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1230,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1230,a,1148,b)].
% 10.00/10.29 1231 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(901,b,848,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(1231,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(1231,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1231,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1231,a,1148,b)].
% 10.00/10.29 1232 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(901,b,849,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1232,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(1232,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1232,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1232,a,1148,b)].
% 10.00/10.29 1233 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(901,b,850,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1233,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(1233,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1233,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1233,a,1148,b)].
% 10.00/10.29 1234 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(901,b,851,a)].
% 10.00/10.29 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1234,a,1121,a)].
% 10.00/10.29 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1234,a,1146,a)].
% 10.00/10.29 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1234,a,1147,b)].
% 10.00/10.29 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1234,a,1148,b)].
% 10.00/10.29 1235 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(901,b,852,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1235,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1235,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1235,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1235,a,1148,b)].
% 10.00/10.29 1236 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(901,b,853,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1236,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(1236,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(1236,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(1236,a,1148,b)].
% 10.00/10.29 1237 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(901,b,854,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1237,a,1121,a)].
% 10.00/10.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(1237,a,1146,a)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(1237,a,1147,b)].
% 10.00/10.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(1237,a,1148,b)].
% 10.00/10.29 1238 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(901,b,855,b)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(1238,a,1121,a)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(1238,a,1146,a)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1238,a,1147,b)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1238,a,1148,b)].
% 10.00/10.29 1239 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(901,b,856,b)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1239,a,1121,a)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(1239,a,1146,a)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1239,a,1147,b)].
% 10.00/10.29 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1239,a,1148,b)].
% 10.00/10.29 1240 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(901,b,857,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1240,a,1121,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1240,a,1146,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1240,a,1147,b)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1240,a,1148,b)].
% 10.00/10.29 1241 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(901,b,858,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1241,a,1121,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1241,a,1146,a)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1241,a,1147,b)].
% 10.00/10.29 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1241,a,1148,b)].
% 10.00/10.29 1242 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(901,b,859,a)].
% 10.00/10.29 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(1242,a,1121,a)].
% 10.00/10.29 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(1242,a,1146,a)].
% 10.00/10.29 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1242,a,1147,b)].
% 10.00/10.30 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1242,a,1148,b)].
% 10.00/10.30 1243 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(901,b,860,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1243,a,1121,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1243,a,1146,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1243,a,1147,b)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1243,a,1148,b)].
% 10.00/10.30 1244 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(901,b,861,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1244,a,1121,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1244,a,1146,a)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1244,a,1147,b)].
% 10.00/10.30 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1244,a,1148,b)].
% 10.00/10.30 1245 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(901,b,862,a)].
% 10.00/10.30 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1245,a,1121,a)].
% 10.00/10.30 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(1245,a,1146,a)].
% 10.00/10.30 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1245,a,1147,b)].
% 10.00/10.30 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1245,a,1148,b)].
% 10.00/10.30 1246 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(901,b,863,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1246,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1246,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1246,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1246,a,1148,b)].
% 10.00/10.30 1247 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(901,b,864,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1247,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1247,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1247,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1247,a,1148,b)].
% 10.00/10.30 1248 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(901,b,865,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1248,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(1248,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1248,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1248,a,1148,b)].
% 10.00/10.30 1249 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(901,b,866,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1249,a,1121,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1249,a,1146,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1249,a,1147,b)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1249,a,1148,b)].
% 10.00/10.30 1250 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(901,b,867,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(1250,a,1121,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(1250,a,1146,a)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1250,a,1147,b)].
% 10.00/10.30 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1250,a,1148,b)].
% 10.00/10.30 1251 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(901,b,868,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1251,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1251,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1251,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1251,a,1148,b)].
% 10.00/10.30 1252 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(901,b,869,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1252,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1252,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1252,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1252,a,1148,b)].
% 10.00/10.30 1253 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(901,b,870,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(1253,a,1121,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(1253,a,1146,a)].
% 10.00/10.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1253,a,1147,b)].
% 10.00/10.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1253,a,1148,b)].
% 10.00/10.30 1254 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(901,b,871,a)].
% 10.00/10.30 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1254,a,1121,a)].
% 10.00/10.30 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1254,a,1146,a)].
% 10.00/10.30 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1254,a,1147,b)].
% 10.09/10.30 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1254,a,1148,b)].
% 10.09/10.30 1255 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(901,b,872,a)].
% 10.09/10.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(1255,a,1121,a)].
% 10.09/10.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(1255,a,1146,a)].
% 10.09/10.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1255,a,1147,b)].
% 10.09/10.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1255,a,1148,b)].
% 10.09/10.30 1256 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(901,b,873,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1256,a,1121,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1256,a,1146,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1256,a,1147,b)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1256,a,1148,b)].
% 10.09/10.30 1257 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(901,b,874,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1257,a,1121,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1257,a,1146,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1257,a,1147,b)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1257,a,1148,b)].
% 10.09/10.30 1258 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(901,b,875,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1258,a,1121,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1258,a,1146,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1258,a,1147,b)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1258,a,1148,b)].
% 10.09/10.30 1259 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(901,b,876,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1259,a,1121,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1259,a,1146,a)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1259,a,1147,b)].
% 10.09/10.30 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1259,a,1148,b)].
% 10.09/10.30 1260 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(901,b,877,a)].
% 10.09/10.30 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1260,a,1121,a)].
% 10.09/10.30 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1260,a,1146,a)].
% 10.09/10.30 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1260,a,1147,b)].
% 10.09/10.30 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1260,a,1148,b)].
% 10.09/10.30 1261 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(901,b,878,a)].
% 10.09/10.30 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1261,a,1121,a)].
% 10.09/10.30 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1261,a,1146,a)].
% 10.09/10.30 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1261,a,1147,b)].
% 10.09/10.30 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1261,a,1148,b)].
% 10.09/10.30 1262 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(901,b,879,a)].
% 10.09/10.30 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1262,a,1121,a)].
% 10.09/10.30 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1262,a,1146,a)].
% 10.09/10.30 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1262,a,1147,b)].
% 10.09/10.30 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1262,a,1148,b)].
% 10.09/10.30 1263 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(901,b,880,a)].
% 10.09/10.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1263,a,1121,a)].
% 10.09/10.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1263,a,1146,a)].
% 10.09/10.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1263,a,1147,b)].
% 10.09/10.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1263,a,1148,b)].
% 10.09/10.30 1264 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(901,b,881,a)].
% 10.09/10.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1264,a,1121,a)].
% 10.09/10.30 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(1264,a,1146,a)].
% 10.09/10.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1264,a,1147,b)].
% 10.09/10.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1264,a,1148,b)].
% 10.09/10.30 1265 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(901,b,882,a)].
% 10.09/10.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(1265,a,1121,a)].
% 10.09/10.31 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(1265,a,1146,a)].
% 10.09/10.31 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1265,a,1147,b)].
% 10.09/10.31 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1265,a,1148,b)].
% 10.09/10.31 1266 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(901,b,883,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1266,a,1121,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1266,a,1146,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1266,a,1147,b)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1266,a,1148,b)].
% 10.09/10.31 1267 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(901,b,884,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1267,a,1121,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1267,a,1146,a)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1267,a,1147,b)].
% 10.09/10.31 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1267,a,1148,b)].
% 10.09/10.31 1268 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(901,b,885,a)].
% 10.09/10.31 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1268,a,1121,a)].
% 10.09/10.31 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(1268,a,1146,a)].
% 10.09/10.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1268,a,1147,b)].
% 10.09/10.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1268,a,1148,b)].
% 10.09/10.32 1269 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(901,b,886,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1269,a,1121,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(1269,a,1146,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1269,a,1147,b)].
% 10.09/10.32 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1269,a,1148,b)].
% 10.09/10.32 1270 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(901,b,887,a)].
% 10.09/10.32 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1270,a,1121,a)].
% 10.09/10.32 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1270,a,1146,a)].
% 10.09/10.32 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1270,a,1147,b)].
% 10.09/10.32 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1270,a,1148,b)].
% 10.09/10.32 1271 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(901,b,888,a)].
% 10.09/10.32 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1271,a,1121,a)].
% 10.09/10.32 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1271,a,1146,a)].
% 10.09/10.32 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1271,a,1147,b)].
% 10.09/10.32 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1271,a,1148,b)].
% 10.09/10.32 1272 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(901,b,889,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1272,a,1121,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)). [resolve(1272,a,1146,a)].
% 10.09/10.32 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1272,a,1147,b)].
% 10.09/10.32 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1272,a,1148,b)].
% 10.09/10.32 1273 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(904,a,901,b)].
% 10.09/10.32 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1273,b,1121,a)].
% 10.09/10.32 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(1273,b,1146,a)].
% 10.09/10.32 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1273,b,1147,b)].
% 10.19/10.49 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1273,b,1148,b)].
% 10.19/10.49 1274 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(905,a,901,b)].
% 10.19/10.49 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1274,b,1121,a)].
% 10.19/10.49 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(1274,b,1146,a)].
% 10.19/10.49 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1274,b,1147,b)].
% 10.19/10.49 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1274,b,1148,b)].
% 10.19/10.49 1275 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1091,b,1076,a)].
% 10.19/10.49 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1275,a,1121,a)].
% 10.19/10.49 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1275,a,1146,a)].
% 10.19/10.49 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1275,a,1147,b)].
% 10.19/10.49 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1275,a,1148,b)].
% 10.19/10.49 1276 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1114,b,1099,a)].
% 10.19/10.49 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1276,a,1121,a)].
% 10.19/10.49 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1276,a,1146,a)].
% 10.19/10.49 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1276,a,1147,b)].
% 10.19/10.49 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1276,a,1148,b)].
% 10.19/10.49 1277 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 10.19/10.49 1278 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_0) # label(axiom). [assumption].
% 10.19/10.49 1279 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_1) # label(axiom). [assumption].
% 10.19/10.49 1280 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_2) # label(axiom). [assumption].
% 10.19/10.49 1281 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_3) # label(axiom). [assumption].
% 10.19/10.49 1282 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_4) # label(axiom). [assumption].
% 10.19/10.49 1283 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_5) # label(axiom). [assumption].
% 10.19/10.49 1284 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_0) # label(axiom). [assumption].
% 10.19/10.49 1285 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_1) # label(axiom). [assumption].
% 10.19/10.49 1286 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_2) # label(axiom). [assumption].
% 10.19/10.49 1287 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_3) # label(axiom). [assumption].
% 10.19/10.49 1288 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_4) # label(axiom). [assumption].
% 10.19/10.49 1289 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_5) # label(axiom). [assumption].
% 10.19/10.49 1290 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_0) # label(axiom). [assumption].
% 10.19/10.49 1291 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_1) # label(axiom). [assumption].
% 10.19/10.49 1292 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_2) # label(axiom). [assumption].
% 10.19/10.49 1293 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_3) # label(axiom). [assumption].
% 10.19/10.49 1294 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_4) # label(axiom). [assumption].
% 10.19/10.49 1295 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_5) # label(axiom). [assumption].
% 10.19/10.49 1296 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_0) # label(axiom). [assumption].
% 10.19/10.49 1297 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_1) # label(axiom). [assumption].
% 10.19/10.49 1298 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_2) # label(axiom). [assumption].
% 10.19/10.49 1299 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_3) # label(axiom). [assumption].
% 10.19/10.49 1300 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_4) # label(axiom). [assumption].
% 10.19/10.49 1301 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_5) # label(axiom). [assumption].
% 10.19/10.49 1302 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0 # label(cls_Ring__and__Field_Omult__eq__0__iff_0) # label(axiom). [assumption].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1277,a,1278,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1277,a,1279,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1280,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1281,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1282,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1283,b)].
% 10.19/10.49 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1277,a,1284,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1277,a,1285,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1286,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1287,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1288,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1289,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1277,a,1290,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,B,tc_IntDef_Oint). [resolve(1277,a,1291,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1277,a,1292,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1293,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1277,a,1294,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1295,b)].
% 10.29/10.50 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1277,a,1296,b)].
% 10.30/10.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint). [resolve(1277,a,1297,b)].
% 10.30/10.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1277,a,1298,b)].
% 10.30/10.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1299,b)].
% 10.30/10.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1277,a,1300,b)].
% 10.30/10.51 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1277,a,1301,b)].
% 10.30/10.51 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(1277,a,1302,a)].
% 10.30/10.51 1303 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__ring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_38) # label(axiom). [assumption].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A). [resolve(1303,b,1278,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A). [resolve(1303,b,1279,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(1303,b,1280,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1303,b,1281,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A). [resolve(1303,b,1282,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1303,b,1283,b)].
% 10.30/10.51 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A). [resolve(1303,b,1284,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A). [resolve(1303,b,1285,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A). [resolve(1303,b,1286,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1303,b,1287,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(1303,b,1288,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1303,b,1289,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A). [resolve(1303,b,1290,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A). [resolve(1303,b,1291,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A). [resolve(1303,b,1292,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A). [resolve(1303,b,1293,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A). [resolve(1303,b,1294,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1303,b,1295,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A). [resolve(1303,b,1296,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A). [resolve(1303,b,1297,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A). [resolve(1303,b,1298,b)].
% 10.30/10.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A). [resolve(1303,b,1299,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A). [resolve(1303,b,1300,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1303,b,1301,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1303,b,1302,a)].
% 10.30/10.53 1304 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__ring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_47) # label(axiom). [assumption].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A). [resolve(1304,b,1278,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A). [resolve(1304,b,1279,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(1304,b,1280,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1304,b,1281,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A). [resolve(1304,b,1282,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1304,b,1283,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A). [resolve(1304,b,1284,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A). [resolve(1304,b,1285,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A). [resolve(1304,b,1286,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1304,b,1287,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(1304,b,1288,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1304,b,1289,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A). [resolve(1304,b,1290,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A). [resolve(1304,b,1291,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A). [resolve(1304,b,1292,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A). [resolve(1304,b,1293,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A). [resolve(1304,b,1294,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A). [resolve(1304,b,1295,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A). [resolve(1304,b,1296,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A). [resolve(1304,b,1297,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A). [resolve(1304,b,1298,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A). [resolve(1304,b,1299,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A). [resolve(1304,b,1300,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A). [resolve(1304,b,1301,b)].
% 10.30/10.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0. [resolve(1304,b,1302,a)].
% 10.30/10.53 1305 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_1) # label(axiom). [assumption].
% 10.30/10.53 1306 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_10) # label(axiom). [assumption].
% 10.30/10.53 1307 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_12) # label(axiom). [assumption].
% 10.30/10.53 1308 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_13) # label(axiom). [assumption].
% 10.30/10.53 1309 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_14) # label(axiom). [assumption].
% 10.30/10.54 1310 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_15) # label(axiom). [assumption].
% 10.30/10.54 1311 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_16) # label(axiom). [assumption].
% 10.30/10.54 1312 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 10.30/10.54 1313 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_2) # label(axiom). [assumption].
% 10.30/10.54 1314 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_21) # label(axiom). [assumption].
% 10.30/10.54 1315 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_22) # label(axiom). [assumption].
% 10.30/10.54 1316 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_23) # label(axiom). [assumption].
% 10.30/10.54 1317 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_24) # label(axiom). [assumption].
% 10.30/10.54 1318 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_25) # label(axiom). [assumption].
% 10.30/10.54 1319 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom). [assumption].
% 10.30/10.54 1320 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 10.30/10.54 1321 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_28) # label(axiom). [assumption].
% 10.30/10.54 Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1321,a,1277,a)].
% 10.30/10.54 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1321,a,1303,b)].
% 10.30/10.54 Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1321,a,1304,b)].
% 10.30/10.54 1322 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_29) # label(axiom). [assumption].
% 10.30/10.54 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1322,a,1277,a)].
% 10.30/10.54 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1322,a,1303,b)].
% 10.30/10.54 Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1322,a,1304,b)].
% 10.30/10.54 1323 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_30) # label(axiom). [assumption].
% 10.30/10.54 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1323,a,1277,a)].
% 10.30/10.54 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1323,a,1303,b)].
% 10.30/10.54 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1323,a,1304,b)].
% 10.30/10.54 1324 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_31) # label(axiom). [assumption].
% 10.30/10.54 Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1324,a,1277,a)].
% 10.30/10.57 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1324,a,1303,b)].
% 10.30/10.57 Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1324,a,1304,b)].
% 10.30/10.57 1325 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_32) # label(axiom). [assumption].
% 10.30/10.57 Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1325,a,1277,a)].
% 10.30/10.57 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1325,a,1303,b)].
% 10.30/10.57 Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1325,a,1304,b)].
% 10.30/10.57 1326 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_33) # label(axiom). [assumption].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1326,a,1277,a)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1326,a,1303,b)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1326,a,1304,b)].
% 10.30/10.57 1327 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_34) # label(axiom). [assumption].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1327,a,1277,a)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1327,a,1303,b)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1327,a,1304,b)].
% 10.30/10.57 1328 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_35) # label(axiom). [assumption].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1328,a,1277,a)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1328,a,1303,b)].
% 10.30/10.57 Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1328,a,1304,b)].
% 10.30/10.57 1329 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_36) # label(axiom). [assumption].
% 10.30/10.57 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1329,a,1277,a)].
% 10.30/10.57 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1329,a,1303,b)].
% 10.30/10.57 Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1329,a,1304,b)].
% 10.30/10.57 1330 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_8) # label(axiom). [assumption].
% 10.30/10.57 1331 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_9) # label(axiom). [assumption].
% 10.30/10.57 1332 -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(30,b,1,a)].
% 10.30/10.57 1333 -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(30,b,3,a)].
% 10.30/10.57 1334 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(30,b,9,a)].
% 10.30/10.57 1335 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(30,b,10,a)].
% 10.30/10.57 1336 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(151,b,131,b)].
% 10.30/10.57 1337 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(151,b,133,b)].
% 10.30/10.59 1338 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(165,a,151,b)].
% 10.30/10.59 1339 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(166,a,151,b)].
% 10.30/10.59 1340 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(171,a,151,b)].
% 10.30/10.59 1341 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(172,a,151,b)].
% 10.30/10.59 1342 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(240,a,225,b)].
% 10.30/10.59 1343 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(241,a,225,b)].
% 10.30/10.59 1344 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(247,b,225,b)].
% 10.30/10.59 1345 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(248,b,225,b)].
% 10.30/10.59 1346 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(305,b,288,a)].
% 10.30/10.59 1347 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(305,b,290,a)].
% 10.30/10.59 1348 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(322,a,305,b)].
% 10.30/10.59 1349 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(323,a,305,b)].
% 10.30/10.59 1350 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(325,a,305,b)].
% 10.30/10.59 1351 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(326,a,305,b)].
% 10.30/10.59 1352 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(346,b,331,b)].
% 10.30/10.59 1353 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(346,b,333,b)].
% 10.30/10.59 1354 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(346,b,334,a)].
% 10.30/10.59 1355 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(346,b,335,a)].
% 10.30/10.59 1356 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(346,b,336,a)].
% 10.30/10.59 1357 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,a,346,b)].
% 10.30/10.59 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1357,b,1303,b)].
% 10.30/10.59 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1357,b,1304,b)].
% 10.30/10.59 1358 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(355,a,346,b)].
% 10.30/10.59 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1358,b,1303,b)].
% 10.30/10.59 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1358,b,1304,b)].
% 10.30/10.59 1359 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(366,b,346,b)].
% 10.30/10.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1359,b,1303,b)].
% 10.30/10.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1359,b,1304,b)].
% 10.30/10.59 1360 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(367,b,346,b)].
% 10.30/10.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1360,b,1303,b)].
% 10.42/10.67 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1360,b,1304,b)].
% 10.42/10.67 1361 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(370,b,346,b)].
% 10.42/10.67 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1361,b,1303,b)].
% 10.42/10.67 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1361,b,1304,b)].
% 10.42/10.67 1362 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(371,b,346,b)].
% 10.42/10.67 1363 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(372,b,346,b)].
% 10.42/10.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1363,b,1303,b)].
% 10.42/10.67 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1363,b,1304,b)].
% 10.42/10.67 1364 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(373,b,346,b)].
% 10.42/10.67 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1364,b,1303,b)].
% 10.42/10.67 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1364,b,1304,b)].
% 10.42/10.67 1365 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(374,a,346,b)].
% 10.42/10.67 1366 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(375,a,346,b)].
% 10.42/10.67 1367 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(376,c,346,b)].
% 10.42/10.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1367,c,1303,b)].
% 10.42/10.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1367,c,1304,b)].
% 10.42/10.67 1368 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(377,c,346,b)].
% 10.42/10.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1368,c,1303,b)].
% 10.42/10.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1368,c,1304,b)].
% 10.42/10.67 1369 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(812,a,734,a)].
% 10.42/10.67 1370 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(812,a,741,a)].
% 10.42/10.67 1371 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(900,b,832,a)].
% 10.42/10.67 1372 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(900,b,833,a)].
% 10.42/10.67 1373 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(900,b,834,a)].
% 10.42/10.67 1374 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(900,b,835,a)].
% 10.42/10.67 1375 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,836,a)].
% 10.42/10.67 1376 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,837,a)].
% 10.42/10.67 1377 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(900,b,838,a)].
% 10.42/10.67 1378 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,839,a)].
% 10.42/10.67 1379 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(900,b,840,a)].
% 10.42/10.67 1380 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,841,a)].
% 10.42/10.67 1381 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(900,b,842,a)].
% 10.42/10.67 1382 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,843,a)].
% 10.42/10.67 1383 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,844,a)].
% 10.42/10.67 1384 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(900,b,845,a)].
% 10.42/10.67 1385 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,846,a)].
% 10.42/10.67 1386 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(900,b,847,a)].
% 10.42/10.67 1387 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(900,b,848,a)].
% 10.42/10.67 1388 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(900,b,849,a)].
% 10.42/10.67 1389 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(900,b,850,a)].
% 10.42/10.67 1390 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(900,b,851,a)].
% 10.42/10.67 1391 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(900,b,852,a)].
% 10.42/10.67 1392 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(900,b,853,a)].
% 10.42/10.67 1393 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(900,b,854,a)].
% 10.42/10.67 1394 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(900,b,855,b)].
% 10.42/10.67 1395 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(900,b,856,b)].
% 10.42/10.67 1396 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(900,b,857,a)].
% 10.42/10.67 1397 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(900,b,858,a)].
% 10.42/10.67 1398 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(900,b,859,a)].
% 10.42/10.68 1399 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(900,b,860,a)].
% 10.42/10.68 1400 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(900,b,861,a)].
% 10.42/10.68 1401 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(900,b,862,a)].
% 10.42/10.68 1402 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(900,b,863,a)].
% 10.42/10.68 1403 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(900,b,864,a)].
% 10.42/10.68 1404 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(900,b,865,a)].
% 10.42/10.68 1405 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(900,b,866,a)].
% 10.42/10.68 1406 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(900,b,867,a)].
% 10.42/10.68 1407 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(900,b,868,a)].
% 10.42/10.68 1408 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(900,b,869,a)].
% 10.42/10.68 1409 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(900,b,870,a)].
% 10.42/10.68 1410 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(900,b,871,a)].
% 10.42/10.68 1411 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(900,b,872,a)].
% 10.42/10.68 1412 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(900,b,873,a)].
% 10.42/10.68 1413 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(900,b,874,a)].
% 10.42/10.68 1414 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(900,b,875,a)].
% 10.42/10.68 1415 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(900,b,876,a)].
% 10.42/10.68 1416 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(900,b,877,a)].
% 10.42/10.68 1417 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(900,b,878,a)].
% 10.42/10.68 1418 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(900,b,879,a)].
% 10.42/10.68 1419 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(900,b,880,a)].
% 10.42/10.68 1420 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(900,b,881,a)].
% 10.42/10.68 1421 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(900,b,882,a)].
% 10.42/10.68 1422 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(900,b,883,a)].
% 10.42/10.68 1423 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(900,b,884,a)].
% 10.70/10.89 1424 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(900,b,885,a)].
% 10.70/10.89 1425 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(900,b,886,a)].
% 10.70/10.89 1426 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(900,b,887,a)].
% 10.70/10.89 1427 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(900,b,888,a)].
% 10.70/10.89 1428 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(900,b,889,a)].
% 10.70/10.89 1429 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(904,a,900,b)].
% 10.70/10.89 1430 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(905,a,900,b)].
% 10.70/10.89 1431 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1090,b,1076,a)].
% 10.70/10.89 1432 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1113,b,1099,a)].
% 10.70/10.89 1433 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 10.70/10.89 1434 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0 # label(cls_OrderedGroup_Oabs__0__eq_0) # label(axiom). [assumption].
% 10.70/10.89 1435 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 = c_HOL_Oabs(c_0,A) # label(cls_OrderedGroup_Oabs__0__eq_1) # label(axiom). [assumption].
% 10.70/10.89 1436 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) # label(cls_OrderedGroup_Oabs__add__abs_0) # label(axiom). [assumption].
% 10.70/10.89 1437 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0 # label(cls_OrderedGroup_Oabs__eq__0_0) # label(axiom). [assumption].
% 10.70/10.89 1438 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_0,A) = c_0 # label(cls_OrderedGroup_Oabs__eq__0_1) # label(axiom). [assumption].
% 10.70/10.89 1439 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 10.70/10.89 1440 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__idempotent_0) # label(axiom). [assumption].
% 10.70/10.89 1441 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0 # label(cls_OrderedGroup_Oabs__le__zero__iff_0) # label(axiom). [assumption].
% 10.70/10.89 1442 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) # label(cls_OrderedGroup_Oabs__le__zero__iff_1) # label(axiom). [assumption].
% 10.70/10.89 1443 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__minus__cancel_0) # label(axiom). [assumption].
% 10.70/10.89 1444 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_HOL_Oabs(B,A),c_0,A) # label(cls_OrderedGroup_Oabs__not__less__zero_0) # label(axiom). [assumption].
% 10.70/10.89 1445 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B # label(cls_OrderedGroup_Oabs__of__nonneg_0) # label(axiom). [assumption].
% 10.70/10.89 1446 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A) # label(cls_OrderedGroup_Oabs__of__nonpos_0) # label(axiom). [assumption].
% 10.70/10.89 1447 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A) # label(cls_OrderedGroup_Ozero__less__abs__iff_0) # label(axiom). [assumption].
% 10.71/10.90 1448 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0 # label(cls_OrderedGroup_Ozero__less__abs__iff_1) # label(axiom). [assumption].
% 10.71/10.90 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1434,a)].
% 10.71/10.90 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(1433,a,1435,a)].
% 10.71/10.90 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1433,a,1436,a)].
% 10.71/10.90 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1433,a,1437,a)].
% 10.71/10.90 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(1433,a,1438,a)].
% 10.71/10.90 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1433,a,1439,a)].
% 10.71/10.90 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1433,a,1440,a)].
% 10.71/10.90 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1441,a)].
% 10.71/10.90 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1433,a,1442,a)].
% 10.71/10.90 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(1433,a,1443,a)].
% 10.71/10.90 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1433,a,1444,a)].
% 10.71/10.90 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(1433,a,1445,a)].
% 10.71/10.90 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(1433,a,1446,a)].
% 10.71/10.90 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1433,a,1447,a)].
% 10.71/10.90 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(1433,a,1448,a)].
% 10.71/10.90 1449 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 10.71/10.90 1450 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_1) # label(axiom). [assumption].
% 10.71/10.90 1451 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 10.71/10.90 1452 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom). [assumption].
% 10.71/10.90 1453 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 10.71/10.90 1454 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 10.71/10.90 1455 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 10.71/10.90 1456 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 10.71/10.90 1457 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom). [assumption].
% 10.71/10.90 1458 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 10.71/10.90 1459 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom). [assumption].
% 10.71/10.90 1460 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_6) # label(axiom). [assumption].
% 10.71/10.90 1461 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_7) # label(axiom). [assumption].
% 10.72/10.92 1462 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_8) # label(axiom). [assumption].
% 10.72/10.92 1463 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Olordered__ring_24) # label(axiom). [assumption].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1463,b,1434,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1463,b,1435,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(1463,b,1436,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1463,b,1437,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1463,b,1438,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1463,b,1439,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1440,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1463,b,1441,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1463,b,1442,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1443,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1463,b,1444,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1463,b,1445,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1463,b,1446,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1463,b,1447,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1463,b,1448,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1463,b,1450,a)].
% 10.72/10.92 1464 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__field_47) # label(axiom). [assumption].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1464,b,1434,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1464,b,1435,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(1464,b,1436,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1464,b,1437,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1464,b,1438,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1464,b,1439,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1464,b,1440,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1464,b,1441,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1464,b,1442,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1464,b,1443,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1464,b,1444,a)].
% 10.72/10.92 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1464,b,1445,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1464,b,1446,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1464,b,1447,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1464,b,1448,a)].
% 10.91/11.12 1465 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom). [assumption].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1465,b,1434,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1465,b,1435,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(1465,b,1436,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1465,b,1437,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1465,b,1438,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1465,b,1439,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1465,b,1440,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1465,b,1441,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1465,b,1442,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1465,b,1443,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1465,b,1444,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1465,b,1445,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1465,b,1446,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1465,b,1447,a)].
% 10.91/11.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1465,b,1448,a)].
% 10.91/11.12 1466 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_HOL_Oabs(c_plus(B,C,A),A),c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) # label(cls_OrderedGroup_Oabs__triangle__ineq_0) # label(axiom). [assumption].
% 10.91/11.12 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint),c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1466,a,1433,a)].
% 10.91/11.12 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1466,a,1463,b)].
% 10.91/11.12 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1466,a,1464,b)].
% 10.91/11.12 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1466,a,1465,b)].
% 10.91/11.12 1467 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(12,b,1,a)].
% 10.91/11.12 1468 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(12,b,3,a)].
% 10.91/11.12 1469 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(50,b,47,a)].
% 10.91/11.12 1470 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(50,b,48,a)].
% 10.91/11.12 1471 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1082,b,1076,a)].
% 10.91/11.12 1472 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1105,b,1099,a)].
% 10.91/11.12 1473 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint). [resolve(1326,a,1277,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1473,a,1449,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(1473,a,1450,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1473,a,1451,a)].
% 10.91/11.12 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1473,a,1452,a)].
% 10.91/11.12 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1473,a,1453,a)].
% 10.91/11.12 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1473,a,1454,a)].
% 10.91/11.12 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1473,a,1455,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(1473,a,1456,a)].
% 10.91/11.12 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(1473,a,1457,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(1473,a,1458,a)].
% 10.91/11.12 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1473,a,1459,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1473,a,1460,a)].
% 10.91/11.12 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1461,a)].
% 10.91/11.13 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1462,a)].
% 10.91/11.13 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1473,a,1467,a)].
% 10.91/11.13 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1473,a,1468,a)].
% 10.91/11.13 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1473,a,1471,a)].
% 10.91/11.13 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1473,a,1472,a)].
% 10.91/11.13 1474 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1326,a,1303,b)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1474,a,1449,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1474,a,1450,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1474,a,1451,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1474,a,1452,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1474,a,1453,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1474,a,1454,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1474,a,1455,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A). [resolve(1474,a,1459,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1474,a,1460,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1474,a,1461,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1474,a,1462,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1474,a,1471,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1474,a,1472,a)].
% 10.91/11.13 1475 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1326,a,1304,b)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1475,a,1449,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1475,a,1450,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1475,a,1451,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1475,a,1452,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1475,a,1453,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1475,a,1454,a)].
% 10.91/11.13 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1475,a,1455,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(1475,a,1459,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1475,a,1460,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1475,a,1461,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1475,a,1462,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1475,a,1471,a)].
% 11.01/11.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1475,a,1472,a)].
% 11.01/11.24 1476 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 11.01/11.24 1477 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__left_0) # label(axiom). [assumption].
% 11.01/11.24 1478 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__left_1) # label(axiom). [assumption].
% 11.01/11.24 1479 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__right_0) # label(axiom). [assumption].
% 11.01/11.24 1480 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__right_1) # label(axiom). [assumption].
% 11.01/11.24 1481 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__left_0) # label(axiom). [assumption].
% 11.01/11.24 1482 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__left_1) # label(axiom). [assumption].
% 11.01/11.24 1483 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__right_0) # label(axiom). [assumption].
% 11.01/11.24 1484 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__right_1) # label(axiom). [assumption].
% 11.01/11.24 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1476,a,1477,a)].
% 11.01/11.24 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1476,a,1478,a)].
% 11.01/11.24 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1476,a,1479,a)].
% 11.01/11.24 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1476,a,1480,a)].
% 11.01/11.24 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1476,a,1481,a)].
% 11.01/11.24 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1476,a,1482,a)].
% 11.01/11.24 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1476,a,1483,a)].
% 11.01/11.24 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1476,a,1484,a)].
% 11.01/11.24 1485 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 11.01/11.24 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1485,a,1477,a)].
% 11.01/11.24 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1485,a,1478,a)].
% 11.01/11.25 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1485,a,1479,a)].
% 11.01/11.25 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1485,a,1480,a)].
% 11.01/11.25 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1485,a,1481,a)].
% 11.01/11.25 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1485,a,1482,a)].
% 11.01/11.25 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1485,a,1483,a)].
% 11.01/11.25 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1485,a,1484,a)].
% 11.01/11.25 1486 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group_5) # label(axiom). [assumption].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1486,b,1477,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1486,b,1478,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1486,b,1479,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1486,b,1480,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1486,b,1481,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1486,b,1482,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1486,b,1483,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1486,b,1484,a)].
% 11.01/11.25 1487 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_5) # label(axiom). [assumption].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1487,b,1477,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1487,b,1478,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1487,b,1479,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1487,b,1480,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1487,b,1481,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1487,b,1482,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1487,b,1483,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1487,b,1484,a)].
% 11.01/11.25 1488 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_5) # label(axiom). [assumption].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1488,b,1477,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1488,b,1478,a)].
% 11.01/11.25 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1488,b,1479,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1488,b,1480,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1488,b,1481,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1488,b,1482,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1488,b,1483,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1488,b,1484,a)].
% 11.01/11.26 1489 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) # label(axiom). [assumption].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1489,b,1477,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1489,b,1478,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1489,b,1479,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1489,b,1480,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1489,b,1481,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1489,b,1482,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1489,b,1483,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1489,b,1484,a)].
% 11.01/11.26 1490 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_12) # label(axiom). [assumption].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1490,b,1477,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1490,b,1478,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1490,b,1479,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1490,b,1480,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1490,b,1481,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1490,b,1482,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1490,b,1483,a)].
% 11.01/11.26 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1490,b,1484,a)].
% 11.01/11.26 1491 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) # label(axiom). [assumption].
% 11.01/11.26 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,a,1486,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,a,1487,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,a,1488,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,a,1489,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,a,1490,b)].
% 11.01/11.27 1492 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) # label(axiom). [assumption].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1492,a,1486,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1492,a,1487,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1492,a,1488,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1492,a,1489,b)].
% 11.01/11.27 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1492,a,1490,b)].
% 11.01/11.27 1493 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) # label(axiom). [assumption].
% 11.01/11.27 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1493,a,1486,b)].
% 11.01/11.27 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1493,a,1487,b)].
% 11.01/11.27 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1493,a,1488,b)].
% 11.01/11.27 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1493,a,1490,b)].
% 11.01/11.27 1494 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) # label(axiom). [assumption].
% 11.01/11.27 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1494,a,1486,b)].
% 11.01/11.27 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1494,a,1487,b)].
% 11.01/11.27 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1494,a,1488,b)].
% 11.01/11.27 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1494,a,1490,b)].
% 11.01/11.27 1495 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) # label(axiom). [assumption].
% 11.01/11.27 1496 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) # label(axiom). [assumption].
% 11.01/11.27 1497 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Olordered__ring_5) # label(axiom). [assumption].
% 11.01/11.27 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1497,b,1477,a)].
% 11.01/11.27 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1497,b,1478,a)].
% 11.01/11.27 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1497,b,1479,a)].
% 11.01/11.27 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1497,b,1480,a)].
% 11.01/11.27 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1497,b,1481,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1497,b,1482,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1497,b,1483,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1497,b,1484,a)].
% 11.01/11.28 1498 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) # label(axiom). [assumption].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1498,b,1477,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1498,b,1478,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1498,b,1479,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1498,b,1480,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1498,b,1481,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1498,b,1482,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1498,b,1483,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1498,b,1484,a)].
% 11.01/11.28 1499 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__field_55) # label(axiom). [assumption].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1499,b,1477,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1499,b,1478,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1499,b,1479,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1499,b,1480,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1499,b,1481,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1499,b,1482,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1499,b,1483,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1499,b,1484,a)].
% 11.01/11.28 1500 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__idom_37) # label(axiom). [assumption].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1500,b,1477,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1500,b,1478,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1500,b,1479,a)].
% 11.01/11.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1500,b,1480,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1500,b,1481,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1500,b,1482,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1500,b,1483,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1500,b,1484,a)].
% 11.11/11.30 1501 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_14) # label(axiom). [assumption].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1501,b,1477,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1501,b,1478,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1501,b,1479,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1501,b,1480,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1501,b,1481,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1501,b,1482,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1501,b,1483,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1501,b,1484,a)].
% 11.11/11.30 1502 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Opordered__ring_20) # label(axiom). [assumption].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1502,b,1477,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1502,b,1478,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1502,b,1479,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1502,b,1480,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1502,b,1481,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1502,b,1482,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1502,b,1483,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1502,b,1484,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1502,b,1492,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1502,b,1493,a)].
% 11.11/11.30 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1502,b,1494,a)].
% 11.11/11.30 1503 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(17,b,1,a)].
% 11.11/11.30 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1503,a,1486,b)].
% 11.11/11.30 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1503,a,1487,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1503,a,1488,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1503,a,1489,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1503,a,1490,b)].
% 11.30/11.51 1504 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(17,b,3,a)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1504,a,1486,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1504,a,1487,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1504,a,1488,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1504,a,1489,b)].
% 11.30/11.51 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1504,a,1490,b)].
% 11.30/11.51 1505 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(81,b,55,b)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1505,b,1486,b)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1505,b,1487,b)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1505,b,1488,b)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1505,b,1489,b)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1505,b,1490,b)].
% 11.30/11.51 1506 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(82,b,55,b)].
% 11.30/11.51 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1506,b,1486,b)].
% 11.30/11.51 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1506,b,1487,b)].
% 11.30/11.51 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1506,b,1488,b)].
% 11.30/11.51 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1506,b,1489,b)].
% 11.30/11.51 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1506,b,1490,b)].
% 11.30/11.51 1507 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1160,a,1121,a)].
% 11.30/11.51 1508 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(1160,a,1146,a)].
% 11.30/11.51 Derived: class_Orderings_Oorder(tc_nat). [resolve(1508,a,1493,a)].
% 11.30/11.51 Derived: class_Orderings_Oord(tc_nat). [resolve(1508,a,1494,a)].
% 11.30/11.51 Derived: class_HOL_Oplus(tc_nat). [resolve(1508,a,1496,a)].
% 11.30/11.51 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1508,a,1503,a)].
% 11.30/11.51 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1508,a,1504,a)].
% 11.30/11.51 1509 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1160,a,1147,b)].
% 11.30/11.51 1510 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1160,a,1148,b)].
% 11.30/11.51 1511 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(1473,a,1460,a)].
% 11.30/11.51 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1511,a,1493,a)].
% 11.30/11.51 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1511,a,1494,a)].
% 11.30/11.51 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1511,a,1495,a)].
% 11.30/11.51 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1511,a,1496,a)].
% 11.30/11.51 1512 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1474,a,1460,a)].
% 11.30/11.51 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1512,b,1493,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1512,b,1494,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1512,b,1495,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1512,b,1496,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1512,b,1503,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1512,b,1504,a)].
% 11.42/11.63 1513 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1475,a,1460,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1513,b,1493,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1513,b,1494,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1513,b,1495,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1513,b,1496,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1513,b,1503,a)].
% 11.42/11.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1513,b,1504,a)].
% 11.42/11.63 1514 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 11.42/11.63 1515 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 11.42/11.63 1516 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 11.42/11.63 1517 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_0) # label(axiom). [assumption].
% 11.42/11.63 1518 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_1) # label(axiom). [assumption].
% 11.42/11.63 1519 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_0) # label(axiom). [assumption].
% 11.42/11.63 1520 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_1) # label(axiom). [assumption].
% 11.42/11.63 1521 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__join__eq__meet_0) # label(axiom). [assumption].
% 11.42/11.63 1522 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__meet__eq__join_0) # label(axiom). [assumption].
% 11.42/11.63 1523 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 11.42/11.63 1524 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0 # label(cls_OrderedGroup_Onprt__eq__0_0) # label(axiom). [assumption].
% 11.42/11.63 1525 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B # label(cls_OrderedGroup_Onprt__eq__id_0) # label(axiom). [assumption].
% 11.42/11.63 1526 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A) # label(cls_OrderedGroup_Onprt__le__zero_0) # label(axiom). [assumption].
% 11.42/11.63 1527 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A) # label(cls_OrderedGroup_Onprt__mono_0) # label(axiom). [assumption].
% 11.42/11.63 1528 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 11.42/11.64 1529 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0 # label(cls_OrderedGroup_Opprt__eq__0_0) # label(axiom). [assumption].
% 11.42/11.64 1530 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B # label(cls_OrderedGroup_Opprt__eq__id_0) # label(axiom). [assumption].
% 11.42/11.64 1531 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A) # label(cls_OrderedGroup_Opprt__mono_0) # label(axiom). [assumption].
% 11.42/11.64 1532 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 11.42/11.64 1533 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 11.42/11.64 1534 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A) # label(cls_OrderedGroup_Ozero__le__pprt_0) # label(axiom). [assumption].
% 11.42/11.64 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(1514,a,1515,a)].
% 11.42/11.64 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1514,a,1516,a)].
% 11.42/11.64 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1514,a,1517,a)].
% 11.42/11.64 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1514,a,1518,a)].
% 11.42/11.64 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(1514,a,1519,a)].
% 11.42/11.64 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(1514,a,1520,a)].
% 11.42/11.64 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1521,a)].
% 11.42/11.64 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1522,a)].
% 11.42/11.64 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1514,a,1523,a)].
% 11.42/11.64 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(1514,a,1524,a)].
% 11.42/11.64 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(1514,a,1525,a)].
% 11.42/11.64 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1514,a,1526,a)].
% 11.42/11.64 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1527,a)].
% 11.42/11.64 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(1514,a,1528,a)].
% 11.42/11.64 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(1514,a,1529,a)].
% 11.42/11.64 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(1514,a,1530,a)].
% 11.42/11.64 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1531,a)].
% 11.42/11.64 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(1514,a,1532,a)].
% 11.42/11.64 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1533,a)].
% 11.42/11.64 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1514,a,1534,a)].
% 11.42/11.64 1535 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 11.42/11.64 1536 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 11.42/11.65 1537 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 11.42/11.65 1538 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom). [assumption].
% 11.42/11.65 1539 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 11.42/11.65 1540 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom). [assumption].
% 11.42/11.65 1541 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 11.42/11.65 1542 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom). [assumption].
% 11.42/11.65 1543 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 11.42/11.65 1544 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 11.42/11.65 1545 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 11.42/11.65 1546 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 11.42/11.65 1547 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1547,b,1515,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1547,b,1516,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1517,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1518,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1519,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1520,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1547,b,1521,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1547,b,1522,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1547,b,1523,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1547,b,1524,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1547,b,1525,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1547,b,1526,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1547,b,1527,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1547,b,1528,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1547,b,1529,a)].
% 11.42/11.65 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1547,b,1530,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1547,b,1531,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1547,b,1532,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1547,b,1533,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1547,b,1534,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1547,b,1535,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1536,a)].
% 11.42/11.66 1548 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1548,b,1515,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1548,b,1516,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1517,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1518,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1519,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1520,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1548,b,1521,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1548,b,1522,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1548,b,1523,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1548,b,1524,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1548,b,1525,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1548,b,1526,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1548,b,1527,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1548,b,1528,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1548,b,1529,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1548,b,1530,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1548,b,1531,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1548,b,1532,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1548,b,1533,a)].
% 11.42/11.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1548,b,1534,a)].
% 11.42/11.67 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1548,b,1535,a)].
% 11.42/11.67 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1536,a)].
% 11.42/11.67 1549 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1549,b,1515,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1549,b,1516,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1517,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1518,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1519,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1520,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1549,b,1521,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1549,b,1522,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1549,b,1523,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1549,b,1524,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1549,b,1525,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1549,b,1526,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1549,b,1527,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1549,b,1528,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1549,b,1529,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1549,b,1530,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1549,b,1531,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1549,b,1532,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1549,b,1533,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1549,b,1534,a)].
% 11.42/11.67 1550 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 11.42/11.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1550,b,1515,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1550,b,1516,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1550,b,1517,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1550,b,1518,a)].
% 11.42/11.67 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1550,b,1519,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1550,b,1520,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1550,b,1521,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1550,b,1522,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1550,b,1523,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1550,b,1524,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1550,b,1525,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1550,b,1526,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1550,b,1527,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1550,b,1528,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1550,b,1529,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1550,b,1530,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1550,b,1531,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1550,b,1532,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1550,b,1533,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1550,b,1534,a)].
% 11.42/11.68 1551 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1551,b,1515,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1551,b,1516,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1551,b,1517,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1551,b,1518,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1551,b,1519,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1551,b,1520,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1551,b,1521,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1551,b,1522,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1551,b,1523,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1551,b,1524,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1551,b,1525,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1551,b,1526,a)].
% 11.42/11.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1551,b,1527,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1551,b,1528,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1551,b,1529,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1551,b,1530,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1551,b,1531,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1551,b,1532,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1551,b,1533,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1551,b,1534,a)].
% 11.72/11.90 1552 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(11,b,1,a)].
% 11.72/11.90 1553 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(11,b,3,a)].
% 11.72/11.90 1554 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(81,b,49,b)].
% 11.72/11.90 1555 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(82,b,49,b)].
% 11.72/11.90 1556 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1081,b,1076,a)].
% 11.72/11.90 1557 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1104,b,1099,a)].
% 11.72/11.90 1558 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1322,a,1277,a)].
% 11.72/11.90 1559 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1322,a,1303,b)].
% 11.72/11.90 1560 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1322,a,1304,b)].
% 11.72/11.90 1561 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(1473,a,1449,a)].
% 11.72/11.90 1562 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1474,a,1449,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1562,b,1536,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A). [resolve(1562,b,1540,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1562,b,1541,a)].
% 11.72/11.90 1563 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(1475,a,1449,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1563,b,1536,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A). [resolve(1563,b,1540,a)].
% 11.72/11.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(1563,b,1541,a)].
% 11.72/11.90 1564 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1486,b,1477,a)].
% 11.72/11.90 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1564,a,1514,a)].
% 11.72/11.90 1565 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1486,b,1478,a)].
% 11.72/11.90 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1565,a,1514,a)].
% 11.72/11.90 1566 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1486,b,1479,a)].
% 11.72/11.90 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1566,a,1514,a)].
% 11.72/11.90 1567 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1486,b,1480,a)].
% 11.72/11.90 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1567,a,1514,a)].
% 11.83/12.04 1568 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1486,b,1481,a)].
% 11.83/12.04 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1568,a,1514,a)].
% 11.83/12.04 1569 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1486,b,1482,a)].
% 11.83/12.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1569,a,1514,a)].
% 11.83/12.04 1570 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1486,b,1483,a)].
% 11.83/12.04 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1570,a,1514,a)].
% 11.83/12.04 1571 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1486,b,1484,a)].
% 11.83/12.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1571,a,1514,a)].
% 11.83/12.04 1572 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1491,a,1486,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1572,b,1514,a)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1572,b,1549,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1572,b,1550,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1572,b,1551,b)].
% 11.83/12.04 1573 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1492,a,1486,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1573,b,1514,a)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1573,b,1549,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1573,b,1550,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1573,b,1551,b)].
% 11.83/12.04 1574 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1493,a,1486,b)].
% 11.83/12.04 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1574,b,1549,b)].
% 11.83/12.04 1575 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1494,a,1486,b)].
% 11.83/12.04 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1575,b,1549,b)].
% 11.83/12.04 1576 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1503,a,1486,b)].
% 11.83/12.04 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1576,c,1514,a)].
% 11.83/12.04 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1576,c,1549,b)].
% 11.83/12.04 1577 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1504,a,1486,b)].
% 11.83/12.04 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1577,c,1514,a)].
% 11.83/12.04 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1577,c,1549,b)].
% 11.83/12.04 1578 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1505,b,1486,b)].
% 11.83/12.04 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1578,b,1549,b)].
% 11.83/12.04 1579 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1506,b,1486,b)].
% 11.83/12.04 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1579,b,1549,b)].
% 11.83/12.04 1580 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 11.83/12.05 1581 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 11.83/12.05 1582 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastAtMost__empty_0) # label(axiom). [assumption].
% 11.83/12.05 1583 -class_Orderings_Oorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_OatLeastAtMost__singleton_0) # label(axiom). [assumption].
% 11.83/12.05 1584 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastLessThan__empty_0) # label(axiom). [assumption].
% 11.83/12.05 1585 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__subset__iff_0) # label(axiom). [assumption].
% 11.83/12.05 1586 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)) # label(cls_SetInterval_OatLeast__subset__iff_1) # label(axiom). [assumption].
% 11.83/12.05 1587 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__subset__iff_0) # label(axiom). [assumption].
% 11.83/12.05 1588 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) # label(cls_SetInterval_OatMost__subset__iff_1) # label(axiom). [assumption].
% 11.83/12.05 1589 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OgreaterThanAtMost__empty_0) # label(axiom). [assumption].
% 11.83/12.05 1590 -class_Orderings_Oorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_Osingle__Diff__lessThan_0) # label(axiom). [assumption].
% 11.83/12.05 1591 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 11.83/12.05 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1580,a,1581,a)].
% 11.83/12.05 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1582,a)].
% 11.83/12.05 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1580,a,1583,a)].
% 11.83/12.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1584,a)].
% 11.83/12.05 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1580,a,1585,a)].
% 11.83/12.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1580,a,1586,a)].
% 11.83/12.05 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1580,a,1587,a)].
% 11.83/12.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1580,a,1588,a)].
% 11.83/12.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1580,a,1589,a)].
% 11.83/12.05 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1580,a,1590,a)].
% 11.83/12.05 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1580,a,1591,a)].
% 11.83/12.05 1592 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 11.83/12.05 Derived: -c_less(A,A,tc_nat). [resolve(1592,a,1581,a)].
% 11.83/12.05 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1582,a)].
% 11.83/12.05 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1592,a,1583,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1584,a)].
% 11.83/12.06 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1592,a,1585,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1592,a,1586,a)].
% 11.83/12.06 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1592,a,1587,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1592,a,1588,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1592,a,1589,a)].
% 11.83/12.06 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1592,a,1590,a)].
% 11.83/12.06 Derived: c_lessequals(A,A,tc_nat). [resolve(1592,a,1591,a)].
% 11.83/12.06 1593 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 11.83/12.06 Derived: -c_less(A,A,tc_set(B)). [resolve(1593,a,1581,a)].
% 11.83/12.06 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1582,a)].
% 11.83/12.06 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(1593,a,1583,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1584,a)].
% 11.83/12.06 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_set(B)),c_SetInterval_OatLeast(C,tc_set(B)),tc_set(tc_set(B))) | c_lessequals(C,A,tc_set(B)). [resolve(1593,a,1585,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_set(C)) | c_lessequals(c_SetInterval_OatLeast(B,tc_set(C)),c_SetInterval_OatLeast(A,tc_set(C)),tc_set(tc_set(C))). [resolve(1593,a,1586,a)].
% 11.83/12.06 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_set(B)),c_SetInterval_OatMost(C,tc_set(B)),tc_set(tc_set(B))) | c_lessequals(A,C,tc_set(B)). [resolve(1593,a,1587,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_set(C)) | c_lessequals(c_SetInterval_OatMost(A,tc_set(C)),c_SetInterval_OatMost(B,tc_set(C)),tc_set(tc_set(C))). [resolve(1593,a,1588,a)].
% 11.83/12.06 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(1593,a,1589,a)].
% 11.83/12.06 Derived: c_minus(c_insert(A,c_emptyset,tc_set(B)),c_SetInterval_OlessThan(A,tc_set(B)),tc_set(tc_set(B))) = c_insert(A,c_emptyset,tc_set(B)). [resolve(1593,a,1590,a)].
% 11.83/12.06 Derived: c_lessequals(A,A,tc_set(B)). [resolve(1593,a,1591,a)].
% 11.83/12.06 1594 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1594,b,1581,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1582,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1594,b,1583,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1594,b,1584,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1594,b,1585,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1594,b,1586,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1594,b,1587,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1594,b,1588,a)].
% 11.83/12.06 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1589,a)].
% 11.83/12.07 Derived: -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1594,b,1590,a)].
% 11.83/12.07 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1594,b,1591,a)].
% 11.83/12.07 1595 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1595,b,1581,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1582,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1583,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1584,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1595,b,1585,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1595,b,1586,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1595,b,1587,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1595,b,1588,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1589,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1595,b,1590,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1595,b,1591,a)].
% 11.83/12.07 1596 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1596,b,1581,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1582,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1583,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1584,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1596,b,1585,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1596,b,1586,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1596,b,1587,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1596,b,1588,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1589,a)].
% 11.83/12.07 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1596,b,1590,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1596,b,1591,a)].
% 11.83/12.08 1597 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1597,b,1581,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1582,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1583,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1584,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1597,b,1585,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1597,b,1586,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1597,b,1587,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1597,b,1588,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1589,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1597,b,1590,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1597,b,1591,a)].
% 11.83/12.08 1598 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A). [resolve(1598,b,1581,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1582,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1598,b,1583,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1598,b,1584,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1598,b,1585,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1598,b,1586,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1598,b,1587,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1598,b,1588,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1598,b,1589,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1598,b,1590,a)].
% 11.83/12.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(1598,b,1591,a)].
% 11.83/12.09 1599 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1599,b,1581,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1582,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1599,b,1583,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1599,b,1584,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1599,b,1585,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1599,b,1586,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1599,b,1587,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1599,b,1588,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1589,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1599,b,1590,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1599,b,1591,a)].
% 11.83/12.09 1600 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1600,b,1581,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1582,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1600,b,1583,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1600,b,1584,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1600,b,1585,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1600,b,1586,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1600,b,1587,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1600,b,1588,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1589,a)].
% 11.83/12.09 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1600,b,1590,a)].
% 11.91/12.10 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1600,b,1591,a)].
% 11.91/12.10 1601 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 11.91/12.10 Derived: class_Orderings_Oord(tc_set(A)). [resolve(1601,a,1593,a)].
% 11.91/12.10 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1601,a,1599,b)].
% 11.91/12.10 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1601,a,1600,b)].
% 11.91/12.10 1602 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1602,b,1581,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1582,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1602,b,1583,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1602,b,1584,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1602,b,1585,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1602,b,1586,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1602,b,1587,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1602,b,1588,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1589,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1602,b,1590,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1602,b,1591,a)].
% 11.91/12.10 1603 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) # label(axiom). [assumption].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1603,b,1581,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1582,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1603,b,1583,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1603,b,1584,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1603,b,1585,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1603,b,1586,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1603,b,1587,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1603,b,1588,a)].
% 11.91/12.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1589,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1603,b,1590,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1603,b,1591,a)].
% 11.91/12.11 1604 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A). [resolve(1604,b,1581,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1604,b,1582,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1604,b,1583,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1604,b,1584,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1604,b,1585,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1604,b,1586,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1604,b,1587,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1604,b,1588,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1604,b,1589,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1604,b,1590,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(1604,b,1591,a)].
% 11.91/12.11 1605 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A). [resolve(1605,b,1581,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1605,b,1582,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1605,b,1583,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1605,b,1584,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1605,b,1585,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1605,b,1586,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1605,b,1587,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1605,b,1588,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1605,b,1589,a)].
% 11.91/12.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1605,b,1590,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(1605,b,1591,a)].
% 11.91/12.12 1606 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom). [assumption].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1606,b,1581,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1582,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1606,b,1583,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1606,b,1584,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1606,b,1585,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1606,b,1586,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1606,b,1587,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1606,b,1588,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1589,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1606,b,1590,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1606,b,1591,a)].
% 11.91/12.12 1607 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) # label(axiom). [assumption].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1607,b,1581,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1582,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1607,b,1583,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1607,b,1584,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1607,b,1585,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1607,b,1586,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1607,b,1587,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1607,b,1588,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1589,a)].
% 11.91/12.12 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1607,b,1590,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1607,b,1591,a)].
% 11.91/12.13 1608 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom). [assumption].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1608,b,1581,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1582,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1608,b,1583,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1608,b,1584,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1608,b,1585,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1608,b,1586,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1608,b,1587,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1608,b,1588,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1589,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1608,b,1590,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1608,b,1591,a)].
% 11.91/12.13 1609 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom). [assumption].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A). [resolve(1609,b,1581,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1609,b,1582,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1609,b,1583,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1609,b,1584,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1609,b,1585,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1609,b,1586,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1609,b,1587,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1609,b,1588,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1609,b,1589,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1609,b,1590,a)].
% 11.91/12.13 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(1609,b,1591,a)].
% 11.91/12.14 1610 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom). [assumption].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1610,b,1581,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1582,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1610,b,1583,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1610,b,1584,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1610,b,1585,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1610,b,1586,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1610,b,1587,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1610,b,1588,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1589,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1610,b,1590,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1610,b,1591,a)].
% 11.91/12.14 1611 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1611,b,1581,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1582,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1611,b,1583,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1611,b,1584,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1611,b,1585,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1611,b,1586,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1611,b,1587,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1611,b,1588,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1589,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1611,b,1590,a)].
% 11.91/12.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1611,b,1591,a)].
% 11.91/12.14 1612 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1612,b,1581,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1582,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1612,b,1583,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1612,b,1584,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1612,b,1585,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1612,b,1586,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1612,b,1587,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1612,b,1588,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1589,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1612,b,1590,a)].
% 11.91/12.15 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1612,b,1591,a)].
% 11.91/12.15 1613 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1613,b,1581,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1582,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1613,b,1583,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1613,b,1584,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1613,b,1585,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1613,b,1586,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1613,b,1587,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1613,b,1588,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1589,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1613,b,1590,a)].
% 11.91/12.15 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1613,b,1591,a)].
% 11.91/12.15 1614 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_lessequals(D,C,A) # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 11.91/12.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1614,a,1580,a)].
% 11.91/12.15 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1614,a,1592,a)].
% 11.91/12.16 Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_lessequals(D,B,tc_set(C)). [resolve(1614,a,1593,a)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1614,a,1594,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1614,a,1595,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1614,a,1596,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1597,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1614,a,1598,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1614,a,1599,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1600,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1614,a,1602,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1614,a,1603,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1614,a,1604,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1614,a,1605,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1614,a,1606,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1614,a,1607,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1614,a,1608,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1614,a,1609,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1614,a,1610,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1614,a,1611,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1614,a,1612,b)].
% 11.91/12.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1614,a,1613,b)].
% 11.91/12.16 1615 -class_Orderings_Oorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_less(B,D,A) # label(cls_Orderings_Oorder__less__le__trans_0) # label(axiom). [assumption].
% 11.91/12.16 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1615,a,1580,a)].
% 11.91/12.16 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(1615,a,1592,a)].
% 11.91/12.16 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(B,D,tc_set(C)) | c_less(A,D,tc_set(C)). [resolve(1615,a,1593,a)].
% 11.91/12.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_LOrder_Olorder(C). [resolve(1615,a,1594,b)].
% 11.91/12.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1615,a,1595,b)].
% 11.91/12.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1615,a,1596,b)].
% 11.91/12.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1597,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1615,a,1598,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1615,a,1599,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1600,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1615,a,1602,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1615,a,1603,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1615,a,1604,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1615,a,1605,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1615,a,1606,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1615,a,1607,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1615,a,1608,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1615,a,1609,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1615,a,1610,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1615,a,1611,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1615,a,1612,b)].
% 12.22/12.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1615,a,1613,b)].
% 12.22/12.40 1616 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(896,a,831,a)].
% 12.22/12.40 1617 class_Orderings_Oorder(tc_nat). [resolve(896,a,890,a)].
% 12.22/12.40 1618 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(896,a,891,b)].
% 12.22/12.40 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1618,a,1601,a)].
% 12.22/12.40 1619 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(903,b,896,a)].
% 12.22/12.40 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1619,b,1601,a)].
% 12.22/12.40 1620 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(1080,b,1079,a)].
% 12.22/12.40 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1620,b,1601,a)].
% 12.22/12.40 1621 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(1086,b,1079,a)].
% 12.22/12.40 1622 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1167,a,1147,b)].
% 12.22/12.40 1623 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1167,a,1148,b)].
% 12.22/12.40 1624 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1473,a,1454,a)].
% 12.22/12.40 1625 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1474,a,1454,a)].
% 12.22/12.40 1626 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1475,a,1454,a)].
% 12.22/12.40 1627 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1493,a,1487,b)].
% 12.22/12.40 1628 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1493,a,1488,b)].
% 12.22/12.40 1629 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1493,a,1490,b)].
% 12.22/12.40 1630 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(1502,b,1493,a)].
% 12.22/12.40 1631 class_Orderings_Oorder(tc_nat). [resolve(1508,a,1493,a)].
% 12.22/12.40 1632 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(1511,a,1493,a)].
% 12.34/12.57 1633 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A). [resolve(1512,b,1493,a)].
% 12.34/12.57 1634 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A). [resolve(1513,b,1493,a)].
% 12.34/12.57 1635 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1574,b,1549,b)].
% 12.34/12.57 1636 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 12.34/12.57 1637 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastAtMost__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1638 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OatLeastAtMost__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1639 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A) # label(cls_SetInterval_OatLeastAtMost__iff_2) # label(axiom). [assumption].
% 12.34/12.57 1640 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastLessThan__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1641 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OatLeastLessThan__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1642 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A) # label(cls_SetInterval_OatLeastLessThan__iff_2) # label(axiom). [assumption].
% 12.34/12.57 1643 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1644 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A) # label(cls_SetInterval_OatLeast__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1645 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1646 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A) # label(cls_SetInterval_OatMost__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1647 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1648 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1649 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A) # label(cls_SetInterval_OgreaterThanAtMost__iff_2) # label(axiom). [assumption].
% 12.34/12.57 1650 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1651 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1652 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A) # label(cls_SetInterval_OgreaterThanLessThan__iff_2) # label(axiom). [assumption].
% 12.34/12.57 1653 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThan__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1654 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A) # label(cls_SetInterval_OgreaterThan__iff_1) # label(axiom). [assumption].
% 12.34/12.57 1655 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A) # label(cls_SetInterval_OlessThan__iff_0) # label(axiom). [assumption].
% 12.34/12.57 1656 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A) # label(cls_SetInterval_OlessThan__iff_1) # label(axiom). [assumption].
% 12.34/12.57 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1637,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1636,a,1638,a)].
% 12.34/12.58 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1639,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1640,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1636,a,1641,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1642,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,a,1643,a)].
% 12.34/12.58 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1644,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1636,a,1645,a)].
% 12.34/12.58 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1646,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1647,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1636,a,1648,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1649,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1650,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1636,a,1651,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1652,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1636,a,1653,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1654,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1636,a,1655,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1636,a,1656,a)].
% 12.34/12.58 1657 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1637,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1657,a,1638,a)].
% 12.34/12.58 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1657,a,1639,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1640,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1657,a,1641,a)].
% 12.34/12.58 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1657,a,1642,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1657,a,1643,a)].
% 12.34/12.58 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1657,a,1644,a)].
% 12.34/12.58 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1657,a,1645,a)].
% 12.34/12.60 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1657,a,1646,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1647,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1657,a,1648,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(1657,a,1649,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1650,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1657,a,1651,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1657,a,1652,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1657,a,1653,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1657,a,1654,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1657,a,1655,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1657,a,1656,a)].
% 12.34/12.60 1658 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1658,a,1637,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1658,a,1638,a)].
% 12.34/12.60 Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,tc_set(C)),tc_set(C)). [resolve(1658,a,1639,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1658,a,1640,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1658,a,1641,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,tc_set(C)),tc_set(C)). [resolve(1658,a,1642,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1658,a,1643,a)].
% 12.34/12.60 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1658,a,1644,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1658,a,1645,a)].
% 12.34/12.60 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1658,a,1646,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1658,a,1647,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1658,a,1648,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(B,D,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,tc_set(C)),tc_set(C)). [resolve(1658,a,1649,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1658,a,1650,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1658,a,1651,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_set(C)) | -c_less(D,A,tc_set(C)) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,tc_set(C)),tc_set(C)). [resolve(1658,a,1652,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1658,a,1653,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1658,a,1654,a)].
% 12.34/12.60 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1658,a,1655,a)].
% 12.34/12.60 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1658,a,1656,a)].
% 12.34/12.60 1659 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1637,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1638,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1659,b,1639,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1640,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1641,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1659,b,1642,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1643,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1644,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1645,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1646,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1647,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1648,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1659,b,1649,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1650,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1651,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1659,b,1652,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1653,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1654,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1655,a)].
% 12.34/12.61 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1656,a)].
% 12.34/12.61 1660 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1637,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1638,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1660,b,1639,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1640,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1641,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1660,b,1642,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1643,a)].
% 12.34/12.61 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1644,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1645,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1646,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1647,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1648,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1660,b,1649,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1650,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1651,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1660,b,1652,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1653,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1654,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1655,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1656,a)].
% 12.44/12.62 1661 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1637,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1638,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1661,b,1639,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1640,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1641,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1661,b,1642,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1643,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1644,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1645,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1646,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1647,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1648,a)].
% 12.44/12.62 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1661,b,1649,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1650,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1651,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1661,b,1652,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1653,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1654,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1655,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1656,a)].
% 12.44/12.63 1662 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1637,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1638,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1662,b,1639,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1640,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1641,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1662,b,1642,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1643,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1644,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1645,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1646,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1647,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1648,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1662,b,1649,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1650,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1651,a)].
% 12.44/12.63 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1662,b,1652,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1653,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1654,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1655,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1656,a)].
% 12.44/12.64 1663 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1637,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1638,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1663,b,1639,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1640,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1641,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1663,b,1642,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1663,b,1643,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1663,b,1644,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1663,b,1645,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1663,b,1646,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1647,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1663,b,1648,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1663,b,1649,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1663,b,1650,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1663,b,1651,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1663,b,1652,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1663,b,1653,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1663,b,1654,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1663,b,1655,a)].
% 12.44/12.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1663,b,1656,a)].
% 12.44/12.64 1664 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1637,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1638,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1664,b,1639,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1640,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1641,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1664,b,1642,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1643,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1664,b,1644,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1664,b,1645,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1664,b,1646,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1647,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1648,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1664,b,1649,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1650,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1651,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1664,b,1652,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1664,b,1653,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1664,b,1654,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1664,b,1655,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1664,b,1656,a)].
% 12.44/12.65 1665 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1637,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1638,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1665,b,1639,a)].
% 12.44/12.65 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1640,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1641,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1665,b,1642,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1643,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1665,b,1644,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1665,b,1645,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1665,b,1646,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1647,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1648,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1665,b,1649,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1650,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1651,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1665,b,1652,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1665,b,1653,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1665,b,1654,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1665,b,1655,a)].
% 12.44/12.66 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1665,b,1656,a)].
% 12.44/12.66 1666 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1637,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1638,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1666,b,1639,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1640,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1641,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1666,b,1642,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1643,a)].
% 12.44/12.66 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1666,b,1644,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1666,b,1645,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1666,b,1646,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1647,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1648,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1666,b,1649,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1650,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1651,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1666,b,1652,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1666,b,1653,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1666,b,1654,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1666,b,1655,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1666,b,1656,a)].
% 12.44/12.67 1667 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1637,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1638,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1667,b,1639,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1640,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1641,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1667,b,1642,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1643,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1667,b,1644,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1667,b,1645,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1667,b,1646,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1647,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1648,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1667,b,1649,a)].
% 12.44/12.67 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1650,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1651,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1667,b,1652,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1667,b,1653,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1667,b,1654,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1667,b,1655,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1667,b,1656,a)].
% 12.44/12.68 1668 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) # label(axiom). [assumption].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1637,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1668,b,1638,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1668,b,1639,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1640,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1668,b,1641,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1668,b,1642,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1643,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1668,b,1644,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1668,b,1645,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1668,b,1646,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1668,b,1647,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1668,b,1648,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1668,b,1649,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1668,b,1650,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1668,b,1651,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1668,b,1652,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1668,b,1653,a)].
% 12.44/12.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1668,b,1654,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1668,b,1655,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1668,b,1656,a)].
% 12.54/12.70 1669 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1637,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1669,b,1638,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1669,b,1639,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1640,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1669,b,1641,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1669,b,1642,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1669,b,1643,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1669,b,1644,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1669,b,1645,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1669,b,1646,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1669,b,1647,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1669,b,1648,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1669,b,1649,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1669,b,1650,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1669,b,1651,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1669,b,1652,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1669,b,1653,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1669,b,1654,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1669,b,1655,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1669,b,1656,a)].
% 12.54/12.70 1670 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1637,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1670,b,1638,a)].
% 12.54/12.70 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1670,b,1639,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1640,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1670,b,1641,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1670,b,1642,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1670,b,1643,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1670,b,1644,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1670,b,1645,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1670,b,1646,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1670,b,1647,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1670,b,1648,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1670,b,1649,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1670,b,1650,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1670,b,1651,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1670,b,1652,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1670,b,1653,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1670,b,1654,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1670,b,1655,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1670,b,1656,a)].
% 12.54/12.71 1671 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1637,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1638,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1671,b,1639,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1640,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1641,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1671,b,1642,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1643,a)].
% 12.54/12.71 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1671,b,1644,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1671,b,1645,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1671,b,1646,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1647,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1648,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1671,b,1649,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1650,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1651,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1671,b,1652,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1671,b,1653,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1671,b,1654,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1671,b,1655,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1671,b,1656,a)].
% 12.54/12.72 1672 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) # label(axiom). [assumption].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1637,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1672,b,1638,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1672,b,1639,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1640,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1672,b,1641,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1672,b,1642,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1643,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1672,b,1644,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1672,b,1645,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1672,b,1646,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1672,b,1647,a)].
% 12.54/12.72 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1672,b,1648,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1672,b,1649,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1672,b,1650,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1672,b,1651,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1672,b,1652,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1672,b,1653,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1672,b,1654,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1672,b,1655,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1672,b,1656,a)].
% 12.54/12.73 1673 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1637,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1638,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1673,b,1639,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1640,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1641,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1673,b,1642,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1643,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1673,b,1644,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1673,b,1645,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1673,b,1646,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1647,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1648,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1673,b,1649,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1650,a)].
% 12.54/12.73 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1651,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1673,b,1652,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1673,b,1653,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1673,b,1654,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1673,b,1655,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1673,b,1656,a)].
% 12.54/12.74 1674 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1674,b,1637,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1674,b,1638,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1674,b,1639,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1674,b,1640,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1674,b,1641,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1674,b,1642,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1674,b,1643,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1674,b,1644,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1674,b,1645,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1674,b,1646,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1674,b,1647,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1674,b,1648,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1674,b,1649,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1674,b,1650,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1674,b,1651,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1674,b,1652,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1674,b,1653,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1674,b,1654,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1674,b,1655,a)].
% 12.54/12.74 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1674,b,1656,a)].
% 12.54/12.75 1675 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1637,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1638,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1675,b,1639,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1640,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1641,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1675,b,1642,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1643,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1675,b,1644,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1675,b,1645,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1675,b,1646,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1647,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1648,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1675,b,1649,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1650,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1651,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1675,b,1652,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1675,b,1653,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1675,b,1654,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1675,b,1655,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1675,b,1656,a)].
% 12.54/12.75 1676 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1637,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1638,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1676,b,1639,a)].
% 12.54/12.75 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1640,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1641,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1676,b,1642,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1643,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1676,b,1644,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1676,b,1645,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1676,b,1646,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1647,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1648,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1676,b,1649,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1650,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1651,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1676,b,1652,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1676,b,1653,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1676,b,1654,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1676,b,1655,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1676,b,1656,a)].
% 12.54/12.76 1677 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1637,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1638,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1677,b,1639,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1640,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1641,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1677,b,1642,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1643,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1677,b,1644,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1677,b,1645,a)].
% 12.54/12.76 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1677,b,1646,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1647,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1648,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1677,b,1649,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1650,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1651,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1677,b,1652,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1677,b,1653,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1677,b,1654,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1677,b,1655,a)].
% 12.54/12.77 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1677,b,1656,a)].
% 12.54/12.77 1678 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1637,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1638,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1678,b,1639,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1640,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1641,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1678,b,1642,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1643,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1678,b,1644,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1678,b,1645,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1678,b,1646,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1647,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1648,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1678,b,1649,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1650,a)].
% 12.54/12.77 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1651,a)].
% 13.66/13.89 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1678,b,1652,a)].
% 13.66/13.89 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1678,b,1653,a)].
% 13.66/13.89 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1678,b,1654,a)].
% 13.66/13.89 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1678,b,1655,a)].
% 13.66/13.89 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1678,b,1656,a)].
% 13.66/13.89 1679 class_Orderings_Oord(tc_IntDef_Oint). [resolve(895,a,831,a)].
% 13.66/13.89 1680 class_Orderings_Oord(tc_nat). [resolve(895,a,890,a)].
% 13.66/13.89 1681 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(895,a,891,b)].
% 13.66/13.89 1682 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(903,b,895,a)].
% 13.66/13.89 1683 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1080,b,1078,a)].
% 13.66/13.89 1684 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1086,b,1078,a)].
% 13.66/13.89 1685 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1168,a,1147,b)].
% 13.66/13.89 1686 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1168,a,1148,b)].
% 13.66/13.89 1687 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1473,a,1455,a)].
% 13.66/13.89 1688 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1474,a,1455,a)].
% 13.66/13.89 1689 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1475,a,1455,a)].
% 13.66/13.89 1690 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1494,a,1487,b)].
% 13.66/13.89 1691 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1494,a,1488,b)].
% 13.66/13.89 1692 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1494,a,1490,b)].
% 13.66/13.89 1693 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(1502,b,1494,a)].
% 13.66/13.89 1694 class_Orderings_Oord(tc_nat). [resolve(1508,a,1494,a)].
% 13.66/13.89 1695 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1511,a,1494,a)].
% 13.66/13.89 1696 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A). [resolve(1512,b,1494,a)].
% 13.66/13.89 1697 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A). [resolve(1513,b,1494,a)].
% 13.66/13.89 1698 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1575,b,1549,b)].
% 13.66/13.89 1699 class_Orderings_Oord(tc_set(A)). [resolve(1601,a,1593,a)].
% 13.66/13.89 1700 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1601,a,1599,b)].
% 13.66/13.89 1701 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1601,a,1600,b)].
% 13.66/13.89 1702 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(1618,a,1601,a)].
% 13.66/13.89 1703 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(1619,b,1601,a)].
% 13.66/13.89 1704 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(1620,b,1601,a)].
% 13.66/13.89 1705 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1080,b,1076,a)].
% 13.66/13.89 1706 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 13.66/13.89 1707 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 13.66/13.89 1708 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 13.66/13.89 1709 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 13.66/13.89 1710 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 13.66/13.89 1711 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 13.84/14.02 1712 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) # label(axiom). [assumption].
% 13.84/14.02 1713 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 13.84/14.02 1714 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 13.84/14.02 1715 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 13.84/14.02 1716 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 13.84/14.02 1717 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(892,a,831,a)].
% 13.84/14.02 1718 class_LOrder_Olorder(tc_nat). [resolve(892,a,890,a)].
% 13.84/14.02 1719 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(892,a,891,b)].
% 13.84/14.02 1720 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(903,b,892,a)].
% 13.84/14.02 1721 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1101,b,1099,a)].
% 13.84/14.02 1722 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1159,a,1147,b)].
% 13.84/14.02 1723 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1159,a,1148,b)].
% 13.84/14.02 1724 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(1473,a,1453,a)].
% 13.84/14.02 1725 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A). [resolve(1474,a,1453,a)].
% 13.84/14.02 1726 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A). [resolve(1475,a,1453,a)].
% 13.84/14.02 1727 -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(1594,b,1581,a)].
% 13.84/14.02 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1727,a,1706,a)].
% 13.84/14.02 Derived: -c_less(A,A,tc_nat). [resolve(1727,a,1707,a)].
% 13.84/14.02 1728 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1582,a)].
% 13.84/14.02 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1728,a,1706,a)].
% 13.84/14.02 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1728,a,1707,a)].
% 13.84/14.02 1729 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1594,b,1583,a)].
% 13.84/14.02 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1729,a,1706,a)].
% 13.84/14.02 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1729,a,1707,a)].
% 13.84/14.02 1730 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1594,b,1584,a)].
% 13.84/14.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1730,a,1706,a)].
% 13.84/14.02 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1730,a,1707,a)].
% 13.84/14.02 1731 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1594,b,1585,a)].
% 13.84/14.02 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1731,a,1706,a)].
% 13.84/14.02 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1731,a,1707,a)].
% 13.84/14.02 1732 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1594,b,1586,a)].
% 13.84/14.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1732,a,1706,a)].
% 13.84/14.02 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1732,a,1707,a)].
% 13.84/14.07 1733 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1594,b,1587,a)].
% 13.84/14.07 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1733,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1733,a,1707,a)].
% 13.84/14.07 1734 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1594,b,1588,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1734,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1734,a,1707,a)].
% 13.84/14.07 1735 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1594,b,1589,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1735,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1735,a,1707,a)].
% 13.84/14.07 1736 -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1594,b,1590,a)].
% 13.84/14.07 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1736,a,1706,a)].
% 13.84/14.07 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1736,a,1707,a)].
% 13.84/14.07 1737 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(1594,b,1591,a)].
% 13.84/14.07 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1737,a,1706,a)].
% 13.84/14.07 Derived: c_lessequals(A,A,tc_nat). [resolve(1737,a,1707,a)].
% 13.84/14.07 1738 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_LOrder_Olorder(C). [resolve(1614,a,1594,b)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(1738,d,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(1738,d,1707,a)].
% 13.84/14.07 1739 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_LOrder_Olorder(C). [resolve(1615,a,1594,b)].
% 13.84/14.07 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1739,d,1706,a)].
% 13.84/14.07 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(1739,d,1707,a)].
% 13.84/14.07 1740 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1637,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1740,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1740,a,1707,a)].
% 13.84/14.07 1741 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1638,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1741,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1741,a,1707,a)].
% 13.84/14.07 1742 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1659,b,1639,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1742,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1742,a,1707,a)].
% 13.84/14.07 1743 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1640,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1743,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1743,a,1707,a)].
% 13.84/14.07 1744 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1641,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1744,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1744,a,1707,a)].
% 13.84/14.07 1745 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1659,b,1642,a)].
% 13.84/14.07 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1745,a,1706,a)].
% 13.84/14.07 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1745,a,1707,a)].
% 13.84/14.07 1746 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1659,b,1643,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1746,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1746,a,1707,a)].
% 13.84/14.07 1747 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1659,b,1644,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1747,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1747,a,1707,a)].
% 13.84/14.07 1748 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1659,b,1645,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1748,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1748,a,1707,a)].
% 13.84/14.07 1749 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1659,b,1646,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1749,a,1706,a)].
% 13.84/14.07 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1749,a,1707,a)].
% 13.84/14.07 1750 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1647,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1750,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1750,a,1707,a)].
% 13.84/14.07 1751 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1659,b,1648,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1751,a,1706,a)].
% 13.84/14.07 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1751,a,1707,a)].
% 13.84/14.07 1752 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1659,b,1649,a)].
% 13.84/14.07 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1752,a,1706,a)].
% 13.84/14.07 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(1752,a,1707,a)].
% 14.05/14.27 1753 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1659,b,1650,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1753,a,1706,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1753,a,1707,a)].
% 14.05/14.27 1754 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1659,b,1651,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1754,a,1706,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1754,a,1707,a)].
% 14.05/14.27 1755 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1659,b,1652,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1755,a,1706,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1755,a,1707,a)].
% 14.05/14.27 1756 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1659,b,1653,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1756,a,1706,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1756,a,1707,a)].
% 14.05/14.27 1757 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1659,b,1654,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1757,a,1706,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1757,a,1707,a)].
% 14.05/14.27 1758 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1659,b,1655,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1758,a,1706,a)].
% 14.05/14.27 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1758,a,1707,a)].
% 14.05/14.27 1759 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1659,b,1656,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1759,a,1706,a)].
% 14.05/14.27 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1759,a,1707,a)].
% 14.05/14.27 1760 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 14.05/14.27 1761 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 14.05/14.27 1762 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 14.05/14.27 1763 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_7) # label(axiom). [assumption].
% 14.05/14.27 1764 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_7) # label(axiom). [assumption].
% 14.05/14.27 1765 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 14.05/14.27 1766 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_9) # label(axiom). [assumption].
% 14.05/14.27 1767 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom). [assumption].
% 14.05/14.28 1768 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 14.05/14.28 1769 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_9) # label(axiom). [assumption].
% 14.05/14.28 1770 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) # label(axiom). [assumption].
% 14.05/14.28 1771 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_57) # label(axiom). [assumption].
% 14.05/14.28 1772 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_43) # label(axiom). [assumption].
% 14.05/14.28 1773 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_16) # label(axiom). [assumption].
% 14.05/14.28 1774 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) # label(axiom). [assumption].
% 14.05/14.28 1775 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_7) # label(axiom). [assumption].
% 14.05/14.28 1776 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_22) # label(axiom). [assumption].
% 14.05/14.28 1777 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_12) # label(axiom). [assumption].
% 14.05/14.28 1778 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_16) # label(axiom). [assumption].
% 14.05/14.28 1779 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_9) # label(axiom). [assumption].
% 14.05/14.28 1780 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_plus(D,B,A),c_plus(E,C,A),A) # label(cls_OrderedGroup_Oadd__mono_0) # label(axiom). [assumption].
% 14.05/14.28 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1780,a,1761,a)].
% 14.05/14.28 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(1780,a,1762,a)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1763,b)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1764,b)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1765,b)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1780,a,1766,b)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1768,b)].
% 14.05/14.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1780,a,1769,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1780,a,1770,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1780,a,1771,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1780,a,1772,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1780,a,1773,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1780,a,1774,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1780,a,1775,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1780,a,1776,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1780,a,1777,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1780,a,1778,b)].
% 14.35/14.52 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1780,a,1779,b)].
% 14.35/14.52 1781 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1166,a,1121,a)].
% 14.35/14.52 1782 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(1166,a,1146,a)].
% 14.35/14.52 1783 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1166,a,1147,b)].
% 14.35/14.52 1784 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1166,a,1148,b)].
% 14.35/14.52 1785 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1462,a)].
% 14.35/14.52 1786 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1474,a,1462,a)].
% 14.35/14.52 1787 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1475,a,1462,a)].
% 14.35/14.52 1788 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1492,a,1487,b)].
% 14.35/14.52 1789 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1492,a,1488,b)].
% 14.35/14.52 1790 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1492,a,1489,b)].
% 14.35/14.52 1791 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1492,a,1490,b)].
% 14.35/14.52 1792 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(1502,b,1492,a)].
% 14.35/14.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1792,b,1760,a)].
% 14.35/14.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1792,b,1767,a)].
% 14.35/14.52 1793 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(1573,b,1514,a)].
% 14.35/14.52 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1793,a,1760,a)].
% 14.35/14.52 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1793,a,1767,a)].
% 14.35/14.52 1794 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1573,b,1549,b)].
% 14.35/14.52 1795 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1573,b,1550,b)].
% 14.35/14.52 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1795,a,1760,a)].
% 14.35/14.54 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(1795,a,1767,a)].
% 14.35/14.54 1796 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1573,b,1551,b)].
% 14.35/14.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1796,a,1760,a)].
% 14.35/14.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(1796,a,1767,a)].
% 14.35/14.54 1797 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1599,b,1581,a)].
% 14.35/14.54 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1797,a,1763,b)].
% 14.35/14.54 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1797,a,1764,b)].
% 14.35/14.54 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1797,a,1765,b)].
% 14.35/14.54 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1797,a,1766,b)].
% 14.35/14.54 1798 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1582,a)].
% 14.35/14.54 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1798,a,1763,b)].
% 14.35/14.54 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1798,a,1764,b)].
% 14.35/14.54 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1798,a,1765,b)].
% 14.35/14.54 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1798,a,1766,b)].
% 14.35/14.54 1799 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1599,b,1583,a)].
% 14.35/14.54 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1799,a,1763,b)].
% 14.35/14.54 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1799,a,1764,b)].
% 14.35/14.54 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1799,a,1765,b)].
% 14.35/14.54 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1799,a,1766,b)].
% 14.35/14.54 1800 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1599,b,1584,a)].
% 14.35/14.54 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1763,b)].
% 14.35/14.54 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1764,b)].
% 14.35/14.54 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1765,b)].
% 14.35/14.54 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1800,a,1766,b)].
% 14.35/14.54 1801 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1599,b,1585,a)].
% 14.35/14.54 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1801,a,1763,b)].
% 14.35/14.54 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1801,a,1764,b)].
% 14.35/14.54 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1801,a,1765,b)].
% 14.35/14.55 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1801,a,1766,b)].
% 14.35/14.55 1802 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1599,b,1586,a)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1802,a,1763,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1802,a,1764,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1802,a,1765,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1802,a,1766,b)].
% 14.35/14.55 1803 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1599,b,1587,a)].
% 14.35/14.55 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1803,a,1763,b)].
% 14.35/14.55 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1803,a,1764,b)].
% 14.35/14.55 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1803,a,1765,b)].
% 14.35/14.55 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1803,a,1766,b)].
% 14.35/14.55 1804 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1599,b,1588,a)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1804,a,1763,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1804,a,1764,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1804,a,1765,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1804,a,1766,b)].
% 14.35/14.55 1805 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1599,b,1589,a)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1763,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1764,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1765,b)].
% 14.35/14.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1805,a,1766,b)].
% 14.35/14.55 1806 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1599,b,1590,a)].
% 14.45/14.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1806,a,1763,b)].
% 14.45/14.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1806,a,1764,b)].
% 14.45/14.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1806,a,1765,b)].
% 14.45/14.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1806,a,1766,b)].
% 14.45/14.61 1807 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1599,b,1591,a)].
% 14.45/14.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1807,a,1763,b)].
% 14.45/14.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1807,a,1764,b)].
% 14.45/14.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1807,a,1765,b)].
% 14.45/14.61 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1807,a,1766,b)].
% 14.45/14.61 1808 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1614,a,1599,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1808,d,1763,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1808,d,1764,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1808,d,1765,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1808,d,1766,b)].
% 14.45/14.61 1809 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(1615,a,1599,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1809,d,1763,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1809,d,1764,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1809,d,1765,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1809,d,1766,b)].
% 14.45/14.61 1810 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1637,a)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1810,a,1763,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1810,a,1764,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1810,a,1765,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1810,a,1766,b)].
% 14.45/14.61 1811 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1638,a)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1811,a,1763,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1811,a,1764,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1811,a,1765,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1811,a,1766,b)].
% 14.45/14.61 1812 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1664,b,1639,a)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1812,a,1763,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1812,a,1764,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1812,a,1765,b)].
% 14.45/14.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1812,a,1766,b)].
% 14.45/14.61 1813 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1640,a)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1813,a,1763,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1813,a,1764,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1813,a,1765,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1813,a,1766,b)].
% 14.45/14.61 1814 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1641,a)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1814,a,1763,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1814,a,1764,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1814,a,1765,b)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1814,a,1766,b)].
% 14.45/14.61 1815 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1664,b,1642,a)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1815,a,1763,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1815,a,1764,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1815,a,1765,b)].
% 14.45/14.61 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1815,a,1766,b)].
% 14.45/14.61 1816 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1664,b,1643,a)].
% 14.45/14.61 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1816,a,1763,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1816,a,1764,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1816,a,1765,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1816,a,1766,b)].
% 14.45/14.62 1817 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1664,b,1644,a)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1817,a,1763,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1817,a,1764,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1817,a,1765,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1817,a,1766,b)].
% 14.45/14.62 1818 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1664,b,1645,a)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1818,a,1763,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1818,a,1764,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1818,a,1765,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1818,a,1766,b)].
% 14.45/14.62 1819 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1664,b,1646,a)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1819,a,1763,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1819,a,1764,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1819,a,1765,b)].
% 14.45/14.62 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1819,a,1766,b)].
% 14.45/14.62 1820 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1647,a)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1820,a,1763,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1820,a,1764,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1820,a,1765,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1820,a,1766,b)].
% 14.45/14.62 1821 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1664,b,1648,a)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1821,a,1763,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1821,a,1764,b)].
% 14.45/14.62 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1821,a,1765,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1821,a,1766,b)].
% 14.45/14.63 1822 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1664,b,1649,a)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1822,a,1763,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1822,a,1764,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1822,a,1765,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1822,a,1766,b)].
% 14.45/14.63 1823 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1664,b,1650,a)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1823,a,1763,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1823,a,1764,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1823,a,1765,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1823,a,1766,b)].
% 14.45/14.63 1824 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1664,b,1651,a)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1824,a,1763,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1824,a,1764,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1824,a,1765,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1824,a,1766,b)].
% 14.45/14.63 1825 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1664,b,1652,a)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1825,a,1763,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1825,a,1764,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1825,a,1765,b)].
% 14.45/14.63 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1825,a,1766,b)].
% 14.45/14.63 1826 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1664,b,1653,a)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1826,a,1763,b)].
% 14.45/14.63 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1826,a,1764,b)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1826,a,1765,b)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1826,a,1766,b)].
% 14.65/14.84 1827 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1664,b,1654,a)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1827,a,1763,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1827,a,1764,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1827,a,1765,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1827,a,1766,b)].
% 14.65/14.84 1828 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1664,b,1655,a)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1828,a,1763,b)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1828,a,1764,b)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1828,a,1765,b)].
% 14.65/14.84 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1828,a,1766,b)].
% 14.65/14.84 1829 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1664,b,1656,a)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1829,a,1763,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1829,a,1764,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1829,a,1765,b)].
% 14.65/14.84 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1829,a,1766,b)].
% 14.65/14.84 1830 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) # label(axiom). [assumption].
% 14.65/14.84 1831 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 14.65/14.84 1832 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 14.65/14.84 1833 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_6) # label(axiom). [assumption].
% 14.65/14.84 1834 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_6) # label(axiom). [assumption].
% 14.65/14.84 1835 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 14.65/14.84 1836 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_13) # label(axiom). [assumption].
% 14.65/14.84 1837 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # label(axiom). [assumption].
% 14.65/14.84 1838 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_6) # label(axiom). [assumption].
% 14.65/14.85 1839 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) # label(axiom). [assumption].
% 14.65/14.85 1840 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_56) # label(axiom). [assumption].
% 14.65/14.85 1841 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_38) # label(axiom). [assumption].
% 14.65/14.85 1842 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_15) # label(axiom). [assumption].
% 14.65/14.85 1843 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_21) # label(axiom). [assumption].
% 14.65/14.85 1844 -class_OrderedGroup_Ocomm__monoid__add(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) # label(cls_OrderedGroup_Oadd__nonneg__nonneg_0) # label(axiom). [assumption].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1844,b,1831,a)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(1844,b,1832,a)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1844,b,1833,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1844,b,1834,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1844,b,1835,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1844,b,1836,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1844,b,1838,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1844,b,1839,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1844,b,1840,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1844,b,1841,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1844,b,1842,b)].
% 14.65/14.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1844,b,1843,b)].
% 14.65/14.85 1845 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(18,b,1,a)].
% 14.95/15.12 1846 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(18,b,3,a)].
% 14.95/15.12 1847 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(18,b,9,a)].
% 14.95/15.12 1848 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(18,b,10,a)].
% 14.95/15.12 1849 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(775,b,734,a)].
% 14.95/15.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1849,a,1839,b)].
% 14.95/15.12 1850 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(775,b,741,a)].
% 14.95/15.12 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1850,a,1839,b)].
% 14.95/15.12 1851 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1161,a,1121,a)].
% 14.95/15.12 1852 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(1161,a,1146,a)].
% 14.95/15.12 1853 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1161,a,1147,b)].
% 14.95/15.12 1854 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1161,a,1148,b)].
% 14.95/15.12 1855 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1473,a,1461,a)].
% 14.95/15.12 1856 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1474,a,1461,a)].
% 14.95/15.12 1857 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(1475,a,1461,a)].
% 14.95/15.12 1858 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1491,a,1487,b)].
% 14.95/15.12 1859 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1491,a,1488,b)].
% 14.95/15.12 1860 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1491,a,1489,b)].
% 14.95/15.12 1861 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1491,a,1490,b)].
% 14.95/15.12 1862 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1572,b,1514,a)].
% 14.95/15.12 1863 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1572,b,1549,b)].
% 14.95/15.12 1864 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1572,b,1550,b)].
% 14.95/15.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1864,a,1845,a)].
% 14.95/15.12 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1864,a,1846,a)].
% 14.95/15.12 1865 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1572,b,1551,b)].
% 14.95/15.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1865,a,1845,a)].
% 14.95/15.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1865,a,1846,a)].
% 14.95/15.12 1866 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1600,b,1581,a)].
% 14.95/15.12 1867 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1582,a)].
% 14.95/15.12 1868 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1600,b,1583,a)].
% 14.95/15.12 1869 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1600,b,1584,a)].
% 14.95/15.12 1870 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1600,b,1585,a)].
% 15.06/15.21 1871 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1600,b,1586,a)].
% 15.06/15.21 1872 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1600,b,1587,a)].
% 15.06/15.21 1873 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1600,b,1588,a)].
% 15.06/15.21 1874 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1600,b,1589,a)].
% 15.06/15.21 1875 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1600,b,1590,a)].
% 15.06/15.21 1876 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1600,b,1591,a)].
% 15.06/15.21 1877 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1600,b)].
% 15.06/15.21 1878 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1600,b)].
% 15.06/15.21 1879 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1637,a)].
% 15.06/15.21 1880 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1638,a)].
% 15.06/15.21 1881 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1665,b,1639,a)].
% 15.06/15.21 1882 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1640,a)].
% 15.06/15.21 1883 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1641,a)].
% 15.06/15.21 1884 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1665,b,1642,a)].
% 15.06/15.21 1885 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1665,b,1643,a)].
% 15.06/15.21 1886 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1665,b,1644,a)].
% 15.06/15.21 1887 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1665,b,1645,a)].
% 15.06/15.21 1888 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1665,b,1646,a)].
% 15.06/15.21 1889 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1647,a)].
% 15.06/15.21 1890 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1665,b,1648,a)].
% 15.06/15.21 1891 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1665,b,1649,a)].
% 15.06/15.21 1892 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1665,b,1650,a)].
% 15.06/15.21 1893 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1665,b,1651,a)].
% 15.06/15.21 1894 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1665,b,1652,a)].
% 15.34/15.50 1895 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1665,b,1653,a)].
% 15.34/15.50 1896 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1665,b,1654,a)].
% 15.34/15.50 1897 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1665,b,1655,a)].
% 15.34/15.50 1898 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1665,b,1656,a)].
% 15.34/15.50 1899 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1768,b)].
% 15.34/15.50 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1899,d,1831,a)].
% 15.34/15.50 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(1899,d,1832,a)].
% 15.34/15.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1899,d,1833,b)].
% 15.34/15.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1899,d,1834,b)].
% 15.34/15.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1899,d,1835,b)].
% 15.34/15.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1899,d,1836,b)].
% 15.34/15.50 1900 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) # label(axiom). [assumption].
% 15.34/15.50 1901 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 15.34/15.50 1902 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 15.34/15.50 1903 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) # label(axiom). [assumption].
% 15.34/15.50 1904 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) # label(axiom). [assumption].
% 15.34/15.50 1905 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_40) # label(axiom). [assumption].
% 15.34/15.50 1906 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_32) # label(axiom). [assumption].
% 15.34/15.50 1907 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_9) # label(axiom). [assumption].
% 15.34/15.50 1908 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(15,b,1,a)].
% 15.34/15.50 1909 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(15,b,3,a)].
% 15.34/15.50 1910 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(81,b,53,b)].
% 15.34/15.50 1911 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(82,b,53,b)].
% 15.34/15.50 1912 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(891,b,832,a)].
% 15.36/15.50 1913 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(891,b,833,a)].
% 15.36/15.50 1914 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(891,b,834,a)].
% 15.36/15.50 1915 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(891,b,835,a)].
% 15.36/15.50 1916 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,836,a)].
% 15.36/15.50 1917 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,837,a)].
% 15.36/15.50 1918 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(891,b,838,a)].
% 15.36/15.50 1919 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,839,a)].
% 15.36/15.50 1920 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(891,b,840,a)].
% 15.36/15.50 1921 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,841,a)].
% 15.36/15.50 1922 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(891,b,842,a)].
% 15.36/15.50 1923 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,843,a)].
% 15.36/15.50 1924 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,844,a)].
% 15.36/15.50 1925 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(891,b,845,a)].
% 15.36/15.50 1926 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,846,a)].
% 15.36/15.50 1927 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(891,b,847,a)].
% 15.36/15.50 1928 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(891,b,848,a)].
% 15.36/15.50 1929 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(891,b,849,a)].
% 15.36/15.50 1930 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(891,b,850,a)].
% 15.36/15.50 1931 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(891,b,851,a)].
% 15.37/15.51 1932 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(891,b,852,a)].
% 15.37/15.51 1933 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(891,b,853,a)].
% 15.37/15.51 1934 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(891,b,854,a)].
% 15.37/15.51 1935 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(891,b,855,b)].
% 15.37/15.51 1936 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(891,b,856,b)].
% 15.37/15.51 1937 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(891,b,857,a)].
% 15.37/15.51 1938 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(891,b,858,a)].
% 15.37/15.51 1939 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(891,b,859,a)].
% 15.37/15.51 1940 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(891,b,860,a)].
% 15.37/15.51 1941 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(891,b,861,a)].
% 15.37/15.51 1942 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(891,b,862,a)].
% 15.37/15.51 1943 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(891,b,863,a)].
% 15.37/15.51 1944 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(891,b,864,a)].
% 15.37/15.51 1945 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(891,b,865,a)].
% 15.37/15.51 1946 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(891,b,866,a)].
% 15.37/15.51 1947 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(891,b,867,a)].
% 15.37/15.51 1948 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(891,b,868,a)].
% 15.37/15.51 1949 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(891,b,869,a)].
% 15.37/15.51 1950 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(891,b,870,a)].
% 15.37/15.51 1951 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(891,b,871,a)].
% 15.37/15.51 1952 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(891,b,872,a)].
% 15.37/15.51 1953 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(891,b,873,a)].
% 15.37/15.51 1954 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(891,b,874,a)].
% 15.37/15.51 1955 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(891,b,875,a)].
% 15.46/15.65 1956 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(891,b,876,a)].
% 15.46/15.65 1957 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(891,b,877,a)].
% 15.46/15.65 1958 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(891,b,878,a)].
% 15.46/15.65 1959 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(891,b,879,a)].
% 15.46/15.65 1960 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(891,b,880,a)].
% 15.46/15.65 1961 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(891,b,881,a)].
% 15.46/15.65 1962 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(891,b,882,a)].
% 15.46/15.65 1963 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(891,b,883,a)].
% 15.46/15.65 1964 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(891,b,884,a)].
% 15.46/15.65 1965 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(891,b,885,a)].
% 15.46/15.65 1966 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(891,b,886,a)].
% 15.46/15.65 1967 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(891,b,887,a)].
% 15.46/15.65 1968 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(891,b,888,a)].
% 15.46/15.65 1969 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(891,b,889,a)].
% 15.46/15.65 1970 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(904,a,891,b)].
% 15.46/15.65 1971 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(905,a,891,b)].
% 15.46/15.65 1972 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1085,b,1076,a)].
% 15.46/15.65 1973 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1108,b,1099,a)].
% 15.46/15.65 1974 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(1158,a,1121,a)].
% 15.46/15.65 1975 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(1158,a,1146,a)].
% 15.46/15.65 1976 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1158,a,1147,b)].
% 15.46/15.65 1977 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1158,a,1148,b)].
% 15.46/15.65 1978 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1489,b,1477,a)].
% 15.46/15.65 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1978,a,1902,a)].
% 15.55/15.70 1979 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1489,b,1478,a)].
% 15.55/15.70 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1979,a,1902,a)].
% 15.55/15.70 1980 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1489,b,1479,a)].
% 15.55/15.70 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1980,a,1902,a)].
% 15.55/15.70 1981 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1489,b,1480,a)].
% 15.55/15.70 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1981,a,1902,a)].
% 15.55/15.70 1982 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1489,b,1481,a)].
% 15.55/15.70 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1982,a,1902,a)].
% 15.55/15.70 1983 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1489,b,1482,a)].
% 15.55/15.70 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1983,a,1902,a)].
% 15.55/15.70 1984 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1489,b,1483,a)].
% 15.55/15.70 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1984,a,1902,a)].
% 15.55/15.70 1985 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1489,b,1484,a)].
% 15.55/15.70 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1985,a,1902,a)].
% 15.55/15.70 1986 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1503,a,1489,b)].
% 15.55/15.70 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1986,c,1904,b)].
% 15.55/15.70 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1986,c,1907,b)].
% 15.55/15.70 1987 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1504,a,1489,b)].
% 15.55/15.70 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1987,c,1904,b)].
% 15.55/15.70 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1987,c,1907,b)].
% 15.55/15.70 1988 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1505,b,1489,b)].
% 15.55/15.70 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1988,b,1902,a)].
% 15.55/15.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1988,b,1907,b)].
% 15.55/15.70 1989 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1506,b,1489,b)].
% 15.55/15.70 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1989,b,1907,b)].
% 15.55/15.70 1990 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(1597,b,1581,a)].
% 15.55/15.70 1991 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1582,a)].
% 15.55/15.70 1992 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1597,b,1583,a)].
% 15.55/15.70 1993 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1597,b,1584,a)].
% 15.55/15.70 1994 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1597,b,1585,a)].
% 15.55/15.70 1995 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1597,b,1586,a)].
% 15.55/15.75 1996 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1597,b,1587,a)].
% 15.55/15.75 1997 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1597,b,1588,a)].
% 15.55/15.75 1998 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1597,b,1589,a)].
% 15.55/15.75 1999 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1597,b,1590,a)].
% 15.55/15.75 2000 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(1597,b,1591,a)].
% 15.55/15.75 2001 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1614,a,1597,b)].
% 15.55/15.75 2002 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1615,a,1597,b)].
% 15.55/15.75 2003 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1637,a)].
% 15.55/15.75 2004 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1638,a)].
% 15.55/15.75 2005 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1662,b,1639,a)].
% 15.55/15.75 2006 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1640,a)].
% 15.55/15.75 2007 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1641,a)].
% 15.55/15.75 2008 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1662,b,1642,a)].
% 15.55/15.75 2009 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1662,b,1643,a)].
% 15.55/15.75 2010 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1662,b,1644,a)].
% 15.55/15.75 2011 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1662,b,1645,a)].
% 15.55/15.75 2012 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1662,b,1646,a)].
% 15.55/15.75 2013 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1647,a)].
% 15.55/15.75 2014 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1662,b,1648,a)].
% 15.55/15.75 2015 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1662,b,1649,a)].
% 15.55/15.75 2016 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1662,b,1650,a)].
% 15.55/15.75 2017 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1662,b,1651,a)].
% 15.55/15.75 2018 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1662,b,1652,a)].
% 15.55/15.75 2019 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1662,b,1653,a)].
% 15.67/15.82 2020 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1662,b,1654,a)].
% 15.67/15.82 2021 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1662,b,1655,a)].
% 15.67/15.82 2022 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1662,b,1656,a)].
% 15.67/15.82 2023 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1780,a,1765,b)].
% 15.67/15.82 2024 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1797,a,1765,b)].
% 15.67/15.82 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2024,b,1901,a)].
% 15.67/15.82 Derived: -c_less(A,A,tc_nat). [resolve(2024,b,1902,a)].
% 15.67/15.82 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2024,b,1904,b)].
% 15.67/15.82 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2024,b,1905,b)].
% 15.67/15.82 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2024,b,1906,b)].
% 15.67/15.82 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2024,b,1907,b)].
% 15.67/15.82 2025 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1798,a,1765,b)].
% 15.67/15.82 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2025,c,1901,a)].
% 15.67/15.82 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2025,c,1902,a)].
% 15.67/15.82 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2025,c,1904,b)].
% 15.67/15.82 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2025,c,1905,b)].
% 15.67/15.82 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2025,c,1906,b)].
% 15.67/15.82 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1907,b)].
% 15.67/15.82 2026 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1799,a,1765,b)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2026,b,1901,a)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2026,b,1902,a)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2026,b,1904,b)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2026,b,1905,b)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2026,b,1906,b)].
% 15.67/15.82 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2026,b,1907,b)].
% 15.67/15.82 2027 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1800,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2027,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2027,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2027,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2027,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2027,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2027,c,1907,b)].
% 15.67/15.82 2028 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1801,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2028,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2028,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2028,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2028,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2028,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2028,c,1907,b)].
% 15.67/15.82 2029 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1802,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2029,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2029,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2029,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2029,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2029,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2029,c,1907,b)].
% 15.67/15.82 2030 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1803,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2030,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2030,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2030,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2030,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2030,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2030,c,1907,b)].
% 15.67/15.82 2031 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1804,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2031,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(2031,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2031,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2031,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2031,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2031,c,1907,b)].
% 15.67/15.82 2032 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1805,a,1765,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2032,c,1901,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2032,c,1902,a)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2032,c,1904,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2032,c,1905,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2032,c,1906,b)].
% 15.67/15.82 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1907,b)].
% 15.67/15.82 2033 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1806,a,1765,b)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2033,b,1901,a)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2033,b,1902,a)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2033,b,1904,b)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2033,b,1905,b)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2033,b,1906,b)].
% 15.67/15.82 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2033,b,1907,b)].
% 15.67/15.82 2034 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1807,a,1765,b)].
% 15.67/15.82 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2034,b,1901,a)].
% 15.67/15.83 Derived: c_lessequals(A,A,tc_nat). [resolve(2034,b,1902,a)].
% 15.67/15.83 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2034,b,1904,b)].
% 15.67/15.83 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2034,b,1905,b)].
% 15.67/15.83 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2034,b,1906,b)].
% 15.67/15.83 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2034,b,1907,b)].
% 15.67/15.83 2035 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1808,d,1765,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2035,d,1901,a)].
% 15.67/15.83 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2035,d,1902,a)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2035,d,1904,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2035,d,1905,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2035,d,1906,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,d,1907,b)].
% 15.67/15.83 2036 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1809,d,1765,b)].
% 15.67/15.83 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2036,d,1901,a)].
% 15.67/15.83 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2036,d,1902,a)].
% 15.67/15.83 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2036,d,1904,b)].
% 15.67/15.83 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2036,d,1905,b)].
% 15.67/15.83 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2036,d,1906,b)].
% 15.67/15.83 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2036,d,1907,b)].
% 15.67/15.83 2037 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1810,a,1765,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2037,c,1901,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2037,c,1902,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2037,c,1904,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2037,c,1905,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2037,c,1906,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2037,c,1907,b)].
% 15.67/15.83 2038 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1811,a,1765,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2038,c,1901,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2038,c,1902,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2038,c,1904,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2038,c,1905,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2038,c,1906,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2038,c,1907,b)].
% 15.67/15.83 2039 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1812,a,1765,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2039,d,1901,a)].
% 15.67/15.83 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2039,d,1902,a)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2039,d,1904,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2039,d,1905,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2039,d,1906,b)].
% 15.67/15.83 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2039,d,1907,b)].
% 15.67/15.83 2040 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1813,a,1765,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2040,c,1901,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2040,c,1902,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2040,c,1904,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2040,c,1905,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2040,c,1906,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2040,c,1907,b)].
% 15.67/15.83 2041 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1814,a,1765,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2041,c,1901,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2041,c,1902,a)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2041,c,1904,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2041,c,1905,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2041,c,1906,b)].
% 15.67/15.83 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2041,c,1907,b)].
% 15.67/15.83 2042 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1815,a,1765,b)].
% 15.67/15.83 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2042,d,1901,a)].
% 15.67/15.84 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2042,d,1902,a)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2042,d,1904,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2042,d,1905,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2042,d,1906,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2042,d,1907,b)].
% 15.67/15.84 2043 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1816,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2043,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2043,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2043,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2043,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2043,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2043,c,1907,b)].
% 15.67/15.84 2044 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1817,a,1765,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2044,c,1901,a)].
% 15.67/15.84 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2044,c,1902,a)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2044,c,1904,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2044,c,1905,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2044,c,1906,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2044,c,1907,b)].
% 15.67/15.84 2045 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1818,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2045,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2045,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2045,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2045,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2045,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2045,c,1907,b)].
% 15.67/15.84 2046 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1819,a,1765,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2046,c,1901,a)].
% 15.67/15.84 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2046,c,1902,a)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2046,c,1904,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2046,c,1905,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2046,c,1906,b)].
% 15.67/15.84 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2046,c,1907,b)].
% 15.67/15.84 2047 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1820,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2047,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2047,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2047,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2047,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2047,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2047,c,1907,b)].
% 15.67/15.84 2048 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1821,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2048,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2048,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2048,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2048,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2048,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2048,c,1907,b)].
% 15.67/15.84 2049 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1822,a,1765,b)].
% 15.67/15.84 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2049,d,1901,a)].
% 15.67/15.84 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2049,d,1902,a)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2049,d,1904,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2049,d,1905,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2049,d,1906,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2049,d,1907,b)].
% 15.67/15.84 2050 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1823,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2050,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2050,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2050,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2050,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2050,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2050,c,1907,b)].
% 15.67/15.84 2051 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1824,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2051,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2051,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2051,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2051,c,1905,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2051,c,1906,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2051,c,1907,b)].
% 15.67/15.84 2052 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1825,a,1765,b)].
% 15.67/15.84 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2052,d,1901,a)].
% 15.67/15.84 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2052,d,1902,a)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2052,d,1904,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2052,d,1905,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2052,d,1906,b)].
% 15.67/15.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2052,d,1907,b)].
% 15.67/15.84 2053 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1826,a,1765,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2053,c,1901,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2053,c,1902,a)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2053,c,1904,b)].
% 15.67/15.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2053,c,1905,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2053,c,1906,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2053,c,1907,b)].
% 15.67/15.85 2054 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1827,a,1765,b)].
% 15.67/15.85 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2054,c,1901,a)].
% 15.67/15.85 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2054,c,1902,a)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2054,c,1904,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2054,c,1905,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2054,c,1906,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2054,c,1907,b)].
% 15.67/15.85 2055 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1828,a,1765,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2055,c,1901,a)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2055,c,1902,a)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2055,c,1904,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2055,c,1905,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2055,c,1906,b)].
% 15.67/15.85 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2055,c,1907,b)].
% 15.67/15.85 2056 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1829,a,1765,b)].
% 15.67/15.85 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2056,c,1901,a)].
% 15.67/15.85 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2056,c,1902,a)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2056,c,1904,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2056,c,1905,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2056,c,1906,b)].
% 15.67/15.85 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2056,c,1907,b)].
% 15.67/15.85 2057 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1844,b,1835,b)].
% 15.67/15.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2057,e,1901,a)].
% 15.67/15.85 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(2057,e,1902,a)].
% 15.67/15.85 2058 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1899,d,1835,b)].
% 15.85/16.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2058,d,1901,a)].
% 15.85/16.03 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2058,d,1902,a)].
% 15.85/16.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2058,d,1904,b)].
% 15.85/16.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2058,d,1905,b)].
% 15.85/16.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2058,d,1906,b)].
% 15.85/16.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2058,d,1907,b)].
% 15.85/16.03 2059 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 15.85/16.03 2060 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 15.85/16.03 2061 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 15.85/16.03 2062 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_8) # label(axiom). [assumption].
% 15.85/16.03 2063 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) # label(axiom). [assumption].
% 15.85/16.03 2064 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_46) # label(axiom). [assumption].
% 15.85/16.03 2065 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_42) # label(axiom). [assumption].
% 15.85/16.03 2066 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_23) # label(axiom). [assumption].
% 15.85/16.03 2067 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) # label(axiom). [assumption].
% 15.85/16.03 2068 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_0) # label(axiom). [assumption].
% 15.85/16.03 2069 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_21) # label(axiom). [assumption].
% 15.85/16.03 2070 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_15) # label(axiom). [assumption].
% 15.85/16.03 2071 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_15) # label(axiom). [assumption].
% 15.85/16.03 2072 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom). [assumption].
% 15.85/16.03 2073 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 15.85/16.03 2074 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 15.85/16.03 2075 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom). [assumption].
% 15.85/16.05 2076 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom). [assumption].
% 15.85/16.05 2077 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(c_0,D,A) | c_lessequals(c_times(B,D,A),c_times(C,D,A),A) # label(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) # label(axiom). [assumption].
% 15.85/16.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2077,a,2060,a)].
% 15.85/16.05 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2077,a,2061,a)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2062,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2077,a,2063,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2077,a,2064,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2077,a,2065,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2077,a,2066,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2067,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2068,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2077,a,2069,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2070,b)].
% 15.85/16.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2071,b)].
% 15.85/16.05 2078 -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(159,b,131,b)].
% 15.85/16.05 2079 -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(159,b,133,b)].
% 15.85/16.05 2080 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(163,a,159,b)].
% 15.85/16.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2080,b,2070,b)].
% 15.85/16.05 2081 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(164,a,159,b)].
% 15.85/16.05 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2081,b,2070,b)].
% 15.85/16.05 2082 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(165,a,159,b)].
% 15.85/16.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2082,b,2063,b)].
% 15.85/16.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2082,b,2066,b)].
% 15.85/16.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2082,b,2067,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2082,b,2068,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2082,b,2070,b)].
% 15.85/16.07 2083 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(166,a,159,b)].
% 15.85/16.07 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2083,b,2063,b)].
% 15.85/16.07 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2083,b,2066,b)].
% 15.85/16.07 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2083,b,2067,b)].
% 15.85/16.07 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2083,b,2068,b)].
% 15.85/16.07 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2083,b,2070,b)].
% 15.85/16.07 2084 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(171,a,159,b)].
% 15.85/16.07 2085 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(172,a,159,b)].
% 15.85/16.07 2086 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(240,a,233,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2086,b,2063,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2086,b,2066,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2086,b,2067,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2086,b,2068,b)].
% 15.85/16.07 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2086,b,2070,b)].
% 15.85/16.07 2087 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(241,a,233,b)].
% 15.85/16.07 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2087,b,2063,b)].
% 15.85/16.07 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2087,b,2066,b)].
% 15.85/16.07 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,b,2067,b)].
% 15.85/16.07 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2087,b,2068,b)].
% 15.85/16.07 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2087,b,2070,b)].
% 15.85/16.07 2088 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__semiring(D). [resolve(247,b,233,b)].
% 15.85/16.07 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2088,b,2063,b)].
% 15.85/16.07 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2088,b,2066,b)].
% 15.85/16.07 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2088,b,2067,b)].
% 15.85/16.07 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2088,b,2068,b)].
% 15.85/16.07 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2088,b,2070,b)].
% 15.85/16.07 2089 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(248,b,233,b)].
% 15.85/16.07 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2089,b,2063,b)].
% 15.85/16.07 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2089,b,2066,b)].
% 16.15/16.30 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2089,b,2067,b)].
% 16.15/16.30 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,b,2068,b)].
% 16.15/16.30 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,b,2070,b)].
% 16.15/16.30 2090 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(1165,a,1121,a)].
% 16.15/16.30 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2090,a,2059,a)].
% 16.15/16.30 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2090,a,2072,a)].
% 16.15/16.30 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2078,a)].
% 16.15/16.30 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2079,a)].
% 16.15/16.30 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2084,b)].
% 16.15/16.30 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2090,a,2085,b)].
% 16.15/16.30 2091 class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(1165,a,1146,a)].
% 16.15/16.30 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2091,a,2059,a)].
% 16.15/16.30 Derived: class_HOL_Otimes(tc_nat). [resolve(2091,a,2072,a)].
% 16.15/16.30 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2091,a,2073,a)].
% 16.15/16.30 Derived: class_HOL_Ozero(tc_nat). [resolve(2091,a,2076,a)].
% 16.15/16.30 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(2091,a,2078,a)].
% 16.15/16.30 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(2091,a,2079,a)].
% 16.15/16.30 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(2091,a,2084,b)].
% 16.15/16.30 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2091,a,2085,b)].
% 16.15/16.30 2092 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1165,a,1147,b)].
% 16.15/16.30 2093 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1165,a,1148,b)].
% 16.15/16.30 2094 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(1612,b,1581,a)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2094,a,2062,b)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2094,a,2067,b)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2094,a,2068,b)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2094,a,2069,b)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2094,a,2070,b)].
% 16.15/16.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2094,a,2071,b)].
% 16.15/16.30 2095 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1582,a)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2095,a,2062,b)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2095,a,2067,b)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2095,a,2068,b)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2095,a,2069,b)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2095,a,2070,b)].
% 16.15/16.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2095,a,2071,b)].
% 16.15/16.30 2096 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1612,b,1583,a)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2096,a,2062,b)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2096,a,2067,b)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2096,a,2068,b)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2096,a,2069,b)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2096,a,2070,b)].
% 16.15/16.31 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2096,a,2071,b)].
% 16.15/16.31 2097 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1612,b,1584,a)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,a,2062,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,a,2067,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2097,a,2068,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2097,a,2069,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2097,a,2070,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2097,a,2071,b)].
% 16.15/16.31 2098 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1612,b,1585,a)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2098,a,2062,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2098,a,2067,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2098,a,2068,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2098,a,2069,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2098,a,2070,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2098,a,2071,b)].
% 16.15/16.31 2099 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1612,b,1586,a)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2099,a,2062,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2099,a,2067,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2099,a,2068,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2099,a,2069,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2099,a,2070,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2099,a,2071,b)].
% 16.15/16.31 2100 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1612,b,1587,a)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2100,a,2062,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2100,a,2067,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2100,a,2068,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2100,a,2069,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2100,a,2070,b)].
% 16.15/16.31 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2100,a,2071,b)].
% 16.15/16.31 2101 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1612,b,1588,a)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2101,a,2062,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2101,a,2067,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2101,a,2068,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2101,a,2069,b)].
% 16.15/16.31 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2101,a,2070,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2101,a,2071,b)].
% 16.15/16.32 2102 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1612,b,1589,a)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,a,2062,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,a,2067,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2102,a,2068,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2102,a,2069,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2102,a,2070,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2102,a,2071,b)].
% 16.15/16.32 2103 -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1612,b,1590,a)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2103,a,2062,b)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2103,a,2067,b)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2103,a,2068,b)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2103,a,2069,b)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2103,a,2070,b)].
% 16.15/16.32 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2103,a,2071,b)].
% 16.15/16.32 2104 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(1612,b,1591,a)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2104,a,2062,b)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2104,a,2067,b)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2104,a,2068,b)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2104,a,2069,b)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2104,a,2070,b)].
% 16.15/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2104,a,2071,b)].
% 16.15/16.32 2105 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1614,a,1612,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2062,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2067,b)].
% 16.15/16.32 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2105,d,2068,b)].
% 16.15/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2105,d,2069,b)].
% 16.15/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2105,d,2070,b)].
% 16.15/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2105,d,2071,b)].
% 16.15/16.38 2106 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1615,a,1612,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,d,2062,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,d,2067,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2106,d,2068,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2106,d,2069,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2106,d,2070,b)].
% 16.15/16.38 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2106,d,2071,b)].
% 16.15/16.38 2107 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1637,a)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2107,a,2062,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2107,a,2067,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2107,a,2068,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2107,a,2069,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2107,a,2070,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2107,a,2071,b)].
% 16.15/16.38 2108 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1638,a)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2108,a,2062,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2108,a,2067,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2108,a,2068,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2108,a,2069,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2108,a,2070,b)].
% 16.15/16.38 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2108,a,2071,b)].
% 16.15/16.38 2109 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1677,b,1639,a)].
% 16.15/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2109,a,2062,b)].
% 16.15/16.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2109,a,2067,b)].
% 16.15/16.39 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2109,a,2068,b)].
% 16.15/16.39 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2109,a,2069,b)].
% 16.15/16.39 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2109,a,2070,b)].
% 16.15/16.39 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2109,a,2071,b)].
% 16.15/16.39 2110 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1640,a)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,a,2062,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2110,a,2067,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2110,a,2068,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2110,a,2069,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2110,a,2070,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2110,a,2071,b)].
% 16.15/16.39 2111 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1641,a)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,a,2062,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2111,a,2067,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2111,a,2068,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2111,a,2069,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2111,a,2070,b)].
% 16.15/16.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2111,a,2071,b)].
% 16.15/16.39 2112 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1677,b,1642,a)].
% 16.15/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2112,a,2062,b)].
% 16.15/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2112,a,2067,b)].
% 16.15/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2112,a,2068,b)].
% 16.15/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2112,a,2069,b)].
% 16.15/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2112,a,2070,b)].
% 16.25/16.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2112,a,2071,b)].
% 16.25/16.39 2113 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1677,b,1643,a)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2113,a,2062,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2113,a,2067,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2113,a,2068,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2113,a,2069,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2113,a,2070,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2113,a,2071,b)].
% 16.25/16.39 2114 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1677,b,1644,a)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2114,a,2062,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2114,a,2067,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2114,a,2068,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2114,a,2069,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2114,a,2070,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2114,a,2071,b)].
% 16.25/16.39 2115 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1677,b,1645,a)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,a,2062,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2115,a,2067,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2115,a,2068,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2115,a,2069,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2115,a,2070,b)].
% 16.25/16.39 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2115,a,2071,b)].
% 16.25/16.39 2116 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1677,b,1646,a)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,a,2062,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2116,a,2067,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2116,a,2068,b)].
% 16.25/16.39 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2116,a,2069,b)].
% 16.25/16.40 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2116,a,2070,b)].
% 16.25/16.40 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2116,a,2071,b)].
% 16.25/16.40 2117 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1647,a)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2117,a,2062,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2117,a,2067,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2117,a,2068,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2117,a,2069,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2117,a,2070,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2117,a,2071,b)].
% 16.25/16.40 2118 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1677,b,1648,a)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2118,a,2062,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2118,a,2067,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2118,a,2068,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2118,a,2069,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2118,a,2070,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2118,a,2071,b)].
% 16.25/16.40 2119 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1677,b,1649,a)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2119,a,2062,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2119,a,2067,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2119,a,2068,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2119,a,2069,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2119,a,2070,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2119,a,2071,b)].
% 16.25/16.40 2120 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1677,b,1650,a)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2120,a,2062,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2120,a,2067,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2120,a,2068,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2120,a,2069,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2120,a,2070,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2120,a,2071,b)].
% 16.25/16.40 2121 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1677,b,1651,a)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2121,a,2062,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2121,a,2067,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2121,a,2068,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2121,a,2069,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2121,a,2070,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2121,a,2071,b)].
% 16.25/16.40 2122 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1677,b,1652,a)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2122,a,2062,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2122,a,2067,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2122,a,2068,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2122,a,2069,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2122,a,2070,b)].
% 16.25/16.40 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2122,a,2071,b)].
% 16.25/16.40 2123 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1677,b,1653,a)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2123,a,2062,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2123,a,2067,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2123,a,2068,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2123,a,2069,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2123,a,2070,b)].
% 16.25/16.40 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2123,a,2071,b)].
% 16.27/16.42 2124 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1677,b,1654,a)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2124,a,2062,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2124,a,2067,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2124,a,2068,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2124,a,2069,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2124,a,2070,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2124,a,2071,b)].
% 16.27/16.42 2125 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1677,b,1655,a)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2125,a,2062,b)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2125,a,2067,b)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2125,a,2068,b)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2125,a,2069,b)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2125,a,2070,b)].
% 16.27/16.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2125,a,2071,b)].
% 16.27/16.42 2126 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1677,b,1656,a)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2126,a,2062,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2126,a,2067,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2126,a,2068,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2126,a,2069,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2126,a,2070,b)].
% 16.27/16.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2126,a,2071,b)].
% 16.27/16.42 2127 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__semiring(C). [resolve(1780,a,1779,b)].
% 16.27/16.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2127,d,2062,b)].
% 16.27/16.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2127,d,2067,b)].
% 16.27/16.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2127,d,2068,b)].
% 16.27/16.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2127,d,2069,b)].
% 16.27/16.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2127,d,2070,b)].
% 16.53/16.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2127,d,2071,b)].
% 16.53/16.68 2128 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_10) # label(axiom). [assumption].
% 16.53/16.68 2129 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 16.53/16.68 2130 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 16.53/16.68 2131 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_7) # label(axiom). [assumption].
% 16.53/16.68 2132 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) # label(axiom). [assumption].
% 16.53/16.68 2133 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_45) # label(axiom). [assumption].
% 16.53/16.68 2134 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_40) # label(axiom). [assumption].
% 16.53/16.68 2135 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_22) # label(axiom). [assumption].
% 16.53/16.68 2136 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) # label(axiom). [assumption].
% 16.53/16.68 2137 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_3) # label(axiom). [assumption].
% 16.53/16.68 2138 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_4) # label(axiom). [assumption].
% 16.53/16.68 2139 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_5) # label(axiom). [assumption].
% 16.53/16.68 2140 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # label(axiom). [assumption].
% 16.53/16.68 2141 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_9) # label(axiom). [assumption].
% 16.53/16.68 2142 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_22) # label(axiom). [assumption].
% 16.53/16.68 2143 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(34,b,1,a)].
% 16.53/16.68 2144 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(34,b,3,a)].
% 16.53/16.68 2145 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(34,b,10,a)].
% 16.53/16.68 2146 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(81,b,72,b)].
% 16.53/16.68 2147 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(155,b,131,b)].
% 16.53/16.68 2148 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(155,b,133,b)].
% 16.53/16.68 2149 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(165,a,155,b)].
% 16.67/16.82 2150 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(166,a,155,b)].
% 16.67/16.82 2151 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(171,a,155,b)].
% 16.67/16.82 2152 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(172,a,155,b)].
% 16.67/16.82 2153 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(240,a,229,b)].
% 16.67/16.82 2154 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(241,a,229,b)].
% 16.67/16.82 2155 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(247,b,229,b)].
% 16.67/16.82 2156 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(248,b,229,b)].
% 16.67/16.82 2157 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(309,b,288,a)].
% 16.67/16.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2157,a,2132,b)].
% 16.67/16.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2157,a,2135,b)].
% 16.67/16.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2157,a,2136,b)].
% 16.67/16.82 2158 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(309,b,290,a)].
% 16.67/16.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2158,a,2132,b)].
% 16.67/16.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2158,a,2135,b)].
% 16.67/16.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2158,a,2136,b)].
% 16.67/16.82 2159 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(322,a,309,b)].
% 16.67/16.82 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2159,c,2136,b)].
% 16.67/16.82 2160 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(323,a,309,b)].
% 16.67/16.82 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2160,c,2136,b)].
% 16.67/16.82 2161 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(326,a,309,b)].
% 16.67/16.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,b,2136,b)].
% 16.67/16.82 2162 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(790,a,734,a)].
% 16.67/16.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,a,2136,b)].
% 16.67/16.82 2163 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(1163,a,1121,a)].
% 16.67/16.82 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2163,a,2157,a)].
% 16.67/16.82 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2163,a,2158,a)].
% 16.67/16.82 2164 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(1163,a,1146,a)].
% 16.67/16.82 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2164,a,2157,a)].
% 16.67/16.82 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2164,a,2158,a)].
% 16.67/16.82 2165 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1163,a,1147,b)].
% 16.67/16.82 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(2165,a,2157,a)].
% 16.67/16.82 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(2165,a,2158,a)].
% 16.67/16.82 2166 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1163,a,1148,b)].
% 16.67/16.82 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(2166,a,2157,a)].
% 16.67/16.82 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(2166,a,2158,a)].
% 16.85/17.01 2167 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(1608,b,1581,a)].
% 16.85/17.01 2168 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1582,a)].
% 16.85/17.01 2169 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1608,b,1583,a)].
% 16.85/17.01 2170 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1608,b,1584,a)].
% 16.85/17.01 2171 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1608,b,1585,a)].
% 16.85/17.01 2172 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1608,b,1586,a)].
% 16.85/17.01 2173 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1608,b,1587,a)].
% 16.85/17.01 2174 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1608,b,1588,a)].
% 16.85/17.01 2175 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1608,b,1589,a)].
% 16.85/17.01 2176 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1608,b,1590,a)].
% 16.85/17.01 2177 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(1608,b,1591,a)].
% 16.85/17.01 2178 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1614,a,1608,b)].
% 16.85/17.01 2179 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1615,a,1608,b)].
% 16.85/17.01 2180 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1637,a)].
% 16.85/17.01 2181 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1638,a)].
% 16.85/17.01 2182 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1673,b,1639,a)].
% 16.85/17.01 2183 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1640,a)].
% 16.85/17.01 2184 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1641,a)].
% 16.85/17.01 2185 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1673,b,1642,a)].
% 16.85/17.01 2186 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1673,b,1643,a)].
% 16.85/17.01 2187 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1673,b,1644,a)].
% 16.85/17.01 2188 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1673,b,1645,a)].
% 16.85/17.01 2189 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1673,b,1646,a)].
% 16.85/17.01 2190 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1647,a)].
% 16.85/17.01 2191 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1673,b,1648,a)].
% 16.85/17.01 2192 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1673,b,1649,a)].
% 16.96/17.10 2193 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1673,b,1650,a)].
% 16.96/17.10 2194 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1673,b,1651,a)].
% 16.96/17.10 2195 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1673,b,1652,a)].
% 16.96/17.10 2196 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1673,b,1653,a)].
% 16.96/17.10 2197 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1673,b,1654,a)].
% 16.96/17.10 2198 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1673,b,1655,a)].
% 16.96/17.10 2199 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1673,b,1656,a)].
% 16.96/17.10 2200 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1780,a,1775,b)].
% 16.96/17.10 2201 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2077,a,2068,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2201,d,2129,a)].
% 16.96/17.10 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2201,d,2130,a)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,d,2131,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,d,2132,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2201,d,2133,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2201,d,2134,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,d,2135,b)].
% 16.96/17.10 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2201,d,2136,b)].
% 16.96/17.10 2202 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2082,b,2068,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2202,b,2131,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2202,b,2132,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2202,b,2133,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2202,b,2134,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2202,b,2135,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2202,b,2136,b)].
% 16.96/17.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2202,b,2142,b)].
% 16.96/17.10 2203 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2083,b,2068,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2203,b,2131,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2203,b,2132,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2203,b,2133,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2203,b,2134,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2203,b,2135,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2203,b,2136,b)].
% 16.96/17.11 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2203,b,2142,b)].
% 16.96/17.11 2204 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2086,b,2068,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2204,b,2129,a)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2204,b,2131,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2204,b,2132,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2204,b,2133,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2204,b,2134,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2204,b,2135,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2204,b,2136,b)].
% 16.96/17.11 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2204,b,2142,b)].
% 16.96/17.11 2205 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2087,b,2068,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2205,b,2129,a)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2205,b,2131,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2205,b,2132,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2205,b,2133,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2205,b,2134,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2205,b,2135,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2205,b,2136,b)].
% 16.96/17.11 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2205,b,2142,b)].
% 16.96/17.11 2206 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2088,b,2068,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,b,2131,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2206,b,2132,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2206,b,2133,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2206,b,2134,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2206,b,2135,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2206,b,2136,b)].
% 16.96/17.11 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2206,b,2142,b)].
% 16.96/17.11 2207 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2089,b,2068,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2207,b,2131,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,b,2132,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2207,b,2133,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2207,b,2134,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2207,b,2135,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2207,b,2136,b)].
% 16.96/17.11 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2207,b,2142,b)].
% 16.96/17.11 2208 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2094,a,2068,b)].
% 16.96/17.11 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2208,b,2129,a)].
% 16.96/17.11 Derived: -c_less(A,A,tc_nat). [resolve(2208,b,2130,a)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2208,b,2131,b)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2208,b,2132,b)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2208,b,2133,b)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2208,b,2134,b)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2208,b,2135,b)].
% 16.96/17.11 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2208,b,2136,b)].
% 16.96/17.11 2209 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2095,a,2068,b)].
% 16.96/17.11 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2209,c,2129,a)].
% 16.96/17.11 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2209,c,2130,a)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2131,b)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2209,c,2132,b)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2209,c,2133,b)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2209,c,2134,b)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2135,b)].
% 16.96/17.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2209,c,2136,b)].
% 16.96/17.11 2210 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2096,a,2068,b)].
% 16.96/17.11 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2210,b,2129,a)].
% 16.96/17.11 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2210,b,2130,a)].
% 16.96/17.11 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2210,b,2131,b)].
% 16.96/17.11 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2210,b,2132,b)].
% 16.96/17.12 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2210,b,2133,b)].
% 16.96/17.12 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2210,b,2134,b)].
% 16.96/17.12 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2210,b,2135,b)].
% 16.96/17.12 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2210,b,2136,b)].
% 16.96/17.12 2211 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2097,a,2068,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2211,c,2129,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2211,c,2130,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2131,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2211,c,2132,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2211,c,2133,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2211,c,2134,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2135,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2211,c,2136,b)].
% 16.96/17.12 2212 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2098,a,2068,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2212,c,2129,a)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2212,c,2130,a)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2212,c,2131,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2212,c,2132,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2212,c,2133,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2212,c,2134,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2212,c,2135,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2212,c,2136,b)].
% 16.96/17.12 2213 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2099,a,2068,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2213,c,2129,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2213,c,2130,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2213,c,2131,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2213,c,2132,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2213,c,2133,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2213,c,2134,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2213,c,2135,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2213,c,2136,b)].
% 16.96/17.12 2214 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2100,a,2068,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2214,c,2129,a)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2214,c,2130,a)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2214,c,2131,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2214,c,2132,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2214,c,2133,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2214,c,2134,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2214,c,2135,b)].
% 16.96/17.12 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2214,c,2136,b)].
% 16.96/17.12 2215 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2101,a,2068,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2215,c,2129,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(2215,c,2130,a)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2215,c,2131,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2215,c,2132,b)].
% 16.96/17.12 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2215,c,2133,b)].
% 16.96/17.13 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(2215,c,2134,b)].
% 16.96/17.13 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(2215,c,2135,b)].
% 16.96/17.13 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_Opordered__cancel__comm__semiring(C). [resolve(2215,c,2136,b)].
% 16.96/17.13 2216 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2102,a,2068,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2216,c,2129,a)].
% 16.96/17.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2216,c,2130,a)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2216,c,2131,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2216,c,2132,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2216,c,2133,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2216,c,2134,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2216,c,2135,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2216,c,2136,b)].
% 16.96/17.13 2217 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2103,a,2068,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2217,b,2129,a)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2217,b,2130,a)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2217,b,2131,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2217,b,2132,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2217,b,2133,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2217,b,2134,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2217,b,2135,b)].
% 16.96/17.13 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2217,b,2136,b)].
% 16.96/17.13 2218 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2104,a,2068,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2218,b,2129,a)].
% 16.96/17.13 Derived: c_lessequals(A,A,tc_nat). [resolve(2218,b,2130,a)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2218,b,2131,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2218,b,2132,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2218,b,2133,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2218,b,2134,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2218,b,2135,b)].
% 16.96/17.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2218,b,2136,b)].
% 16.96/17.13 2219 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2105,d,2068,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2219,d,2129,a)].
% 16.96/17.13 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2219,d,2130,a)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2219,d,2131,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2219,d,2132,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2219,d,2133,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2219,d,2134,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2219,d,2135,b)].
% 16.96/17.13 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2219,d,2136,b)].
% 16.96/17.13 2220 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2106,d,2068,b)].
% 16.96/17.13 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2220,d,2129,a)].
% 16.96/17.13 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2220,d,2130,a)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2220,d,2131,b)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2220,d,2132,b)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2220,d,2133,b)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2220,d,2134,b)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2220,d,2135,b)].
% 16.96/17.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2220,d,2136,b)].
% 16.96/17.13 2221 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2107,a,2068,b)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2221,c,2129,a)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2221,c,2130,a)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2221,c,2131,b)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2221,c,2132,b)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2221,c,2133,b)].
% 16.96/17.13 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2221,c,2134,b)].
% 16.96/17.14 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(2221,c,2135,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2221,c,2136,b)].
% 16.96/17.14 2222 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2108,a,2068,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2222,c,2129,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2222,c,2130,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2222,c,2131,b)].
% 16.96/17.14 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(2222,c,2132,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2222,c,2133,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2222,c,2134,b)].
% 16.96/17.14 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(2222,c,2135,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2222,c,2136,b)].
% 16.96/17.14 2223 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2109,a,2068,b)].
% 16.96/17.14 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(2223,d,2129,a)].
% 16.96/17.14 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(2223,d,2130,a)].
% 16.96/17.14 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_Olordered__ring(C). [resolve(2223,d,2131,b)].
% 16.96/17.14 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(2223,d,2132,b)].
% 16.96/17.14 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(2223,d,2133,b)].
% 16.96/17.14 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(2223,d,2134,b)].
% 16.96/17.14 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(2223,d,2135,b)].
% 16.96/17.14 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_Opordered__cancel__comm__semiring(C). [resolve(2223,d,2136,b)].
% 16.96/17.14 2224 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2110,a,2068,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2224,c,2129,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2224,c,2130,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2224,c,2131,b)].
% 16.96/17.14 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(2224,c,2132,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2224,c,2133,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2224,c,2134,b)].
% 16.96/17.14 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(2224,c,2135,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2224,c,2136,b)].
% 16.96/17.14 2225 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2111,a,2068,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2225,c,2129,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2225,c,2130,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2225,c,2131,b)].
% 16.96/17.14 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(2225,c,2132,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2225,c,2133,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2225,c,2134,b)].
% 16.96/17.14 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(2225,c,2135,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2225,c,2136,b)].
% 16.96/17.14 2226 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2112,a,2068,b)].
% 16.96/17.14 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(2226,d,2129,a)].
% 16.96/17.14 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(2226,d,2130,a)].
% 16.96/17.14 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_Olordered__ring(C). [resolve(2226,d,2131,b)].
% 16.96/17.14 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(2226,d,2132,b)].
% 16.96/17.14 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(2226,d,2133,b)].
% 16.96/17.14 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(2226,d,2134,b)].
% 16.96/17.14 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(2226,d,2135,b)].
% 16.96/17.14 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_Opordered__cancel__comm__semiring(C). [resolve(2226,d,2136,b)].
% 16.96/17.14 2227 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2113,a,2068,b)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2227,c,2129,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2227,c,2130,a)].
% 16.96/17.14 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2227,c,2131,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2227,c,2132,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2227,c,2133,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2227,c,2134,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2227,c,2135,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2227,c,2136,b)].
% 16.96/17.15 2228 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2114,a,2068,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2228,c,2129,a)].
% 16.96/17.15 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2228,c,2130,a)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2228,c,2131,b)].
% 16.96/17.15 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(2228,c,2132,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2228,c,2133,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2228,c,2134,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2228,c,2135,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2228,c,2136,b)].
% 16.96/17.15 2229 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2115,a,2068,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2229,c,2129,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2229,c,2130,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2229,c,2131,b)].
% 16.96/17.15 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(2229,c,2132,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2229,c,2133,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2229,c,2134,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2229,c,2135,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2229,c,2136,b)].
% 16.96/17.15 2230 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2116,a,2068,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2230,c,2129,a)].
% 16.96/17.15 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2230,c,2130,a)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2230,c,2131,b)].
% 16.96/17.15 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(2230,c,2132,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2230,c,2133,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2230,c,2134,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2230,c,2135,b)].
% 16.96/17.15 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2230,c,2136,b)].
% 16.96/17.15 2231 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2117,a,2068,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2231,c,2129,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2231,c,2130,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2231,c,2131,b)].
% 16.96/17.15 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(2231,c,2132,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2231,c,2133,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2231,c,2134,b)].
% 16.96/17.15 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(2231,c,2135,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2231,c,2136,b)].
% 16.96/17.15 2232 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2118,a,2068,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2232,c,2129,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2232,c,2130,a)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2232,c,2131,b)].
% 16.96/17.15 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(2232,c,2132,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2232,c,2133,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2232,c,2134,b)].
% 16.96/17.15 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(2232,c,2135,b)].
% 16.96/17.15 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2232,c,2136,b)].
% 16.96/17.15 2233 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2119,a,2068,b)].
% 16.96/17.15 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(2233,d,2129,a)].
% 16.96/17.15 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(2233,d,2130,a)].
% 16.96/17.15 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_Olordered__ring(C). [resolve(2233,d,2131,b)].
% 16.96/17.15 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(2233,d,2132,b)].
% 16.96/17.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2233,d,2133,b)].
% 16.96/17.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2233,d,2134,b)].
% 16.96/17.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2233,d,2135,b)].
% 16.96/17.16 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2233,d,2136,b)].
% 16.96/17.16 2234 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2120,a,2068,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2234,c,2129,a)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2234,c,2130,a)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2234,c,2131,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2234,c,2132,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2234,c,2133,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2234,c,2134,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2234,c,2135,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2234,c,2136,b)].
% 16.96/17.16 2235 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2121,a,2068,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2235,c,2129,a)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2235,c,2130,a)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2235,c,2131,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2235,c,2132,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2235,c,2133,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2235,c,2134,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2235,c,2135,b)].
% 16.96/17.16 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2235,c,2136,b)].
% 16.96/17.16 2236 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2122,a,2068,b)].
% 16.96/17.16 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(2236,d,2129,a)].
% 16.96/17.16 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(2236,d,2130,a)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2236,d,2131,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2236,d,2132,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2236,d,2133,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2236,d,2134,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2236,d,2135,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2236,d,2136,b)].
% 16.96/17.17 2237 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2123,a,2068,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2237,c,2129,a)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2237,c,2130,a)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2237,c,2131,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2237,c,2132,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2237,c,2133,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2237,c,2134,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2237,c,2135,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2237,c,2136,b)].
% 16.96/17.17 2238 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2124,a,2068,b)].
% 16.96/17.17 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2238,c,2129,a)].
% 16.96/17.17 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2238,c,2130,a)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2238,c,2131,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2238,c,2132,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2238,c,2133,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2238,c,2134,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2238,c,2135,b)].
% 16.96/17.17 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2238,c,2136,b)].
% 16.96/17.17 2239 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2125,a,2068,b)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2239,c,2129,a)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2239,c,2130,a)].
% 16.96/17.17 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,c,2131,b)].
% 17.17/17.38 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2239,c,2132,b)].
% 17.17/17.38 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2239,c,2133,b)].
% 17.17/17.38 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2239,c,2134,b)].
% 17.17/17.38 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2239,c,2135,b)].
% 17.17/17.38 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2239,c,2136,b)].
% 17.17/17.38 2240 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2126,a,2068,b)].
% 17.17/17.38 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2240,c,2129,a)].
% 17.17/17.38 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2240,c,2130,a)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,c,2131,b)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2240,c,2132,b)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2240,c,2133,b)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2240,c,2134,b)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2240,c,2135,b)].
% 17.17/17.38 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2240,c,2136,b)].
% 17.17/17.38 2241 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2127,d,2068,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2241,d,2129,a)].
% 17.17/17.38 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2241,d,2130,a)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2241,d,2131,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2241,d,2132,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2241,d,2133,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2241,d,2134,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2241,d,2135,b)].
% 17.17/17.38 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2241,d,2136,b)].
% 17.17/17.38 2242 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_2) # label(axiom). [assumption].
% 17.17/17.38 2243 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 17.17/17.38 2244 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 17.25/17.41 2245 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) # label(axiom). [assumption].
% 17.25/17.41 2246 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_39) # label(axiom). [assumption].
% 17.25/17.41 2247 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_31) # label(axiom). [assumption].
% 17.25/17.41 2248 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_3) # label(axiom). [assumption].
% 17.25/17.41 2249 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_4) # label(axiom). [assumption].
% 17.25/17.41 2250 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_6) # label(axiom). [assumption].
% 17.25/17.41 2251 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_7) # label(axiom). [assumption].
% 17.25/17.41 2252 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_8) # label(axiom). [assumption].
% 17.25/17.41 2253 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(32,b,1,a)].
% 17.25/17.41 2254 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(32,b,3,a)].
% 17.25/17.41 2255 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(81,b,70,b)].
% 17.25/17.41 2256 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(82,b,70,b)].
% 17.25/17.41 2257 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(153,b,131,b)].
% 17.25/17.41 2258 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(153,b,133,b)].
% 17.25/17.41 2259 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(165,a,153,b)].
% 17.25/17.41 2260 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(166,a,153,b)].
% 17.25/17.41 2261 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(171,a,153,b)].
% 17.25/17.41 2262 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(172,a,153,b)].
% 17.25/17.41 2263 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(240,a,227,b)].
% 17.25/17.41 2264 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(241,a,227,b)].
% 17.25/17.41 2265 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(247,b,227,b)].
% 17.25/17.41 2266 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(248,b,227,b)].
% 17.25/17.41 2267 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(307,b,288,a)].
% 17.25/17.41 2268 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(307,b,290,a)].
% 17.25/17.41 2269 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(322,a,307,b)].
% 17.25/17.41 2270 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(323,a,307,b)].
% 17.25/17.48 2271 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(789,a,734,a)].
% 17.25/17.48 2272 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(789,a,741,a)].
% 17.25/17.48 2273 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(902,b,832,a)].
% 17.25/17.48 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2273,a,2245,b)].
% 17.25/17.48 2274 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(902,b,833,a)].
% 17.25/17.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2274,a,2245,b)].
% 17.25/17.48 2275 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(902,b,834,a)].
% 17.25/17.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2275,a,2245,b)].
% 17.25/17.48 2276 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(902,b,835,a)].
% 17.25/17.48 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2276,a,2245,b)].
% 17.25/17.48 2277 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,836,a)].
% 17.25/17.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2277,a,2245,b)].
% 17.25/17.48 2278 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,837,a)].
% 17.25/17.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2278,a,2245,b)].
% 17.25/17.48 2279 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(902,b,838,a)].
% 17.25/17.48 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2279,a,2245,b)].
% 17.25/17.48 2280 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,839,a)].
% 17.25/17.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2280,a,2245,b)].
% 17.25/17.48 2281 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(902,b,840,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2281,a,2245,b)].
% 17.25/17.49 2282 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,841,a)].
% 17.25/17.49 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2245,b)].
% 17.25/17.49 2283 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(902,b,842,a)].
% 17.25/17.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2283,a,2245,b)].
% 17.25/17.49 2284 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,843,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2284,a,2245,b)].
% 17.25/17.49 2285 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,844,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2285,a,2245,b)].
% 17.25/17.49 2286 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(902,b,845,a)].
% 17.25/17.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2286,a,2245,b)].
% 17.25/17.49 2287 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,846,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2287,a,2245,b)].
% 17.25/17.49 2288 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(902,b,847,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2288,a,2245,b)].
% 17.25/17.49 2289 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(902,b,848,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2289,a,2245,b)].
% 17.25/17.49 2290 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(902,b,849,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2290,a,2245,b)].
% 17.25/17.49 2291 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(902,b,850,a)].
% 17.25/17.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2291,a,2245,b)].
% 17.25/17.49 2292 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(902,b,851,a)].
% 17.25/17.49 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,a,2245,b)].
% 17.25/17.49 2293 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(902,b,852,a)].
% 17.25/17.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2293,a,2245,b)].
% 17.25/17.49 2294 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(902,b,853,a)].
% 17.25/17.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2294,a,2245,b)].
% 17.25/17.49 2295 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(902,b,854,a)].
% 17.25/17.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2295,a,2245,b)].
% 17.25/17.49 2296 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(902,b,855,b)].
% 17.25/17.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2296,a,2245,b)].
% 17.25/17.49 2297 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(902,b,856,b)].
% 17.25/17.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2297,a,2245,b)].
% 17.25/17.49 2298 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(902,b,857,a)].
% 17.25/17.49 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2298,a,2245,b)].
% 17.25/17.49 2299 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(902,b,858,a)].
% 17.25/17.49 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2299,a,2245,b)].
% 17.25/17.49 2300 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(902,b,859,a)].
% 17.25/17.49 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2300,a,2245,b)].
% 17.25/17.49 2301 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(902,b,860,a)].
% 17.25/17.49 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2301,a,2245,b)].
% 17.36/17.50 2302 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(902,b,861,a)].
% 17.36/17.50 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2302,a,2245,b)].
% 17.36/17.50 2303 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(902,b,862,a)].
% 17.36/17.50 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2303,a,2245,b)].
% 17.36/17.50 2304 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(902,b,863,a)].
% 17.36/17.50 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2304,a,2245,b)].
% 17.36/17.50 2305 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(902,b,864,a)].
% 17.36/17.50 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2305,a,2245,b)].
% 17.36/17.50 2306 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(902,b,865,a)].
% 17.36/17.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2306,a,2245,b)].
% 17.36/17.50 2307 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(902,b,866,a)].
% 17.36/17.50 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2307,a,2245,b)].
% 17.36/17.50 2308 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(902,b,867,a)].
% 17.36/17.50 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2308,a,2245,b)].
% 17.36/17.50 2309 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(902,b,868,a)].
% 17.36/17.50 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2309,a,2245,b)].
% 17.36/17.50 2310 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(902,b,869,a)].
% 17.36/17.50 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2310,a,2245,b)].
% 17.36/17.50 2311 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(902,b,870,a)].
% 17.36/17.50 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2311,a,2245,b)].
% 17.36/17.51 2312 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(902,b,871,a)].
% 17.36/17.51 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2312,a,2245,b)].
% 17.36/17.51 2313 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(902,b,872,a)].
% 17.36/17.51 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2313,a,2245,b)].
% 17.36/17.51 2314 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(902,b,873,a)].
% 17.36/17.51 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2314,a,2245,b)].
% 17.36/17.51 2315 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(902,b,874,a)].
% 17.36/17.51 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2315,a,2245,b)].
% 17.36/17.51 2316 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(902,b,875,a)].
% 17.36/17.51 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2316,a,2245,b)].
% 17.36/17.51 2317 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(902,b,876,a)].
% 17.36/17.51 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2317,a,2245,b)].
% 17.36/17.51 2318 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(902,b,877,a)].
% 17.36/17.51 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2318,a,2245,b)].
% 17.36/17.51 2319 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(902,b,878,a)].
% 17.36/17.51 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2319,a,2245,b)].
% 17.36/17.51 2320 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(902,b,879,a)].
% 17.36/17.51 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2320,a,2245,b)].
% 17.36/17.51 2321 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(902,b,880,a)].
% 17.36/17.51 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2321,a,2245,b)].
% 17.36/17.51 2322 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(902,b,881,a)].
% 17.36/17.51 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2322,a,2245,b)].
% 17.36/17.51 2323 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(902,b,882,a)].
% 17.36/17.51 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2323,a,2245,b)].
% 17.36/17.51 2324 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(902,b,883,a)].
% 17.36/17.51 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2324,a,2245,b)].
% 17.36/17.51 2325 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(902,b,884,a)].
% 17.36/17.51 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2325,a,2245,b)].
% 17.47/17.64 2326 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(902,b,885,a)].
% 17.47/17.64 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2326,a,2245,b)].
% 17.47/17.64 2327 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(902,b,886,a)].
% 17.47/17.64 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2327,a,2245,b)].
% 17.47/17.64 2328 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(902,b,887,a)].
% 17.47/17.64 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,a,2245,b)].
% 17.47/17.64 2329 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(902,b,888,a)].
% 17.47/17.64 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2329,a,2245,b)].
% 17.47/17.64 2330 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(902,b,889,a)].
% 17.47/17.64 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2330,a,2245,b)].
% 17.47/17.64 2331 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(904,a,902,b)].
% 17.47/17.64 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2331,b,2245,b)].
% 17.47/17.64 2332 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(905,a,902,b)].
% 17.47/17.64 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2332,b,2245,b)].
% 17.47/17.64 2333 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1092,b,1076,a)].
% 17.47/17.64 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2333,a,2245,b)].
% 17.47/17.64 2334 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1115,b,1099,a)].
% 17.47/17.64 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2334,a,2245,b)].
% 17.47/17.64 2335 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(1157,a,1121,a)].
% 17.47/17.64 2336 class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(1157,a,1146,a)].
% 17.47/17.64 2337 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1157,a,1147,b)].
% 17.47/17.64 2338 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1157,a,1148,b)].
% 17.47/17.64 2339 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1501,b,1477,a)].
% 17.47/17.64 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2339,a,2245,b)].
% 17.47/17.64 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2339,a,2246,b)].
% 17.47/17.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2339,a,2247,b)].
% 17.47/17.65 2340 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1501,b,1478,a)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2340,a,2245,b)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2340,a,2246,b)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2340,a,2247,b)].
% 17.47/17.65 2341 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1501,b,1479,a)].
% 17.47/17.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2341,a,2245,b)].
% 17.47/17.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2341,a,2246,b)].
% 17.47/17.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2341,a,2247,b)].
% 17.47/17.65 2342 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1501,b,1480,a)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2342,a,2245,b)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2342,a,2246,b)].
% 17.47/17.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2342,a,2247,b)].
% 17.47/17.65 2343 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1501,b,1481,a)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2343,a,2245,b)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2343,a,2246,b)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2343,a,2247,b)].
% 17.47/17.65 2344 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1501,b,1482,a)].
% 17.47/17.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2344,a,2245,b)].
% 17.47/17.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2344,a,2246,b)].
% 17.47/17.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2344,a,2247,b)].
% 17.47/17.65 2345 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1501,b,1483,a)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2345,a,2245,b)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2345,a,2246,b)].
% 17.47/17.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2345,a,2247,b)].
% 17.47/17.65 2346 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1501,b,1484,a)].
% 17.47/17.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2346,a,2245,b)].
% 17.47/17.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2346,a,2246,b)].
% 17.56/17.75 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2346,a,2247,b)].
% 17.56/17.75 2347 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(1606,b,1581,a)].
% 17.56/17.75 2348 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1582,a)].
% 17.56/17.75 2349 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1606,b,1583,a)].
% 17.56/17.75 2350 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1606,b,1584,a)].
% 17.56/17.75 2351 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1606,b,1585,a)].
% 17.56/17.75 2352 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1606,b,1586,a)].
% 17.56/17.75 2353 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1606,b,1587,a)].
% 17.56/17.75 2354 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1606,b,1588,a)].
% 17.56/17.75 2355 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1606,b,1589,a)].
% 17.56/17.75 2356 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1606,b,1590,a)].
% 17.56/17.75 2357 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1606,b,1591,a)].
% 17.56/17.75 2358 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1614,a,1606,b)].
% 17.56/17.75 2359 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1615,a,1606,b)].
% 17.56/17.75 2360 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1637,a)].
% 17.56/17.75 2361 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1638,a)].
% 17.56/17.75 2362 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1671,b,1639,a)].
% 17.56/17.75 2363 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1640,a)].
% 17.56/17.75 2364 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1641,a)].
% 17.56/17.75 2365 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1671,b,1642,a)].
% 17.56/17.75 2366 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1671,b,1643,a)].
% 17.56/17.75 2367 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1671,b,1644,a)].
% 17.56/17.75 2368 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1671,b,1645,a)].
% 17.56/17.75 2369 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1671,b,1646,a)].
% 17.56/17.75 2370 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1647,a)].
% 17.65/17.81 2371 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1671,b,1648,a)].
% 17.65/17.81 2372 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1671,b,1649,a)].
% 17.65/17.81 2373 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1671,b,1650,a)].
% 17.65/17.81 2374 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1671,b,1651,a)].
% 17.65/17.81 2375 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1671,b,1652,a)].
% 17.65/17.81 2376 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1671,b,1653,a)].
% 17.65/17.81 2377 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1671,b,1654,a)].
% 17.65/17.81 2378 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1671,b,1655,a)].
% 17.65/17.81 2379 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1671,b,1656,a)].
% 17.65/17.81 2380 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1780,a,1773,b)].
% 17.65/17.81 2381 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1844,b,1842,b)].
% 17.65/17.81 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2381,e,2245,b)].
% 17.65/17.81 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2381,e,2246,b)].
% 17.65/17.81 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2381,e,2247,b)].
% 17.65/17.81 2382 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1986,c,1907,b)].
% 17.65/17.81 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2382,c,2243,a)].
% 17.65/17.81 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2382,c,2244,a)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2382,c,2245,b)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2382,c,2246,b)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2382,c,2247,b)].
% 17.65/17.81 2383 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1987,c,1907,b)].
% 17.65/17.81 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2383,c,2243,a)].
% 17.65/17.81 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2383,c,2244,a)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2383,c,2245,b)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2383,c,2246,b)].
% 17.65/17.81 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2383,c,2247,b)].
% 17.65/17.81 2384 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1988,b,1907,b)].
% 17.65/17.81 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2384,b,2243,a)].
% 17.65/17.81 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2384,b,2244,a)].
% 17.65/17.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2384,b,2245,b)].
% 17.65/17.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2384,b,2246,b)].
% 17.65/17.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2384,b,2247,b)].
% 17.65/17.84 2385 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1989,b,1907,b)].
% 17.65/17.84 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(2385,b,2243,a)].
% 17.65/17.84 Derived: class_HOL_Oplus(tc_nat). [resolve(2385,b,2244,a)].
% 17.65/17.84 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2385,b,2245,b)].
% 17.65/17.84 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2385,b,2246,b)].
% 17.65/17.84 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2385,b,2247,b)].
% 17.65/17.84 2386 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2024,b,1907,b)].
% 17.65/17.84 2387 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2025,c,1907,b)].
% 17.65/17.84 2388 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2026,b,1907,b)].
% 17.65/17.84 2389 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2027,c,1907,b)].
% 17.65/17.84 2390 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2028,c,1907,b)].
% 17.65/17.84 2391 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2029,c,1907,b)].
% 17.65/17.84 2392 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2030,c,1907,b)].
% 17.65/17.84 2393 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2031,c,1907,b)].
% 17.65/17.84 2394 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2032,c,1907,b)].
% 17.65/17.84 2395 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2033,b,1907,b)].
% 17.65/17.84 2396 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2034,b,1907,b)].
% 17.65/17.84 2397 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2035,d,1907,b)].
% 17.65/17.84 2398 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2036,d,1907,b)].
% 17.65/17.84 2399 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2037,c,1907,b)].
% 17.65/17.84 2400 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2038,c,1907,b)].
% 17.65/17.84 2401 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2039,d,1907,b)].
% 17.65/17.84 2402 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2040,c,1907,b)].
% 17.65/17.84 2403 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2041,c,1907,b)].
% 17.65/17.84 2404 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2042,d,1907,b)].
% 17.65/17.84 2405 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2043,c,1907,b)].
% 17.77/17.92 2406 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2044,c,1907,b)].
% 17.77/17.92 2407 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2045,c,1907,b)].
% 17.77/17.92 2408 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2046,c,1907,b)].
% 17.77/17.92 2409 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2047,c,1907,b)].
% 17.77/17.92 2410 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2048,c,1907,b)].
% 17.77/17.92 2411 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2049,d,1907,b)].
% 17.77/17.92 2412 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2050,c,1907,b)].
% 17.77/17.92 2413 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2051,c,1907,b)].
% 17.77/17.92 2414 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2052,d,1907,b)].
% 17.77/17.92 2415 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2053,c,1907,b)].
% 17.77/17.92 2416 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2054,c,1907,b)].
% 17.77/17.92 2417 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2055,c,1907,b)].
% 17.77/17.92 2418 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2056,c,1907,b)].
% 17.77/17.92 2419 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2058,d,1907,b)].
% 17.77/17.92 2420 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2077,a,2066,b)].
% 17.77/17.92 2421 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2082,b,2066,b)].
% 17.77/17.92 2422 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2083,b,2066,b)].
% 17.77/17.92 2423 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2086,b,2066,b)].
% 17.77/17.92 2424 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2087,b,2066,b)].
% 17.77/17.92 2425 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2088,b,2066,b)].
% 17.77/17.92 2426 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2089,b,2066,b)].
% 17.77/17.92 2427 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2157,a,2135,b)].
% 17.77/17.92 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2427,b,2245,b)].
% 17.77/17.92 2428 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2158,a,2135,b)].
% 17.77/17.92 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2428,b,2245,b)].
% 17.77/17.92 2429 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2201,d,2135,b)].
% 17.77/17.92 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2429,d,2243,a)].
% 17.77/17.92 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2429,d,2244,a)].
% 17.77/17.92 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2429,d,2245,b)].
% 17.77/17.92 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2429,d,2246,b)].
% 17.77/17.92 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2429,d,2247,b)].
% 17.77/17.92 2430 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2202,b,2135,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2430,b,2243,a)].
% 17.77/17.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2430,b,2244,a)].
% 17.77/17.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2430,b,2245,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2430,b,2246,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2430,b,2247,b)].
% 17.77/17.92 2431 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2203,b,2135,b)].
% 17.77/17.92 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(2431,b,2243,a)].
% 17.77/17.92 Derived: class_HOL_Otimes(tc_nat). [resolve(2431,b,2244,a)].
% 17.77/17.92 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2431,b,2245,b)].
% 17.77/17.92 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2431,b,2246,b)].
% 17.77/17.92 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2431,b,2247,b)].
% 17.77/17.92 2432 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2204,b,2135,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(2432,b,2243,a)].
% 17.77/17.92 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(2432,b,2244,a)].
% 17.77/17.92 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2432,b,2245,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2432,b,2246,b)].
% 17.77/17.92 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2432,b,2247,b)].
% 17.77/17.92 2433 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2205,b,2135,b)].
% 17.77/17.92 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(2433,b,2243,a)].
% 17.77/17.92 Derived: class_HOL_Ozero(tc_nat). [resolve(2433,b,2244,a)].
% 17.77/17.92 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2433,b,2245,b)].
% 17.77/17.92 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2433,b,2246,b)].
% 17.77/17.92 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2433,b,2247,b)].
% 17.77/17.92 2434 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2206,b,2135,b)].
% 17.77/17.92 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2434,b,2243,a)].
% 17.77/17.92 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(2434,b,2244,a)].
% 17.77/17.92 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2434,b,2245,b)].
% 17.77/17.92 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2434,b,2246,b)].
% 17.77/17.92 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2434,b,2247,b)].
% 17.77/17.93 2435 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2207,b,2135,b)].
% 17.77/17.93 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2435,b,2243,a)].
% 17.77/17.93 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(2435,b,2244,a)].
% 17.77/17.93 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2435,b,2245,b)].
% 17.77/17.93 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2435,b,2246,b)].
% 17.77/17.93 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2435,b,2247,b)].
% 17.77/17.93 2436 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2208,b,2135,b)].
% 17.77/17.93 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2436,b,2243,a)].
% 17.77/17.93 Derived: -c_less(A,A,tc_nat). [resolve(2436,b,2244,a)].
% 17.77/17.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2436,b,2245,b)].
% 17.77/17.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2436,b,2246,b)].
% 17.77/17.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2436,b,2247,b)].
% 17.77/17.93 2437 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2209,c,2135,b)].
% 17.77/17.93 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2437,c,2243,a)].
% 17.77/17.93 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2437,c,2244,a)].
% 17.77/17.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2437,c,2245,b)].
% 17.77/17.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2437,c,2246,b)].
% 17.77/17.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2437,c,2247,b)].
% 17.77/17.93 2438 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2210,b,2135,b)].
% 17.77/17.93 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2438,b,2243,a)].
% 17.77/17.93 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2438,b,2244,a)].
% 17.77/17.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2438,b,2245,b)].
% 17.77/17.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2438,b,2246,b)].
% 17.77/17.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2438,b,2247,b)].
% 17.77/17.93 2439 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2211,c,2135,b)].
% 17.77/17.93 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2439,c,2243,a)].
% 17.77/17.93 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2439,c,2244,a)].
% 17.77/17.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2439,c,2245,b)].
% 17.77/17.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2439,c,2246,b)].
% 17.77/17.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2439,c,2247,b)].
% 17.77/17.94 2440 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2212,c,2135,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2440,c,2243,a)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2440,c,2244,a)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2440,c,2245,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2440,c,2246,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2440,c,2247,b)].
% 17.77/17.94 2441 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2213,c,2135,b)].
% 17.77/17.94 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2441,c,2243,a)].
% 17.77/17.94 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(2441,c,2244,a)].
% 17.77/17.94 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2441,c,2245,b)].
% 17.77/17.94 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2441,c,2246,b)].
% 17.77/17.94 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2441,c,2247,b)].
% 17.77/17.94 2442 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2214,c,2135,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2442,c,2243,a)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2442,c,2244,a)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2442,c,2245,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2442,c,2246,b)].
% 17.77/17.94 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2442,c,2247,b)].
% 17.77/17.94 2443 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2215,c,2135,b)].
% 17.77/17.94 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2443,c,2243,a)].
% 17.77/17.94 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(2443,c,2244,a)].
% 17.77/17.94 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2443,c,2245,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2443,c,2246,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2443,c,2247,b)].
% 17.77/17.95 2444 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2216,c,2135,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2444,c,2243,a)].
% 17.77/17.95 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2444,c,2244,a)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2444,c,2245,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2444,c,2246,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2444,c,2247,b)].
% 17.77/17.95 2445 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2217,b,2135,b)].
% 17.77/17.95 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2445,b,2243,a)].
% 17.77/17.95 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2445,b,2244,a)].
% 17.77/17.95 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2445,b,2245,b)].
% 17.77/17.95 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2445,b,2246,b)].
% 17.77/17.95 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2445,b,2247,b)].
% 17.77/17.95 2446 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2218,b,2135,b)].
% 17.77/17.95 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2446,b,2243,a)].
% 17.77/17.95 Derived: c_lessequals(A,A,tc_nat). [resolve(2446,b,2244,a)].
% 17.77/17.95 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2446,b,2245,b)].
% 17.77/17.95 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2446,b,2246,b)].
% 17.77/17.95 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2446,b,2247,b)].
% 17.77/17.95 2447 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2219,d,2135,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(2447,d,2243,a)].
% 17.77/17.95 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(2447,d,2244,a)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2447,d,2245,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2447,d,2246,b)].
% 17.77/17.95 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2447,d,2247,b)].
% 17.77/17.95 2448 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2220,d,2135,b)].
% 17.77/17.95 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2448,d,2243,a)].
% 17.77/17.96 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(2448,d,2244,a)].
% 17.77/17.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2448,d,2245,b)].
% 17.77/17.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2448,d,2246,b)].
% 17.77/17.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2448,d,2247,b)].
% 17.77/17.96 2449 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2221,c,2135,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2449,c,2243,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2449,c,2244,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2449,c,2245,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2449,c,2246,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2449,c,2247,b)].
% 17.77/17.96 2450 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2222,c,2135,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2450,c,2243,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2450,c,2244,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2450,c,2245,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2450,c,2246,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2450,c,2247,b)].
% 17.77/17.96 2451 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2223,d,2135,b)].
% 17.77/17.96 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2451,d,2243,a)].
% 17.77/17.96 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2451,d,2244,a)].
% 17.77/17.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2451,d,2245,b)].
% 17.77/17.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2451,d,2246,b)].
% 17.77/17.96 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2451,d,2247,b)].
% 17.77/17.96 2452 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2224,c,2135,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2452,c,2243,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2452,c,2244,a)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2452,c,2245,b)].
% 17.77/17.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2452,c,2246,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2452,c,2247,b)].
% 17.77/17.97 2453 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2225,c,2135,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2453,c,2243,a)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2453,c,2244,a)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2453,c,2245,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2453,c,2246,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2453,c,2247,b)].
% 17.77/17.97 2454 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2226,d,2135,b)].
% 17.77/17.97 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(2454,d,2243,a)].
% 17.77/17.97 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2454,d,2244,a)].
% 17.77/17.97 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2454,d,2245,b)].
% 17.77/17.97 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2454,d,2246,b)].
% 17.77/17.97 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2454,d,2247,b)].
% 17.77/17.97 2455 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2227,c,2135,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2455,c,2243,a)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2455,c,2244,a)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2455,c,2245,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2455,c,2246,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2455,c,2247,b)].
% 17.77/17.97 2456 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2228,c,2135,b)].
% 17.77/17.97 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2456,c,2243,a)].
% 17.77/17.97 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2456,c,2244,a)].
% 17.77/17.97 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2456,c,2245,b)].
% 17.77/17.97 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2456,c,2246,b)].
% 17.77/17.97 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2456,c,2247,b)].
% 17.77/17.97 2457 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2229,c,2135,b)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2457,c,2243,a)].
% 17.77/17.97 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2457,c,2244,a)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2457,c,2245,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2457,c,2246,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2457,c,2247,b)].
% 17.77/17.98 2458 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2230,c,2135,b)].
% 17.77/17.98 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2458,c,2243,a)].
% 17.77/17.98 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2458,c,2244,a)].
% 17.77/17.98 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2458,c,2245,b)].
% 17.77/17.98 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2458,c,2246,b)].
% 17.77/17.98 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2458,c,2247,b)].
% 17.77/17.98 2459 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2231,c,2135,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2459,c,2243,a)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2459,c,2244,a)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2459,c,2245,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2459,c,2246,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2459,c,2247,b)].
% 17.77/17.98 2460 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2232,c,2135,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2460,c,2243,a)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2460,c,2244,a)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2460,c,2245,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2460,c,2246,b)].
% 17.77/17.98 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2460,c,2247,b)].
% 17.77/17.98 2461 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2233,d,2135,b)].
% 17.77/17.98 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2461,d,2243,a)].
% 17.77/17.98 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2461,d,2244,a)].
% 17.77/17.98 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2461,d,2245,b)].
% 17.77/17.98 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2461,d,2246,b)].
% 17.77/17.98 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2461,d,2247,b)].
% 17.77/17.99 2462 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2234,c,2135,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2462,c,2243,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2462,c,2244,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2462,c,2245,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2462,c,2246,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2462,c,2247,b)].
% 17.77/17.99 2463 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2235,c,2135,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2463,c,2243,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2463,c,2244,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2463,c,2245,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2463,c,2246,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2463,c,2247,b)].
% 17.77/17.99 2464 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2236,d,2135,b)].
% 17.77/17.99 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(2464,d,2243,a)].
% 17.77/17.99 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(2464,d,2244,a)].
% 17.77/17.99 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2464,d,2245,b)].
% 17.77/17.99 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2464,d,2246,b)].
% 17.77/17.99 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2464,d,2247,b)].
% 17.77/17.99 2465 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2237,c,2135,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2465,c,2243,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2465,c,2244,a)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2465,c,2245,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2465,c,2246,b)].
% 17.77/17.99 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2465,c,2247,b)].
% 17.77/17.99 2466 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2238,c,2135,b)].
% 17.77/17.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2466,c,2243,a)].
% 17.77/17.99 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2466,c,2244,a)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2466,c,2245,b)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2466,c,2246,b)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2466,c,2247,b)].
% 18.08/18.21 2467 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2239,c,2135,b)].
% 18.08/18.21 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2467,c,2243,a)].
% 18.08/18.21 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2467,c,2244,a)].
% 18.08/18.21 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2467,c,2245,b)].
% 18.08/18.21 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2467,c,2246,b)].
% 18.08/18.21 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2467,c,2247,b)].
% 18.08/18.21 2468 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2240,c,2135,b)].
% 18.08/18.21 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2468,c,2243,a)].
% 18.08/18.21 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2468,c,2244,a)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2468,c,2245,b)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2468,c,2246,b)].
% 18.08/18.21 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2468,c,2247,b)].
% 18.08/18.21 2469 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2241,d,2135,b)].
% 18.08/18.21 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2469,d,2243,a)].
% 18.08/18.21 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(2469,d,2244,a)].
% 18.08/18.21 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2469,d,2245,b)].
% 18.08/18.21 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2469,d,2246,b)].
% 18.08/18.21 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2469,d,2247,b)].
% 18.08/18.21 2470 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_10) # label(axiom). [assumption].
% 18.08/18.21 2471 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 18.08/18.21 2472 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 18.08/18.21 2473 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) # label(axiom). [assumption].
% 18.08/18.21 2474 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_37) # label(axiom). [assumption].
% 18.08/18.21 2475 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_41) # label(axiom). [assumption].
% 18.26/18.44 2476 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) # label(axiom). [assumption].
% 18.26/18.44 2477 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_20) # label(axiom). [assumption].
% 18.26/18.44 2478 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_11) # label(axiom). [assumption].
% 18.26/18.44 2479 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_5) # label(axiom). [assumption].
% 18.26/18.44 2480 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_6) # label(axiom). [assumption].
% 18.26/18.44 2481 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_7) # label(axiom). [assumption].
% 18.26/18.44 2482 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_9) # label(axiom). [assumption].
% 18.26/18.44 2483 -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(157,b,131,b)].
% 18.26/18.44 2484 -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(157,b,133,b)].
% 18.26/18.44 2485 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(163,a,157,b)].
% 18.26/18.44 2486 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(164,a,157,b)].
% 18.26/18.44 2487 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(165,a,157,b)].
% 18.26/18.44 2488 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(166,a,157,b)].
% 18.26/18.44 2489 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(171,a,157,b)].
% 18.26/18.44 2490 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(172,a,157,b)].
% 18.26/18.44 2491 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(240,a,231,b)].
% 18.26/18.44 2492 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(241,a,231,b)].
% 18.26/18.44 2493 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(247,b,231,b)].
% 18.26/18.44 2494 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(248,b,231,b)].
% 18.26/18.44 2495 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(1164,a,1121,a)].
% 18.26/18.44 2496 class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(1164,a,1146,a)].
% 18.26/18.44 2497 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1164,a,1147,b)].
% 18.26/18.44 2498 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1164,a,1148,b)].
% 18.26/18.44 2499 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(1610,b,1581,a)].
% 18.26/18.44 2500 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1582,a)].
% 18.26/18.44 2501 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1610,b,1583,a)].
% 18.26/18.44 2502 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1610,b,1584,a)].
% 18.38/18.51 2503 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1610,b,1585,a)].
% 18.38/18.51 2504 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1610,b,1586,a)].
% 18.38/18.51 2505 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1610,b,1587,a)].
% 18.38/18.51 2506 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1610,b,1588,a)].
% 18.38/18.51 2507 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1610,b,1589,a)].
% 18.38/18.51 2508 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1610,b,1590,a)].
% 18.38/18.51 2509 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1610,b,1591,a)].
% 18.38/18.51 2510 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1614,a,1610,b)].
% 18.38/18.51 2511 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1615,a,1610,b)].
% 18.38/18.51 2512 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1637,a)].
% 18.38/18.51 2513 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1638,a)].
% 18.38/18.51 2514 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1675,b,1639,a)].
% 18.38/18.51 2515 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1640,a)].
% 18.38/18.51 2516 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1641,a)].
% 18.38/18.51 2517 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1675,b,1642,a)].
% 18.38/18.51 2518 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1675,b,1643,a)].
% 18.38/18.51 2519 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1675,b,1644,a)].
% 18.38/18.51 2520 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1675,b,1645,a)].
% 18.38/18.51 2521 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1675,b,1646,a)].
% 18.38/18.51 2522 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1647,a)].
% 18.38/18.51 2523 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1675,b,1648,a)].
% 18.38/18.51 2524 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1675,b,1649,a)].
% 18.38/18.51 2525 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1675,b,1650,a)].
% 18.38/18.51 2526 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1675,b,1651,a)].
% 18.38/18.51 2527 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1675,b,1652,a)].
% 18.38/18.59 2528 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1675,b,1653,a)].
% 18.38/18.59 2529 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1675,b,1654,a)].
% 18.38/18.59 2530 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1675,b,1655,a)].
% 18.38/18.59 2531 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1675,b,1656,a)].
% 18.38/18.59 2532 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1780,a,1777,b)].
% 18.38/18.59 2533 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2077,a,2070,b)].
% 18.38/18.59 Derived: -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2533,d,2477,b)].
% 18.38/18.59 2534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2080,b,2070,b)].
% 18.38/18.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2534,b,2477,b)].
% 18.38/18.59 2535 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2081,b,2070,b)].
% 18.38/18.59 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2535,b,2477,b)].
% 18.38/18.59 2536 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2082,b,2070,b)].
% 18.38/18.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2536,b,2477,b)].
% 18.38/18.59 2537 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2083,b,2070,b)].
% 18.38/18.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2537,b,2477,b)].
% 18.38/18.59 2538 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2086,b,2070,b)].
% 18.38/18.59 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2538,b,2477,b)].
% 18.38/18.59 2539 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2087,b,2070,b)].
% 18.38/18.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2539,b,2477,b)].
% 18.38/18.59 2540 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2088,b,2070,b)].
% 18.38/18.59 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2540,b,2477,b)].
% 18.38/18.59 2541 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2089,b,2070,b)].
% 18.38/18.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2541,b,2477,b)].
% 18.38/18.59 2542 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2094,a,2070,b)].
% 18.38/18.59 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2542,b,2477,b)].
% 18.38/18.59 2543 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2095,a,2070,b)].
% 18.38/18.59 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2543,c,2477,b)].
% 18.38/18.59 2544 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2096,a,2070,b)].
% 18.38/18.59 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2544,b,2477,b)].
% 18.48/18.61 2545 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2097,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2545,c,2477,b)].
% 18.48/18.61 2546 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2098,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2546,c,2477,b)].
% 18.48/18.61 2547 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2099,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2547,c,2477,b)].
% 18.48/18.61 2548 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2100,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2548,c,2477,b)].
% 18.48/18.61 2549 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2101,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2549,c,2477,b)].
% 18.48/18.61 2550 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2102,a,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2550,c,2477,b)].
% 18.48/18.61 2551 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2103,a,2070,b)].
% 18.48/18.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2551,b,2477,b)].
% 18.48/18.61 2552 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2104,a,2070,b)].
% 18.48/18.61 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2552,b,2477,b)].
% 18.48/18.61 2553 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2105,d,2070,b)].
% 18.48/18.61 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2553,d,2477,b)].
% 18.48/18.61 2554 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2106,d,2070,b)].
% 18.48/18.61 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2554,d,2477,b)].
% 18.48/18.61 2555 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2107,a,2070,b)].
% 18.48/18.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2555,c,2477,b)].
% 18.48/18.61 2556 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2108,a,2070,b)].
% 18.48/18.61 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2556,c,2477,b)].
% 18.48/18.61 2557 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2109,a,2070,b)].
% 18.48/18.63 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2557,d,2477,b)].
% 18.48/18.63 2558 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2110,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2558,c,2477,b)].
% 18.48/18.63 2559 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2111,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2559,c,2477,b)].
% 18.48/18.63 2560 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2112,a,2070,b)].
% 18.48/18.63 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2560,d,2477,b)].
% 18.48/18.63 2561 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2113,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2561,c,2477,b)].
% 18.48/18.63 2562 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2114,a,2070,b)].
% 18.48/18.63 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2562,c,2477,b)].
% 18.48/18.63 2563 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2115,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2563,c,2477,b)].
% 18.48/18.63 2564 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2116,a,2070,b)].
% 18.48/18.63 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2564,c,2477,b)].
% 18.48/18.63 2565 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2117,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2565,c,2477,b)].
% 18.48/18.63 2566 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2118,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2566,c,2477,b)].
% 18.48/18.63 2567 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2119,a,2070,b)].
% 18.48/18.63 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2567,d,2477,b)].
% 18.48/18.63 2568 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2120,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2568,c,2477,b)].
% 18.48/18.63 2569 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2121,a,2070,b)].
% 18.48/18.63 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2569,c,2477,b)].
% 18.48/18.63 2570 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2122,a,2070,b)].
% 18.77/18.91 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2570,d,2477,b)].
% 18.77/18.91 2571 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2123,a,2070,b)].
% 18.77/18.91 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2571,c,2477,b)].
% 18.77/18.91 2572 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2124,a,2070,b)].
% 18.77/18.91 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2572,c,2477,b)].
% 18.77/18.91 2573 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2125,a,2070,b)].
% 18.77/18.91 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2573,c,2477,b)].
% 18.77/18.91 2574 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2126,a,2070,b)].
% 18.77/18.91 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2574,c,2477,b)].
% 18.77/18.91 2575 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2127,d,2070,b)].
% 18.77/18.91 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2575,d,2477,b)].
% 18.77/18.91 2576 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) # label(axiom). [assumption].
% 18.77/18.91 2577 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 18.77/18.91 2578 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 18.77/18.91 2579 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) # label(axiom). [assumption].
% 18.77/18.91 2580 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_36) # label(axiom). [assumption].
% 18.77/18.91 2581 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_39) # label(axiom). [assumption].
% 18.77/18.91 2582 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) # label(axiom). [assumption].
% 18.77/18.91 2583 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) # label(axiom). [assumption].
% 18.77/18.91 2584 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) # label(axiom). [assumption].
% 18.77/18.91 2585 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) # label(axiom). [assumption].
% 18.77/18.91 2586 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) # label(axiom). [assumption].
% 18.77/18.91 2587 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(33,b,1,a)].
% 18.77/18.91 2588 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(33,b,3,a)].
% 18.96/19.13 2589 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(33,b,9,a)].
% 18.96/19.13 2590 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(33,b,10,a)].
% 18.96/19.13 2591 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(154,b,131,b)].
% 18.96/19.13 2592 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(154,b,133,b)].
% 18.96/19.13 2593 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(165,a,154,b)].
% 18.96/19.13 2594 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(166,a,154,b)].
% 18.96/19.13 2595 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(171,a,154,b)].
% 18.96/19.13 2596 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(172,a,154,b)].
% 18.96/19.13 2597 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(201,b,195,b)].
% 18.96/19.13 2598 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(202,b,195,b)].
% 18.96/19.13 2599 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(240,a,228,b)].
% 18.96/19.13 2600 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(241,a,228,b)].
% 18.96/19.13 2601 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(247,b,228,b)].
% 18.96/19.13 2602 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(248,b,228,b)].
% 18.96/19.13 2603 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(308,b,288,a)].
% 18.96/19.13 2604 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(308,b,290,a)].
% 18.96/19.13 2605 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(322,a,308,b)].
% 18.96/19.13 2606 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(323,a,308,b)].
% 18.96/19.13 2607 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(1162,a,1121,a)].
% 18.96/19.13 2608 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(1162,a,1146,a)].
% 18.96/19.13 2609 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1162,a,1147,b)].
% 18.96/19.13 2610 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1162,a,1148,b)].
% 18.96/19.13 2611 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(1607,b,1581,a)].
% 18.96/19.13 2612 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1582,a)].
% 18.96/19.13 2613 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1607,b,1583,a)].
% 18.96/19.13 2614 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1607,b,1584,a)].
% 18.96/19.13 2615 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1607,b,1585,a)].
% 18.96/19.13 2616 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1607,b,1586,a)].
% 19.06/19.19 2617 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1607,b,1587,a)].
% 19.06/19.19 2618 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1607,b,1588,a)].
% 19.06/19.19 2619 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1607,b,1589,a)].
% 19.06/19.19 2620 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1607,b,1590,a)].
% 19.06/19.19 2621 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(1607,b,1591,a)].
% 19.06/19.19 2622 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1614,a,1607,b)].
% 19.06/19.19 2623 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1615,a,1607,b)].
% 19.06/19.19 2624 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1637,a)].
% 19.06/19.19 2625 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1672,b,1638,a)].
% 19.06/19.19 2626 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1672,b,1639,a)].
% 19.06/19.19 2627 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1640,a)].
% 19.06/19.19 2628 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1672,b,1641,a)].
% 19.06/19.19 2629 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1672,b,1642,a)].
% 19.06/19.19 2630 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1672,b,1643,a)].
% 19.06/19.19 2631 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1672,b,1644,a)].
% 19.06/19.19 2632 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1672,b,1645,a)].
% 19.06/19.19 2633 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1672,b,1646,a)].
% 19.06/19.19 2634 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1672,b,1647,a)].
% 19.06/19.19 2635 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1672,b,1648,a)].
% 19.06/19.19 2636 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1672,b,1649,a)].
% 19.06/19.19 2637 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1672,b,1650,a)].
% 19.06/19.19 2638 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1672,b,1651,a)].
% 19.06/19.19 2639 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1672,b,1652,a)].
% 19.06/19.19 2640 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1672,b,1653,a)].
% 19.08/19.28 2641 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1672,b,1654,a)].
% 19.08/19.28 2642 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1672,b,1655,a)].
% 19.08/19.28 2643 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1672,b,1656,a)].
% 19.08/19.28 2644 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1780,a,1774,b)].
% 19.08/19.28 2645 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2077,a,2067,b)].
% 19.08/19.28 2646 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2082,b,2067,b)].
% 19.08/19.28 2647 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2083,b,2067,b)].
% 19.08/19.28 2648 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2086,b,2067,b)].
% 19.08/19.28 2649 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,b,2067,b)].
% 19.08/19.28 2650 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2088,b,2067,b)].
% 19.08/19.28 2651 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2089,b,2067,b)].
% 19.08/19.28 2652 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2094,a,2067,b)].
% 19.08/19.28 2653 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2095,a,2067,b)].
% 19.08/19.28 2654 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2096,a,2067,b)].
% 19.08/19.28 2655 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,a,2067,b)].
% 19.08/19.28 2656 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2098,a,2067,b)].
% 19.08/19.28 2657 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2099,a,2067,b)].
% 19.08/19.28 2658 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2100,a,2067,b)].
% 19.08/19.28 2659 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2101,a,2067,b)].
% 19.08/19.28 2660 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,a,2067,b)].
% 19.08/19.28 2661 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2103,a,2067,b)].
% 19.08/19.28 2662 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2104,a,2067,b)].
% 19.08/19.28 2663 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2067,b)].
% 19.08/19.28 2664 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,d,2067,b)].
% 19.08/19.28 2665 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2107,a,2067,b)].
% 19.08/19.28 2666 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2108,a,2067,b)].
% 19.18/19.31 2667 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2109,a,2067,b)].
% 19.18/19.31 2668 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2110,a,2067,b)].
% 19.18/19.31 2669 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2111,a,2067,b)].
% 19.18/19.31 2670 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2112,a,2067,b)].
% 19.18/19.31 2671 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2113,a,2067,b)].
% 19.18/19.31 2672 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2114,a,2067,b)].
% 19.18/19.31 2673 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2115,a,2067,b)].
% 19.18/19.31 2674 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2116,a,2067,b)].
% 19.18/19.31 2675 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2117,a,2067,b)].
% 19.18/19.31 2676 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2118,a,2067,b)].
% 19.18/19.31 2677 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2119,a,2067,b)].
% 19.18/19.31 2678 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2120,a,2067,b)].
% 19.18/19.31 2679 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2121,a,2067,b)].
% 19.18/19.31 2680 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2122,a,2067,b)].
% 19.18/19.31 2681 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2123,a,2067,b)].
% 19.18/19.31 2682 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2124,a,2067,b)].
% 19.18/19.31 2683 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2125,a,2067,b)].
% 19.18/19.31 2684 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2126,a,2067,b)].
% 19.18/19.31 2685 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2127,d,2067,b)].
% 19.18/19.31 2686 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2157,a,2136,b)].
% 19.18/19.31 2687 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2158,a,2136,b)].
% 19.18/19.31 2688 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2159,c,2136,b)].
% 19.18/19.31 2689 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2160,c,2136,b)].
% 19.18/19.31 2690 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2161,b,2136,b)].
% 19.18/19.31 2691 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2162,a,2136,b)].
% 19.18/19.31 2692 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2201,d,2136,b)].
% 19.18/19.35 2693 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2202,b,2136,b)].
% 19.18/19.35 2694 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2203,b,2136,b)].
% 19.18/19.35 2695 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2204,b,2136,b)].
% 19.18/19.35 2696 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2205,b,2136,b)].
% 19.18/19.35 2697 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2206,b,2136,b)].
% 19.18/19.35 2698 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2207,b,2136,b)].
% 19.18/19.35 2699 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2208,b,2136,b)].
% 19.18/19.35 2700 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2209,c,2136,b)].
% 19.18/19.35 2701 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2210,b,2136,b)].
% 19.18/19.35 2702 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2211,c,2136,b)].
% 19.18/19.35 2703 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2212,c,2136,b)].
% 19.18/19.35 2704 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2213,c,2136,b)].
% 19.18/19.35 2705 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2214,c,2136,b)].
% 19.18/19.35 2706 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2215,c,2136,b)].
% 19.18/19.35 2707 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2216,c,2136,b)].
% 19.18/19.35 2708 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2217,b,2136,b)].
% 19.18/19.35 2709 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2218,b,2136,b)].
% 19.18/19.35 2710 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2219,d,2136,b)].
% 19.18/19.35 2711 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2220,d,2136,b)].
% 19.18/19.35 2712 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2221,c,2136,b)].
% 19.18/19.35 2713 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2222,c,2136,b)].
% 19.18/19.35 2714 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2223,d,2136,b)].
% 19.18/19.35 2715 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2224,c,2136,b)].
% 19.18/19.35 2716 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2225,c,2136,b)].
% 19.18/19.35 2717 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2226,d,2136,b)].
% 19.39/19.58 2718 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2227,c,2136,b)].
% 19.39/19.58 2719 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2228,c,2136,b)].
% 19.39/19.58 2720 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2229,c,2136,b)].
% 19.39/19.58 2721 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2230,c,2136,b)].
% 19.39/19.58 2722 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2231,c,2136,b)].
% 19.39/19.58 2723 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2232,c,2136,b)].
% 19.39/19.58 2724 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2233,d,2136,b)].
% 19.39/19.58 2725 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2234,c,2136,b)].
% 19.39/19.58 2726 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2235,c,2136,b)].
% 19.39/19.58 2727 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2236,d,2136,b)].
% 19.39/19.58 2728 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2237,c,2136,b)].
% 19.39/19.58 2729 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2238,c,2136,b)].
% 19.39/19.58 2730 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2239,c,2136,b)].
% 19.39/19.58 2731 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2240,c,2136,b)].
% 19.39/19.58 2732 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2241,d,2136,b)].
% 19.39/19.58 2733 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) # label(axiom). [assumption].
% 19.39/19.58 2734 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 19.39/19.58 2735 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 19.39/19.58 2736 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) # label(axiom). [assumption].
% 19.39/19.58 2737 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) # label(axiom). [assumption].
% 19.39/19.58 2738 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) # label(axiom). [assumption].
% 19.39/19.58 2739 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) # label(axiom). [assumption].
% 19.39/19.58 2740 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) # label(axiom). [assumption].
% 19.39/19.58 2741 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_35) # label(axiom). [assumption].
% 19.48/19.65 2742 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_30) # label(axiom). [assumption].
% 19.48/19.65 2743 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(27,b,1,a)].
% 19.48/19.65 2744 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(27,b,3,a)].
% 19.48/19.65 2745 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(27,b,10,a)].
% 19.48/19.65 2746 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(81,b,65,b)].
% 19.48/19.65 2747 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(148,b,131,b)].
% 19.48/19.65 2748 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(148,b,133,b)].
% 19.48/19.65 2749 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(165,a,148,b)].
% 19.48/19.65 2750 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(166,a,148,b)].
% 19.48/19.65 2751 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(171,a,148,b)].
% 19.48/19.65 2752 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(172,a,148,b)].
% 19.48/19.65 2753 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(201,b,191,b)].
% 19.48/19.65 2754 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(202,b,191,b)].
% 19.48/19.65 2755 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(240,a,222,b)].
% 19.48/19.65 2756 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(241,a,222,b)].
% 19.48/19.65 2757 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(247,b,222,b)].
% 19.48/19.65 2758 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(248,b,222,b)].
% 19.48/19.65 2759 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(302,b,288,a)].
% 19.48/19.65 2760 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(302,b,290,a)].
% 19.48/19.65 2761 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(322,a,302,b)].
% 19.48/19.65 2762 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(323,a,302,b)].
% 19.48/19.65 2763 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(897,b,832,a)].
% 19.48/19.65 2764 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(897,b,833,a)].
% 19.48/19.65 2765 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(897,b,834,a)].
% 19.48/19.65 2766 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(897,b,835,a)].
% 19.48/19.65 2767 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,836,a)].
% 19.48/19.65 2768 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,837,a)].
% 19.48/19.65 2769 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(897,b,838,a)].
% 19.48/19.65 2770 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,839,a)].
% 19.48/19.65 2771 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(897,b,840,a)].
% 19.48/19.65 2772 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,841,a)].
% 19.48/19.65 2773 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(897,b,842,a)].
% 19.48/19.65 2774 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,843,a)].
% 19.48/19.65 2775 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,844,a)].
% 19.48/19.65 2776 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(897,b,845,a)].
% 19.48/19.65 2777 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,846,a)].
% 19.48/19.65 2778 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(897,b,847,a)].
% 19.48/19.65 2779 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(897,b,848,a)].
% 19.48/19.65 2780 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(897,b,849,a)].
% 19.48/19.65 2781 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(897,b,850,a)].
% 19.48/19.65 2782 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(897,b,851,a)].
% 19.48/19.65 2783 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(897,b,852,a)].
% 19.48/19.65 2784 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(897,b,853,a)].
% 19.48/19.65 2785 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(897,b,854,a)].
% 19.48/19.66 2786 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(897,b,855,b)].
% 19.48/19.66 2787 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(897,b,856,b)].
% 19.48/19.66 2788 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(897,b,857,a)].
% 19.48/19.66 2789 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(897,b,858,a)].
% 19.48/19.66 2790 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(897,b,859,a)].
% 19.48/19.66 2791 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(897,b,860,a)].
% 19.48/19.66 2792 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(897,b,861,a)].
% 19.48/19.66 2793 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(897,b,862,a)].
% 19.48/19.66 2794 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(897,b,863,a)].
% 19.48/19.66 2795 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(897,b,864,a)].
% 19.48/19.66 2796 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(897,b,865,a)].
% 19.48/19.66 2797 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(897,b,866,a)].
% 19.48/19.66 2798 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(897,b,867,a)].
% 19.48/19.66 2799 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(897,b,868,a)].
% 19.48/19.66 2800 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(897,b,869,a)].
% 19.48/19.66 2801 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(897,b,870,a)].
% 19.48/19.66 2802 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(897,b,871,a)].
% 19.48/19.66 2803 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(897,b,872,a)].
% 19.48/19.66 2804 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(897,b,873,a)].
% 19.48/19.66 2805 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(897,b,874,a)].
% 19.48/19.66 2806 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(897,b,875,a)].
% 19.48/19.66 2807 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(897,b,876,a)].
% 19.48/19.66 2808 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(897,b,877,a)].
% 19.48/19.66 2809 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(897,b,878,a)].
% 19.48/19.66 2810 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(897,b,879,a)].
% 19.48/19.66 2811 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(897,b,880,a)].
% 19.65/19.78 2812 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(897,b,881,a)].
% 19.65/19.78 2813 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(897,b,882,a)].
% 19.65/19.78 2814 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(897,b,883,a)].
% 19.65/19.78 2815 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(897,b,884,a)].
% 19.65/19.78 2816 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(897,b,885,a)].
% 19.65/19.78 2817 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(897,b,886,a)].
% 19.65/19.78 2818 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(897,b,887,a)].
% 19.65/19.78 2819 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(897,b,888,a)].
% 19.65/19.78 2820 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(897,b,889,a)].
% 19.65/19.78 2821 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(904,a,897,b)].
% 19.65/19.78 2822 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(905,a,897,b)].
% 19.65/19.78 2823 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1087,b,1076,a)].
% 19.65/19.78 2824 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1110,b,1099,a)].
% 19.65/19.78 2825 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(1156,a,1121,a)].
% 19.65/19.78 2826 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(1156,a,1146,a)].
% 19.65/19.78 2827 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1156,a,1147,b)].
% 19.65/19.78 2828 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1156,a,1148,b)].
% 19.65/19.79 2829 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1498,b,1477,a)].
% 19.65/19.79 2830 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1498,b,1478,a)].
% 19.65/19.79 2831 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1498,b,1479,a)].
% 19.65/19.79 2832 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1498,b,1480,a)].
% 19.65/19.79 2833 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1498,b,1481,a)].
% 19.65/19.79 2834 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1498,b,1482,a)].
% 19.65/19.79 2835 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1498,b,1483,a)].
% 19.68/19.86 2836 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1498,b,1484,a)].
% 19.68/19.86 2837 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(1603,b,1581,a)].
% 19.68/19.86 2838 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1582,a)].
% 19.68/19.86 2839 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1603,b,1583,a)].
% 19.68/19.86 2840 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1603,b,1584,a)].
% 19.68/19.86 2841 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1603,b,1585,a)].
% 19.68/19.86 2842 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1603,b,1586,a)].
% 19.68/19.86 2843 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1603,b,1587,a)].
% 19.68/19.86 2844 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1603,b,1588,a)].
% 19.68/19.86 2845 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1603,b,1589,a)].
% 19.68/19.86 2846 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1603,b,1590,a)].
% 19.68/19.86 2847 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(1603,b,1591,a)].
% 19.68/19.86 2848 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1614,a,1603,b)].
% 19.68/19.86 2849 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1615,a,1603,b)].
% 19.68/19.86 2850 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1637,a)].
% 19.68/19.86 2851 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1668,b,1638,a)].
% 19.68/19.86 2852 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1668,b,1639,a)].
% 19.68/19.86 2853 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1640,a)].
% 19.68/19.86 2854 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1668,b,1641,a)].
% 19.68/19.86 2855 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1668,b,1642,a)].
% 19.68/19.86 2856 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1668,b,1643,a)].
% 19.68/19.86 2857 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1668,b,1644,a)].
% 19.68/19.86 2858 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1668,b,1645,a)].
% 19.68/19.86 2859 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1668,b,1646,a)].
% 19.68/19.86 2860 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1668,b,1647,a)].
% 19.78/19.92 2861 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1668,b,1648,a)].
% 19.78/19.92 2862 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1668,b,1649,a)].
% 19.78/19.92 2863 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1668,b,1650,a)].
% 19.78/19.92 2864 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1668,b,1651,a)].
% 19.78/19.92 2865 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1668,b,1652,a)].
% 19.78/19.92 2866 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1668,b,1653,a)].
% 19.78/19.92 2867 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1668,b,1654,a)].
% 19.78/19.92 2868 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1668,b,1655,a)].
% 19.78/19.92 2869 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1668,b,1656,a)].
% 19.78/19.92 2870 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1780,a,1770,b)].
% 19.78/19.92 2871 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1844,b,1839,b)].
% 19.78/19.92 2872 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1849,a,1839,b)].
% 19.78/19.92 2873 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1850,a,1839,b)].
% 19.78/19.92 2874 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1986,c,1904,b)].
% 19.78/19.92 2875 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1987,c,1904,b)].
% 19.78/19.92 2876 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2024,b,1904,b)].
% 19.78/19.92 2877 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2025,c,1904,b)].
% 19.78/19.92 2878 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2026,b,1904,b)].
% 19.78/19.92 2879 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2027,c,1904,b)].
% 19.78/19.92 2880 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2028,c,1904,b)].
% 19.78/19.92 2881 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2029,c,1904,b)].
% 19.78/19.92 2882 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2030,c,1904,b)].
% 19.78/19.92 2883 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2031,c,1904,b)].
% 19.78/19.92 2884 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2032,c,1904,b)].
% 19.78/19.92 2885 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2033,b,1904,b)].
% 19.78/19.95 2886 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2034,b,1904,b)].
% 19.78/19.95 2887 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2035,d,1904,b)].
% 19.78/19.95 2888 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2036,d,1904,b)].
% 19.78/19.95 2889 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2037,c,1904,b)].
% 19.78/19.95 2890 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2038,c,1904,b)].
% 19.78/19.95 2891 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2039,d,1904,b)].
% 19.78/19.95 2892 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2040,c,1904,b)].
% 19.78/19.95 2893 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2041,c,1904,b)].
% 19.78/19.95 2894 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2042,d,1904,b)].
% 19.78/19.95 2895 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2043,c,1904,b)].
% 19.78/19.95 2896 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2044,c,1904,b)].
% 19.78/19.95 2897 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2045,c,1904,b)].
% 19.78/19.95 2898 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2046,c,1904,b)].
% 19.78/19.95 2899 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2047,c,1904,b)].
% 19.78/19.95 2900 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2048,c,1904,b)].
% 19.78/19.95 2901 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2049,d,1904,b)].
% 19.78/19.95 2902 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2050,c,1904,b)].
% 19.78/19.95 2903 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2051,c,1904,b)].
% 19.78/19.95 2904 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2052,d,1904,b)].
% 19.78/19.95 2905 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2053,c,1904,b)].
% 19.78/19.95 2906 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2054,c,1904,b)].
% 19.78/19.95 2907 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2055,c,1904,b)].
% 19.78/19.95 2908 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2056,c,1904,b)].
% 19.78/19.95 2909 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2058,d,1904,b)].
% 19.78/19.95 2910 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2077,a,2063,b)].
% 19.86/19.99 2911 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2082,b,2063,b)].
% 19.86/19.99 2912 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2083,b,2063,b)].
% 19.86/19.99 2913 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2086,b,2063,b)].
% 19.86/19.99 2914 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2087,b,2063,b)].
% 19.86/19.99 2915 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2088,b,2063,b)].
% 19.86/19.99 2916 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2089,b,2063,b)].
% 19.86/19.99 2917 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2157,a,2132,b)].
% 19.86/19.99 2918 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2158,a,2132,b)].
% 19.86/19.99 2919 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,d,2132,b)].
% 19.86/19.99 2920 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2202,b,2132,b)].
% 19.86/19.99 2921 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2203,b,2132,b)].
% 19.86/19.99 2922 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2204,b,2132,b)].
% 19.86/19.99 2923 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2205,b,2132,b)].
% 19.86/19.99 2924 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2206,b,2132,b)].
% 19.86/19.99 2925 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,b,2132,b)].
% 19.86/19.99 2926 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2208,b,2132,b)].
% 19.86/19.99 2927 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2209,c,2132,b)].
% 19.86/19.99 2928 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2210,b,2132,b)].
% 19.86/19.99 2929 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2211,c,2132,b)].
% 19.86/19.99 2930 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2212,c,2132,b)].
% 19.86/19.99 2931 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2213,c,2132,b)].
% 19.86/19.99 2932 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2214,c,2132,b)].
% 19.86/19.99 2933 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2215,c,2132,b)].
% 19.86/19.99 2934 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2216,c,2132,b)].
% 19.86/19.99 2935 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2217,b,2132,b)].
% 19.86/19.99 2936 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2218,b,2132,b)].
% 19.86/20.02 2937 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2219,d,2132,b)].
% 19.86/20.02 2938 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2220,d,2132,b)].
% 19.86/20.02 2939 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2221,c,2132,b)].
% 19.86/20.02 2940 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2222,c,2132,b)].
% 19.86/20.02 2941 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2223,d,2132,b)].
% 19.86/20.02 2942 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2224,c,2132,b)].
% 19.86/20.02 2943 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2225,c,2132,b)].
% 19.86/20.02 2944 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2226,d,2132,b)].
% 19.86/20.02 2945 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2227,c,2132,b)].
% 19.86/20.02 2946 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2228,c,2132,b)].
% 19.86/20.02 2947 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2229,c,2132,b)].
% 19.86/20.02 2948 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2230,c,2132,b)].
% 19.86/20.02 2949 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2231,c,2132,b)].
% 19.86/20.02 2950 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2232,c,2132,b)].
% 19.86/20.02 2951 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2233,d,2132,b)].
% 19.86/20.02 2952 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2234,c,2132,b)].
% 19.86/20.02 2953 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2235,c,2132,b)].
% 19.86/20.02 2954 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2236,d,2132,b)].
% 19.86/20.02 2955 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2237,c,2132,b)].
% 19.86/20.02 2956 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2238,c,2132,b)].
% 19.86/20.02 2957 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2239,c,2132,b)].
% 19.86/20.02 2958 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2240,c,2132,b)].
% 19.86/20.02 2959 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2241,d,2132,b)].
% 19.86/20.02 2960 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2273,a,2245,b)].
% 19.86/20.02 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(2960,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(2960,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2960,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2960,e,2742,b)].
% 19.86/20.03 2961 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2274,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(2961,d,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2961,d,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2961,d,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2961,d,2742,b)].
% 19.86/20.03 2962 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2275,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2962,d,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(2962,d,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2962,d,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2962,d,2742,b)].
% 19.86/20.03 2963 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2276,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(2963,f,2734,a)].
% 19.86/20.03 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(2963,f,2735,a)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2963,f,2741,b)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2963,f,2742,b)].
% 19.86/20.03 2964 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2277,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2964,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2964,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2964,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2964,e,2742,b)].
% 19.86/20.03 2965 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2278,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2965,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2965,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2965,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2965,e,2742,b)].
% 19.86/20.03 2966 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2279,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(2966,f,2734,a)].
% 19.86/20.03 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(2966,f,2735,a)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2966,f,2741,b)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2966,f,2742,b)].
% 19.86/20.03 2967 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2280,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2967,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2967,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2967,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2967,e,2742,b)].
% 19.86/20.03 2968 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2281,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2968,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2968,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2968,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2968,e,2742,b)].
% 19.86/20.03 2969 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2282,a,2245,b)].
% 19.86/20.03 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2969,b,2734,a)].
% 19.86/20.03 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2969,b,2735,a)].
% 19.86/20.03 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2969,b,2741,b)].
% 19.86/20.03 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2969,b,2742,b)].
% 19.86/20.03 2970 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2283,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2970,f,2734,a)].
% 19.86/20.03 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(2970,f,2735,a)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2970,f,2741,b)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2970,f,2742,b)].
% 19.86/20.03 2971 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2284,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2971,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2971,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2971,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2971,e,2742,b)].
% 19.86/20.03 2972 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2285,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2972,e,2734,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2972,e,2735,a)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2972,e,2741,b)].
% 19.86/20.03 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2972,e,2742,b)].
% 19.86/20.03 2973 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2286,a,2245,b)].
% 19.86/20.03 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2973,f,2734,a)].
% 19.86/20.03 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(2973,f,2735,a)].
% 19.86/20.03 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2973,f,2741,b)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2973,f,2742,b)].
% 19.86/20.04 2974 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2287,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2974,e,2734,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2974,e,2735,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2974,e,2741,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2974,e,2742,b)].
% 19.86/20.04 2975 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2288,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2975,e,2734,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2975,e,2735,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2975,e,2741,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2975,e,2742,b)].
% 19.86/20.04 2976 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2289,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(2976,d,2734,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2976,d,2735,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2976,d,2741,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2976,d,2742,b)].
% 19.86/20.04 2977 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2290,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2977,d,2734,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(2977,d,2735,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2977,d,2741,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2977,d,2742,b)].
% 19.86/20.04 2978 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2291,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2978,e,2734,a)].
% 19.86/20.04 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(2978,e,2735,a)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2978,e,2741,b)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2978,e,2742,b)].
% 19.86/20.04 2979 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,a,2245,b)].
% 19.86/20.04 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2979,b,2734,a)].
% 19.86/20.04 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2979,b,2735,a)].
% 19.86/20.04 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2979,b,2741,b)].
% 19.86/20.04 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2979,b,2742,b)].
% 19.86/20.04 2980 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2293,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2980,d,2734,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2980,d,2735,a)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2980,d,2741,b)].
% 19.86/20.04 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,d,2742,b)].
% 19.86/20.04 2981 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2294,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2981,e,2734,a)].
% 19.86/20.04 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(2981,e,2735,a)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(2981,e,2741,b)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(2981,e,2742,b)].
% 19.86/20.04 2982 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2295,a,2245,b)].
% 19.86/20.04 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2982,e,2734,a)].
% 19.86/20.04 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(2982,e,2735,a)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(2982,e,2741,b)].
% 19.86/20.04 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(2982,e,2742,b)].
% 19.86/20.04 2983 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2296,a,2245,b)].
% 19.86/20.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(2983,d,2734,a)].
% 19.86/20.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(2983,d,2735,a)].
% 19.86/20.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2983,d,2741,b)].
% 19.86/20.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2983,d,2742,b)].
% 19.86/20.05 2984 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2297,a,2245,b)].
% 19.86/20.05 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2984,d,2734,a)].
% 19.86/20.05 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(2984,d,2735,a)].
% 19.86/20.05 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2984,d,2741,b)].
% 19.86/20.05 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2984,d,2742,b)].
% 19.86/20.05 2985 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2298,a,2245,b)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2985,c,2734,a)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2985,c,2735,a)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2985,c,2741,b)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2985,c,2742,b)].
% 19.86/20.05 2986 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2299,a,2245,b)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2986,c,2734,a)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2986,c,2735,a)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2986,c,2741,b)].
% 19.86/20.05 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2986,c,2742,b)].
% 19.86/20.05 2987 -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2300,a,2245,b)].
% 19.86/20.05 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2987,d,2734,a)].
% 19.86/20.05 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2987,d,2735,a)].
% 19.86/20.05 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2987,d,2741,b)].
% 19.86/20.05 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2987,d,2742,b)].
% 19.86/20.05 2988 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2301,a,2245,b)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2988,c,2734,a)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2988,c,2735,a)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2988,c,2741,b)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2988,c,2742,b)].
% 19.86/20.05 2989 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2302,a,2245,b)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2989,c,2734,a)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2989,c,2735,a)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2989,c,2741,b)].
% 19.86/20.05 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2989,c,2742,b)].
% 19.86/20.05 2990 -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2303,a,2245,b)].
% 19.86/20.05 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2990,d,2734,a)].
% 19.86/20.05 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(2990,d,2735,a)].
% 19.86/20.05 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2990,d,2741,b)].
% 19.86/20.05 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2990,d,2742,b)].
% 19.86/20.05 2991 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2304,a,2245,b)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2991,c,2734,a)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2991,c,2735,a)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2991,c,2741,b)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2991,c,2742,b)].
% 19.86/20.05 2992 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2305,a,2245,b)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2992,c,2734,a)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2992,c,2735,a)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2992,c,2741,b)].
% 19.86/20.05 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2992,c,2742,b)].
% 19.86/20.05 2993 -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2306,a,2245,b)].
% 19.86/20.05 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2993,d,2734,a)].
% 19.86/20.05 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(2993,d,2735,a)].
% 19.86/20.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2993,d,2741,b)].
% 19.86/20.05 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2993,d,2742,b)].
% 19.86/20.05 2994 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2307,a,2245,b)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2994,b,2734,a)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2994,b,2735,a)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2994,b,2741,b)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2742,b)].
% 19.86/20.05 2995 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2308,a,2245,b)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(2995,b,2734,a)].
% 19.86/20.05 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2995,b,2735,a)].
% 19.86/20.06 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2995,b,2741,b)].
% 19.86/20.06 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2995,b,2742,b)].
% 19.86/20.06 2996 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2309,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2996,c,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2996,c,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2996,c,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2996,c,2742,b)].
% 19.86/20.06 2997 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2310,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2997,c,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2997,c,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2997,c,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2997,c,2742,b)].
% 19.86/20.06 2998 -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2311,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2998,d,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2998,d,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2998,d,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2998,d,2742,b)].
% 19.86/20.06 2999 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2312,a,2245,b)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2999,b,2734,a)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2999,b,2735,a)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2999,b,2741,b)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2999,b,2742,b)].
% 19.86/20.06 3000 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2313,a,2245,b)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(3000,b,2734,a)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(3000,b,2735,a)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3000,b,2741,b)].
% 19.86/20.06 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3000,b,2742,b)].
% 19.86/20.06 3001 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2314,a,2245,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(3001,b,2734,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(3001,b,2735,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3001,b,2741,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3001,b,2742,b)].
% 19.86/20.06 3002 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2315,a,2245,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(3002,b,2734,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(3002,b,2735,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3002,b,2741,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3002,b,2742,b)].
% 19.86/20.06 3003 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2316,a,2245,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(3003,b,2734,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(3003,b,2735,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3003,b,2741,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3003,b,2742,b)].
% 19.86/20.06 3004 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2317,a,2245,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(3004,b,2734,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(3004,b,2735,a)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3004,b,2741,b)].
% 19.86/20.06 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3004,b,2742,b)].
% 19.86/20.06 3005 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2318,a,2245,b)].
% 19.86/20.06 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(3005,c,2734,a)].
% 19.86/20.06 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(3005,c,2735,a)].
% 19.86/20.06 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3005,c,2741,b)].
% 19.86/20.06 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3005,c,2742,b)].
% 19.86/20.06 3006 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2319,a,2245,b)].
% 19.86/20.06 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(3006,c,2734,a)].
% 19.86/20.06 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(3006,c,2735,a)].
% 19.86/20.06 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3006,c,2741,b)].
% 19.86/20.06 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3006,c,2742,b)].
% 19.86/20.06 3007 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2320,a,2245,b)].
% 19.86/20.06 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(3007,c,2734,a)].
% 19.86/20.06 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(3007,c,2735,a)].
% 19.86/20.06 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3007,c,2741,b)].
% 19.86/20.06 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,c,2742,b)].
% 19.86/20.06 3008 -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2321,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3008,c,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(3008,c,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3008,c,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,c,2742,b)].
% 19.86/20.06 3009 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2322,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3009,c,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(3009,c,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3009,c,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3009,c,2742,b)].
% 19.86/20.06 3010 -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2323,a,2245,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(3010,c,2734,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(3010,c,2735,a)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3010,c,2741,b)].
% 19.86/20.06 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3010,c,2742,b)].
% 19.86/20.06 3011 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2324,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3011,d,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3011,d,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3011,d,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3011,d,2742,b)].
% 19.86/20.07 3012 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2325,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3012,d,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3012,d,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3012,d,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3012,d,2742,b)].
% 19.86/20.07 3013 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2326,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3013,c,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(3013,c,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3013,c,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3013,c,2742,b)].
% 19.86/20.07 3014 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2327,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3014,d,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(3014,d,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3014,d,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3014,d,2742,b)].
% 19.86/20.07 3015 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,a,2245,b)].
% 19.86/20.07 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(3015,c,2734,a)].
% 19.86/20.07 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(3015,c,2735,a)].
% 19.86/20.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3015,c,2741,b)].
% 19.86/20.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3015,c,2742,b)].
% 19.86/20.07 3016 -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2329,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3016,c,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(3016,c,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3016,c,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3016,c,2742,b)].
% 19.86/20.07 3017 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2330,a,2245,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3017,c,2734,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)). [resolve(3017,c,2735,a)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3017,c,2741,b)].
% 19.86/20.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3017,c,2742,b)].
% 19.86/20.07 3018 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2331,b,2245,b)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3018,b,2734,a)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(A,B,tc_nat),tc_nat). [resolve(3018,b,2735,a)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3018,b,2741,b)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3018,b,2742,b)].
% 19.86/20.07 3019 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2332,b,2245,b)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3019,b,2734,a)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(B,A,tc_nat),tc_nat). [resolve(3019,b,2735,a)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3019,b,2741,b)].
% 19.86/20.07 Derived: c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3019,b,2742,b)].
% 19.86/20.07 3020 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2333,a,2245,b)].
% 19.86/20.08 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(3020,b,2734,a)].
% 19.86/20.08 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(3020,b,2735,a)].
% 19.86/20.08 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3020,b,2741,b)].
% 19.86/20.08 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3020,b,2742,b)].
% 19.86/20.08 3021 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2334,a,2245,b)].
% 19.86/20.08 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(3021,b,2734,a)].
% 19.86/20.08 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(3021,b,2735,a)].
% 19.86/20.08 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3021,b,2741,b)].
% 19.86/20.08 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3021,b,2742,b)].
% 19.86/20.08 3022 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2339,a,2245,b)].
% 19.86/20.08 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(3022,c,2734,a)].
% 19.86/20.08 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(3022,c,2735,a)].
% 19.86/20.08 3023 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2340,a,2245,b)].
% 19.86/20.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3023,c,2734,a)].
% 19.86/20.08 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(3023,c,2735,a)].
% 19.86/20.08 3024 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2341,a,2245,b)].
% 19.86/20.08 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3024,c,2734,a)].
% 19.86/20.08 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3024,c,2735,a)].
% 19.86/20.08 3025 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2342,a,2245,b)].
% 19.86/20.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3025,c,2734,a)].
% 19.86/20.08 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(3025,c,2735,a)].
% 19.86/20.08 3026 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2343,a,2245,b)].
% 19.86/20.08 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(3026,c,2734,a)].
% 19.86/20.08 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(3026,c,2735,a)].
% 19.86/20.08 3027 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2344,a,2245,b)].
% 19.86/20.08 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3027,c,2734,a)].
% 19.86/20.08 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(3027,c,2735,a)].
% 19.86/20.08 3028 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2345,a,2245,b)].
% 19.86/20.08 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3028,c,2734,a)].
% 19.86/20.08 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3028,c,2735,a)].
% 19.86/20.08 3029 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2346,a,2245,b)].
% 19.86/20.08 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3029,c,2734,a)].
% 19.96/20.09 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(3029,c,2735,a)].
% 19.96/20.09 3030 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2381,e,2245,b)].
% 19.96/20.09 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3030,e,2734,a)].
% 19.96/20.09 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_plus(B,A,tc_nat),tc_nat). [resolve(3030,e,2735,a)].
% 19.96/20.09 3031 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2382,c,2245,b)].
% 19.96/20.09 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(3031,c,2734,a)].
% 19.96/20.09 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(3031,c,2735,a)].
% 19.96/20.09 3032 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2383,c,2245,b)].
% 19.96/20.09 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(3032,c,2734,a)].
% 19.96/20.09 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(3032,c,2735,a)].
% 19.96/20.09 3033 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2384,b,2245,b)].
% 19.96/20.09 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3033,b,2734,a)].
% 19.96/20.09 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(3033,b,2735,a)].
% 19.96/20.09 3034 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2385,b,2245,b)].
% 19.96/20.09 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3034,b,2734,a)].
% 19.96/20.09 Derived: class_HOL_Oplus(tc_nat). [resolve(3034,b,2735,a)].
% 19.96/20.09 3035 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2427,b,2245,b)].
% 19.96/20.09 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3035,b,2734,a)].
% 19.96/20.09 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(3035,b,2735,a)].
% 19.96/20.09 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3035,b,2741,b)].
% 19.96/20.09 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3035,b,2742,b)].
% 19.96/20.09 3036 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2428,b,2245,b)].
% 19.96/20.09 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3036,b,2734,a)].
% 19.96/20.09 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(3036,b,2735,a)].
% 19.96/20.09 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3036,b,2741,b)].
% 19.96/20.09 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3036,b,2742,b)].
% 19.96/20.09 3037 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2429,d,2245,b)].
% 19.96/20.09 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(c_0,C,tc_IntDef_Oint) | c_lessequals(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3037,d,2734,a)].
% 19.96/20.09 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(c_0,C,tc_nat) | c_lessequals(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(3037,d,2735,a)].
% 19.96/20.09 3038 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2430,b,2245,b)].
% 19.96/20.09 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3038,b,2734,a)].
% 19.96/20.09 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(3038,b,2735,a)].
% 19.96/20.09 3039 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2431,b,2245,b)].
% 19.96/20.09 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3039,b,2734,a)].
% 19.96/20.09 Derived: class_HOL_Otimes(tc_nat). [resolve(3039,b,2735,a)].
% 19.96/20.09 3040 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2432,b,2245,b)].
% 19.96/20.10 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3040,b,2734,a)].
% 19.96/20.10 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(3040,b,2735,a)].
% 19.96/20.10 3041 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2433,b,2245,b)].
% 19.96/20.10 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3041,b,2734,a)].
% 19.96/20.10 Derived: class_HOL_Ozero(tc_nat). [resolve(3041,b,2735,a)].
% 19.96/20.10 3042 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2434,b,2245,b)].
% 19.96/20.10 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3042,b,2734,a)].
% 19.96/20.10 Derived: c_times(A,c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(A,B,tc_nat),c_times(A,C,tc_nat),tc_nat). [resolve(3042,b,2735,a)].
% 19.96/20.10 3043 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2435,b,2245,b)].
% 19.96/20.10 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3043,b,2734,a)].
% 19.96/20.10 Derived: c_times(c_plus(A,B,tc_nat),C,tc_nat) = c_plus(c_times(A,C,tc_nat),c_times(B,C,tc_nat),tc_nat). [resolve(3043,b,2735,a)].
% 19.96/20.10 3044 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2436,b,2245,b)].
% 19.96/20.10 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(3044,b,2734,a)].
% 19.96/20.10 Derived: -c_less(A,A,tc_nat). [resolve(3044,b,2735,a)].
% 19.96/20.10 3045 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2437,c,2245,b)].
% 19.96/20.10 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3045,c,2734,a)].
% 19.96/20.10 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(3045,c,2735,a)].
% 19.96/20.10 3046 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2438,b,2245,b)].
% 19.96/20.10 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3046,b,2734,a)].
% 19.96/20.10 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(3046,b,2735,a)].
% 19.96/20.10 3047 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2439,c,2245,b)].
% 19.96/20.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3047,c,2734,a)].
% 19.96/20.10 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(3047,c,2735,a)].
% 19.96/20.10 3048 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2440,c,2245,b)].
% 19.96/20.10 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(3048,c,2734,a)].
% 19.96/20.10 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(3048,c,2735,a)].
% 19.96/20.10 3049 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2441,c,2245,b)].
% 19.96/20.10 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(3049,c,2734,a)].
% 19.96/20.10 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(3049,c,2735,a)].
% 19.96/20.10 3050 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2442,c,2245,b)].
% 19.98/20.11 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3050,c,2734,a)].
% 19.98/20.11 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(3050,c,2735,a)].
% 19.98/20.11 3051 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2443,c,2245,b)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3051,c,2734,a)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(3051,c,2735,a)].
% 19.98/20.11 3052 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2444,c,2245,b)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3052,c,2734,a)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(3052,c,2735,a)].
% 19.98/20.11 3053 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2445,b,2245,b)].
% 19.98/20.11 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3053,b,2734,a)].
% 19.98/20.11 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(3053,b,2735,a)].
% 19.98/20.11 3054 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2446,b,2245,b)].
% 19.98/20.11 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3054,b,2734,a)].
% 19.98/20.11 Derived: c_lessequals(A,A,tc_nat). [resolve(3054,b,2735,a)].
% 19.98/20.11 3055 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2447,d,2245,b)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(3055,d,2734,a)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_lessequals(C,B,tc_nat). [resolve(3055,d,2735,a)].
% 19.98/20.11 3056 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2448,d,2245,b)].
% 19.98/20.11 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3056,d,2734,a)].
% 19.98/20.11 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_less(A,C,tc_nat). [resolve(3056,d,2735,a)].
% 19.98/20.11 3057 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2449,c,2245,b)].
% 19.98/20.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3057,c,2734,a)].
% 19.98/20.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3057,c,2735,a)].
% 19.98/20.11 3058 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2450,c,2245,b)].
% 19.98/20.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3058,c,2734,a)].
% 19.98/20.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3058,c,2735,a)].
% 19.98/20.11 3059 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2451,d,2245,b)].
% 19.98/20.11 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3059,d,2734,a)].
% 19.98/20.13 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(3059,d,2735,a)].
% 19.98/20.13 3060 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2452,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3060,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3060,c,2735,a)].
% 19.98/20.13 3061 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2453,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3061,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3061,c,2735,a)].
% 19.98/20.13 3062 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2454,d,2245,b)].
% 19.98/20.13 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3062,d,2734,a)].
% 19.98/20.13 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(3062,d,2735,a)].
% 19.98/20.13 3063 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2455,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(3063,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3063,c,2735,a)].
% 19.98/20.13 3064 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2456,c,2245,b)].
% 19.98/20.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3064,c,2734,a)].
% 19.98/20.13 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3064,c,2735,a)].
% 19.98/20.13 3065 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2457,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3065,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3065,c,2735,a)].
% 19.98/20.13 3066 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2458,c,2245,b)].
% 19.98/20.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3066,c,2734,a)].
% 19.98/20.13 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3066,c,2735,a)].
% 19.98/20.13 3067 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2459,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3067,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3067,c,2735,a)].
% 19.98/20.13 3068 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2460,c,2245,b)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3068,c,2734,a)].
% 19.98/20.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3068,c,2735,a)].
% 20.14/20.35 3069 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2461,d,2245,b)].
% 20.14/20.35 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3069,d,2734,a)].
% 20.14/20.35 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(3069,d,2735,a)].
% 20.14/20.35 3070 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2462,c,2245,b)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3070,c,2734,a)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3070,c,2735,a)].
% 20.14/20.35 3071 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2463,c,2245,b)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3071,c,2734,a)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3071,c,2735,a)].
% 20.14/20.35 3072 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2464,d,2245,b)].
% 20.14/20.35 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3072,d,2734,a)].
% 20.14/20.35 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(3072,d,2735,a)].
% 20.14/20.35 3073 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2465,c,2245,b)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(3073,c,2734,a)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3073,c,2735,a)].
% 20.14/20.35 3074 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2466,c,2245,b)].
% 20.14/20.35 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3074,c,2734,a)].
% 20.14/20.35 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3074,c,2735,a)].
% 20.14/20.35 3075 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2467,c,2245,b)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(3075,c,2734,a)].
% 20.14/20.35 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3075,c,2735,a)].
% 20.14/20.35 3076 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2468,c,2245,b)].
% 20.14/20.35 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3076,c,2734,a)].
% 20.14/20.35 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3076,c,2735,a)].
% 20.14/20.35 3077 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2469,d,2245,b)].
% 20.14/20.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(D,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3077,d,2734,a)].
% 20.14/20.35 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(D,B,tc_nat),tc_nat). [resolve(3077,d,2735,a)].
% 20.14/20.35 3078 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_0) # label(axiom). [assumption].
% 20.75/20.95 3079 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 20.75/20.95 3080 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_2) # label(axiom). [assumption].
% 20.75/20.95 3081 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__field_42) # label(axiom). [assumption].
% 20.75/20.95 3082 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__idom_46) # label(axiom). [assumption].
% 20.75/20.95 3083 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint). [resolve(1321,a,1277,a)].
% 20.75/20.95 3084 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1321,a,1303,b)].
% 20.75/20.95 3085 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1321,a,1304,b)].
% 20.75/20.95 3086 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1637,a)].
% 20.75/20.95 3087 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1638,a)].
% 20.75/20.95 3088 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1666,b,1639,a)].
% 20.75/20.95 3089 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1640,a)].
% 20.75/20.95 3090 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1641,a)].
% 20.75/20.95 3091 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1666,b,1642,a)].
% 20.75/20.95 3092 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1666,b,1643,a)].
% 20.75/20.95 3093 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1666,b,1644,a)].
% 20.75/20.95 3094 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1666,b,1645,a)].
% 20.75/20.95 3095 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1666,b,1646,a)].
% 20.75/20.95 3096 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1647,a)].
% 20.75/20.95 3097 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1666,b,1648,a)].
% 20.75/20.95 3098 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1666,b,1649,a)].
% 20.75/20.95 3099 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1666,b,1650,a)].
% 20.75/20.95 3100 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1666,b,1651,a)].
% 20.75/20.95 3101 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1666,b,1652,a)].
% 20.75/20.95 3102 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1666,b,1653,a)].
% 20.75/20.95 3103 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1666,b,1654,a)].
% 20.75/20.95 3104 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1666,b,1655,a)].
% 20.75/20.95 3105 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1666,b,1656,a)].
% 20.75/20.95 3106 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 20.75/20.97 3107 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 20.75/20.97 3108 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Olordered__ring_0) # label(axiom). [assumption].
% 20.75/20.97 3109 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_44) # label(axiom). [assumption].
% 20.75/20.97 3110 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_49) # label(axiom). [assumption].
% 20.75/20.97 3111 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 20.75/20.97 3112 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 20.75/20.97 3113 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom). [assumption].
% 20.75/20.97 3114 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom). [assumption].
% 20.75/20.97 3115 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_19) # label(axiom). [assumption].
% 20.75/20.97 3116 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom). [assumption].
% 20.75/20.97 3117 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 20.75/20.97 3118 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom). [assumption].
% 20.75/20.97 3119 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(36,b,1,a)].
% 20.75/20.97 3120 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(36,b,3,a)].
% 20.75/20.97 3121 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(36,b,9,a)].
% 20.75/20.97 3122 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(36,b,10,a)].
% 20.75/20.97 3123 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(158,b,131,b)].
% 20.75/20.97 3124 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(158,b,133,b)].
% 20.75/20.97 3125 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(165,a,158,b)].
% 20.75/20.97 3126 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(166,a,158,b)].
% 20.75/20.97 3127 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(171,a,158,b)].
% 20.75/20.97 3128 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(172,a,158,b)].
% 20.75/20.97 3129 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(240,a,232,b)].
% 20.75/20.97 3130 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(241,a,232,b)].
% 20.75/20.97 3131 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(247,b,232,b)].
% 20.75/20.97 3132 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(248,b,232,b)].
% 20.75/20.97 3133 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(311,b,288,a)].
% 20.75/20.97 3134 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(311,b,290,a)].
% 20.84/20.99 3135 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(322,a,311,b)].
% 20.84/20.99 3136 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(323,a,311,b)].
% 20.84/20.99 3137 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(325,a,311,b)].
% 20.84/20.99 3138 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(326,a,311,b)].
% 20.84/20.99 3139 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(348,b,331,b)].
% 20.84/20.99 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3139,a,3108,b)].
% 20.84/20.99 3140 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(348,b,333,b)].
% 20.84/20.99 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3140,a,3108,b)].
% 20.84/20.99 3141 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(348,b,334,a)].
% 20.84/20.99 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3141,a,3108,b)].
% 20.84/20.99 3142 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,335,a)].
% 20.84/20.99 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3142,a,3108,b)].
% 20.84/20.99 3143 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(348,b,336,a)].
% 20.84/20.99 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3143,a,3108,b)].
% 20.84/20.99 3144 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,a,348,b)].
% 20.84/20.99 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3108,b)].
% 20.84/20.99 3145 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(355,a,348,b)].
% 20.84/20.99 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3108,b)].
% 20.84/20.99 3146 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(366,b,348,b)].
% 20.84/20.99 3147 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(367,b,348,b)].
% 20.84/20.99 3148 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(370,b,348,b)].
% 20.84/20.99 3149 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(371,b,348,b)].
% 20.84/20.99 3150 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(372,b,348,b)].
% 20.84/20.99 3151 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(373,b,348,b)].
% 20.84/20.99 3152 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(374,a,348,b)].
% 20.84/20.99 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3152,b,3108,b)].
% 20.84/20.99 3153 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(375,a,348,b)].
% 20.84/20.99 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3153,b,3108,b)].
% 20.84/20.99 3154 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(376,c,348,b)].
% 20.84/20.99 3155 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(377,c,348,b)].
% 20.97/21.13 3156 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(814,a,734,a)].
% 20.97/21.13 3157 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(814,a,741,a)].
% 20.97/21.13 3158 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint). [resolve(1325,a,1277,a)].
% 20.97/21.13 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3158,a,3139,a)].
% 20.97/21.13 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3158,a,3140,a)].
% 20.97/21.13 Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint). [resolve(3158,a,3141,a)].
% 20.97/21.13 Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3158,a,3142,a)].
% 20.97/21.13 Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3158,a,3143,a)].
% 20.97/21.13 3159 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1325,a,1303,b)].
% 20.97/21.13 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(3159,a,3139,a)].
% 20.97/21.13 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(3159,a,3140,a)].
% 20.97/21.13 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(3159,a,3141,a)].
% 20.97/21.13 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(3159,a,3142,a)].
% 20.97/21.13 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(3159,a,3143,a)].
% 20.97/21.13 3160 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1325,a,1304,b)].
% 20.97/21.13 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(3160,a,3139,a)].
% 20.97/21.13 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(3160,a,3140,a)].
% 20.97/21.13 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(3160,a,3141,a)].
% 20.97/21.13 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(3160,a,3142,a)].
% 20.97/21.13 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(3160,a,3143,a)].
% 20.97/21.13 3161 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1502,b,1477,a)].
% 20.97/21.13 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(3161,a,3108,b)].
% 20.97/21.13 3162 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1502,b,1478,a)].
% 20.97/21.13 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(3162,a,3108,b)].
% 21.07/21.21 3163 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1502,b,1479,a)].
% 21.07/21.21 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3163,a,3108,b)].
% 21.07/21.21 3164 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1502,b,1480,a)].
% 21.07/21.21 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3164,a,3108,b)].
% 21.07/21.21 3165 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1502,b,1481,a)].
% 21.07/21.21 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3165,a,3108,b)].
% 21.07/21.21 3166 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1502,b,1482,a)].
% 21.07/21.21 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3166,a,3108,b)].
% 21.07/21.21 3167 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1502,b,1483,a)].
% 21.07/21.21 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3167,a,3108,b)].
% 21.07/21.21 3168 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1502,b,1484,a)].
% 21.07/21.21 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(3168,a,3108,b)].
% 21.07/21.21 3169 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(1611,b,1581,a)].
% 21.07/21.21 3170 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1582,a)].
% 21.07/21.21 3171 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1611,b,1583,a)].
% 21.07/21.21 3172 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1611,b,1584,a)].
% 21.07/21.21 3173 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1611,b,1585,a)].
% 21.07/21.21 3174 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1611,b,1586,a)].
% 21.07/21.21 3175 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1611,b,1587,a)].
% 21.07/21.21 3176 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1611,b,1588,a)].
% 21.07/21.21 3177 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1611,b,1589,a)].
% 21.07/21.21 3178 -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1611,b,1590,a)].
% 21.07/21.21 3179 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(1611,b,1591,a)].
% 21.07/21.21 3180 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1614,a,1611,b)].
% 21.07/21.21 3181 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1615,a,1611,b)].
% 21.07/21.21 3182 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1637,a)].
% 21.07/21.21 3183 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1638,a)].
% 21.07/21.21 3184 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1676,b,1639,a)].
% 21.07/21.28 3185 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1640,a)].
% 21.07/21.28 3186 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1641,a)].
% 21.07/21.28 3187 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1676,b,1642,a)].
% 21.07/21.28 3188 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1676,b,1643,a)].
% 21.07/21.28 3189 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1676,b,1644,a)].
% 21.07/21.28 3190 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1676,b,1645,a)].
% 21.07/21.28 3191 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1676,b,1646,a)].
% 21.07/21.28 3192 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1647,a)].
% 21.07/21.28 3193 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1676,b,1648,a)].
% 21.07/21.28 3194 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1676,b,1649,a)].
% 21.07/21.28 3195 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1676,b,1650,a)].
% 21.07/21.28 3196 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1676,b,1651,a)].
% 21.07/21.28 3197 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1676,b,1652,a)].
% 21.07/21.28 3198 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1676,b,1653,a)].
% 21.07/21.28 3199 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1676,b,1654,a)].
% 21.07/21.28 3200 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1676,b,1655,a)].
% 21.07/21.28 3201 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1676,b,1656,a)].
% 21.07/21.28 3202 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1780,a,1778,b)].
% 21.07/21.28 3203 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1792,b,1760,a)].
% 21.07/21.28 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3203,a,3108,b)].
% 21.07/21.28 3204 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1792,b,1767,a)].
% 21.07/21.28 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3204,a,3108,b)].
% 21.07/21.28 3205 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1844,b,1843,b)].
% 21.07/21.28 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3205,e,3108,b)].
% 21.07/21.28 3206 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2077,a,2071,b)].
% 21.07/21.28 3207 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2094,a,2071,b)].
% 21.07/21.28 3208 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2095,a,2071,b)].
% 21.07/21.28 3209 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2096,a,2071,b)].
% 21.07/21.28 3210 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2097,a,2071,b)].
% 21.16/21.30 3211 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2098,a,2071,b)].
% 21.16/21.30 3212 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2099,a,2071,b)].
% 21.16/21.30 3213 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2100,a,2071,b)].
% 21.16/21.30 3214 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2101,a,2071,b)].
% 21.16/21.30 3215 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(2102,a,2071,b)].
% 21.16/21.30 3216 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2103,a,2071,b)].
% 21.16/21.30 3217 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(2104,a,2071,b)].
% 21.16/21.30 3218 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2105,d,2071,b)].
% 21.16/21.30 3219 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2106,d,2071,b)].
% 21.16/21.30 3220 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2107,a,2071,b)].
% 21.16/21.30 3221 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2108,a,2071,b)].
% 21.16/21.30 3222 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2109,a,2071,b)].
% 21.16/21.30 3223 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2110,a,2071,b)].
% 21.16/21.30 3224 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2111,a,2071,b)].
% 21.16/21.30 3225 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2112,a,2071,b)].
% 21.16/21.30 3226 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2113,a,2071,b)].
% 21.16/21.30 3227 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2114,a,2071,b)].
% 21.16/21.30 3228 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2115,a,2071,b)].
% 21.16/21.30 3229 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2116,a,2071,b)].
% 21.16/21.30 3230 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2117,a,2071,b)].
% 21.16/21.30 3231 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2118,a,2071,b)].
% 21.16/21.30 3232 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2119,a,2071,b)].
% 21.16/21.30 3233 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2120,a,2071,b)].
% 21.16/21.30 3234 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2121,a,2071,b)].
% 21.16/21.30 3235 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2122,a,2071,b)].
% 21.16/21.30 3236 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2123,a,2071,b)].
% 21.16/21.30 3237 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2124,a,2071,b)].
% 21.46/21.59 3238 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2125,a,2071,b)].
% 21.46/21.59 3239 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2126,a,2071,b)].
% 21.46/21.59 3240 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2127,d,2071,b)].
% 21.46/21.59 3241 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2202,b,2142,b)].
% 21.46/21.59 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3241,b,3108,b)].
% 21.46/21.59 3242 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2203,b,2142,b)].
% 21.46/21.59 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3242,b,3108,b)].
% 21.46/21.59 3243 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2204,b,2142,b)].
% 21.46/21.59 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3243,b,3108,b)].
% 21.46/21.59 3244 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2205,b,2142,b)].
% 21.46/21.59 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3244,b,3108,b)].
% 21.46/21.59 3245 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2206,b,2142,b)].
% 21.46/21.59 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(3245,b,3108,b)].
% 21.46/21.59 3246 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2207,b,2142,b)].
% 21.46/21.59 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3246,b,3108,b)].
% 21.46/21.59 3247 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_0) # label(axiom). [assumption].
% 21.46/21.59 3248 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 21.46/21.59 3249 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 21.46/21.59 3250 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 21.46/21.59 3251 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom). [assumption].
% 21.46/21.59 3252 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom). [assumption].
% 21.46/21.59 3253 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 21.46/21.59 3254 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom). [assumption].
% 21.46/21.59 3255 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Olordered__ring_29) # label(axiom). [assumption].
% 21.46/21.59 3256 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__field_48) # label(axiom). [assumption].
% 21.46/21.59 3257 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__idom_51) # label(axiom). [assumption].
% 21.46/21.59 3258 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(14,b,1,a)].
% 21.46/21.59 3259 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(14,b,3,a)].
% 21.57/21.76 3260 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(81,b,52,b)].
% 21.57/21.76 3261 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(82,b,52,b)].
% 21.57/21.76 3262 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1084,b,1076,a)].
% 21.57/21.76 3263 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1107,b,1099,a)].
% 21.57/21.76 3264 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint). [resolve(1327,a,1277,a)].
% 21.57/21.76 3265 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1327,a,1303,b)].
% 21.57/21.76 3266 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1327,a,1304,b)].
% 21.57/21.76 3267 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1488,b,1477,a)].
% 21.57/21.76 3268 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1488,b,1478,a)].
% 21.57/21.76 3269 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1488,b,1479,a)].
% 21.57/21.76 3270 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1488,b,1480,a)].
% 21.57/21.76 3271 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1488,b,1481,a)].
% 21.57/21.76 3272 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1488,b,1482,a)].
% 21.57/21.76 3273 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1488,b,1483,a)].
% 21.57/21.76 3274 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1488,b,1484,a)].
% 21.57/21.76 3275 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1503,a,1488,b)].
% 21.57/21.76 3276 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1504,a,1488,b)].
% 21.57/21.76 3277 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1505,b,1488,b)].
% 21.57/21.76 3278 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1506,b,1488,b)].
% 21.57/21.76 3279 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1548,b,1515,a)].
% 21.57/21.76 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3279,a,3248,a)].
% 21.57/21.76 3280 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1548,b,1516,a)].
% 21.57/21.76 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3280,a,3248,a)].
% 21.57/21.76 3281 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1517,a)].
% 21.57/21.76 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3281,a,3248,a)].
% 21.57/21.76 3282 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1518,a)].
% 21.57/21.76 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3282,a,3248,a)].
% 21.57/21.76 3283 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1548,b,1519,a)].
% 21.57/21.76 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3283,a,3248,a)].
% 21.57/21.76 3284 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1548,b,1520,a)].
% 21.57/21.76 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3284,a,3248,a)].
% 21.57/21.76 3285 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1548,b,1521,a)].
% 21.57/21.77 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3285,a,3248,a)].
% 21.57/21.77 3286 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1548,b,1522,a)].
% 21.57/21.77 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3286,a,3248,a)].
% 21.57/21.77 3287 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1548,b,1523,a)].
% 21.57/21.77 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3287,a,3248,a)].
% 21.57/21.77 3288 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1548,b,1524,a)].
% 21.57/21.77 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(3288,a,3248,a)].
% 21.57/21.77 3289 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1548,b,1525,a)].
% 21.57/21.77 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(3289,a,3248,a)].
% 21.57/21.77 3290 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1548,b,1526,a)].
% 21.57/21.77 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3290,a,3248,a)].
% 21.57/21.77 3291 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1548,b,1527,a)].
% 21.57/21.77 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3291,a,3248,a)].
% 21.57/21.77 3292 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1548,b,1528,a)].
% 21.57/21.77 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3292,a,3248,a)].
% 21.57/21.77 3293 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1548,b,1529,a)].
% 21.57/21.77 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(3293,a,3248,a)].
% 21.57/21.77 3294 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1548,b,1530,a)].
% 21.57/21.77 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(3294,a,3248,a)].
% 21.57/21.77 3295 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1548,b,1531,a)].
% 21.57/21.77 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3295,a,3248,a)].
% 21.57/21.77 3296 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1548,b,1532,a)].
% 21.57/21.77 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3296,a,3248,a)].
% 21.57/21.77 3297 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1548,b,1533,a)].
% 21.57/21.77 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3297,a,3248,a)].
% 21.57/21.77 3298 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1548,b,1534,a)].
% 21.57/21.77 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3298,a,3248,a)].
% 21.57/21.77 3299 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1548,b,1535,a)].
% 21.57/21.77 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3299,a,3248,a)].
% 21.57/21.77 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3299,a,3255,b)].
% 21.67/21.81 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3299,a,3256,b)].
% 21.67/21.81 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3299,a,3257,b)].
% 21.67/21.81 3300 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1548,b,1536,a)].
% 21.67/21.81 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(3300,a,3248,a)].
% 21.67/21.81 3301 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(1596,b,1581,a)].
% 21.67/21.81 3302 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1582,a)].
% 21.67/21.81 3303 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1596,b,1583,a)].
% 21.67/21.81 3304 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1596,b,1584,a)].
% 21.67/21.81 3305 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1596,b,1585,a)].
% 21.67/21.81 3306 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1596,b,1586,a)].
% 21.67/21.81 3307 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1596,b,1587,a)].
% 21.67/21.81 3308 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1596,b,1588,a)].
% 21.67/21.81 3309 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1596,b,1589,a)].
% 21.67/21.81 3310 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1596,b,1590,a)].
% 21.67/21.81 3311 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(1596,b,1591,a)].
% 21.67/21.81 3312 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1614,a,1596,b)].
% 21.67/21.81 3313 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1615,a,1596,b)].
% 21.67/21.81 3314 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1637,a)].
% 21.67/21.81 3315 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1638,a)].
% 21.67/21.81 3316 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1661,b,1639,a)].
% 21.67/21.81 3317 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1640,a)].
% 21.67/21.81 3318 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1641,a)].
% 21.67/21.81 3319 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1661,b,1642,a)].
% 21.67/21.81 3320 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1661,b,1643,a)].
% 21.67/21.81 3321 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1661,b,1644,a)].
% 21.67/21.81 3322 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1661,b,1645,a)].
% 21.67/21.81 3323 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1661,b,1646,a)].
% 21.67/21.85 3324 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1647,a)].
% 21.67/21.85 3325 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1661,b,1648,a)].
% 21.67/21.85 3326 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1661,b,1649,a)].
% 21.67/21.85 3327 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1661,b,1650,a)].
% 21.67/21.85 3328 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1661,b,1651,a)].
% 21.67/21.85 3329 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1661,b,1652,a)].
% 21.67/21.85 3330 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1661,b,1653,a)].
% 21.67/21.85 3331 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1661,b,1654,a)].
% 21.67/21.85 3332 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1661,b,1655,a)].
% 21.67/21.85 3333 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1661,b,1656,a)].
% 21.67/21.85 3334 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1780,a,1764,b)].
% 21.67/21.85 3335 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1797,a,1764,b)].
% 21.67/21.85 3336 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1798,a,1764,b)].
% 21.67/21.85 3337 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1799,a,1764,b)].
% 21.67/21.85 3338 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1800,a,1764,b)].
% 21.67/21.85 3339 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1801,a,1764,b)].
% 21.67/21.85 3340 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1802,a,1764,b)].
% 21.67/21.85 3341 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1803,a,1764,b)].
% 21.67/21.85 3342 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1804,a,1764,b)].
% 21.67/21.85 3343 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1805,a,1764,b)].
% 21.67/21.85 3344 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1806,a,1764,b)].
% 21.67/21.85 3345 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1807,a,1764,b)].
% 21.67/21.85 3346 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1808,d,1764,b)].
% 21.67/21.85 3347 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1809,d,1764,b)].
% 21.67/21.85 3348 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1810,a,1764,b)].
% 21.67/21.85 3349 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1811,a,1764,b)].
% 21.96/22.18 3350 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1812,a,1764,b)].
% 21.96/22.18 3351 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1813,a,1764,b)].
% 21.96/22.18 3352 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1814,a,1764,b)].
% 21.96/22.18 3353 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1815,a,1764,b)].
% 21.96/22.18 3354 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1816,a,1764,b)].
% 21.96/22.18 3355 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1817,a,1764,b)].
% 21.96/22.18 3356 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1818,a,1764,b)].
% 21.96/22.18 3357 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1819,a,1764,b)].
% 21.96/22.18 3358 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1820,a,1764,b)].
% 21.96/22.18 3359 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1821,a,1764,b)].
% 21.96/22.18 3360 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1822,a,1764,b)].
% 21.96/22.18 3361 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1823,a,1764,b)].
% 21.96/22.18 3362 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1824,a,1764,b)].
% 21.96/22.18 3363 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1825,a,1764,b)].
% 21.96/22.18 3364 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1826,a,1764,b)].
% 21.96/22.18 3365 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1827,a,1764,b)].
% 21.96/22.18 3366 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1828,a,1764,b)].
% 21.96/22.18 3367 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1829,a,1764,b)].
% 21.96/22.18 3368 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1844,b,1834,b)].
% 21.96/22.18 3369 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1899,d,1834,b)].
% 21.96/22.18 3370 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_0) # label(axiom). [assumption].
% 21.96/22.18 3371 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 21.96/22.18 3372 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 21.96/22.18 3373 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 21.96/22.18 3374 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom). [assumption].
% 21.96/22.18 3375 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom). [assumption].
% 22.17/22.35 3376 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 22.17/22.35 3377 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom). [assumption].
% 22.17/22.35 3378 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Olordered__ring_30) # label(axiom). [assumption].
% 22.17/22.35 3379 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__field_49) # label(axiom). [assumption].
% 22.17/22.35 3380 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__idom_52) # label(axiom). [assumption].
% 22.17/22.35 3381 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(13,b,1,a)].
% 22.17/22.35 3382 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(13,b,3,a)].
% 22.17/22.35 3383 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(81,b,51,b)].
% 22.17/22.35 3384 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(82,b,51,b)].
% 22.17/22.35 3385 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1083,b,1076,a)].
% 22.17/22.35 3386 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1106,b,1099,a)].
% 22.17/22.35 3387 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint). [resolve(1328,a,1277,a)].
% 22.17/22.35 3388 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1328,a,1303,b)].
% 22.17/22.35 3389 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1328,a,1304,b)].
% 22.17/22.35 3390 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1487,b,1477,a)].
% 22.17/22.35 3391 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1487,b,1478,a)].
% 22.17/22.35 3392 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1487,b,1479,a)].
% 22.17/22.35 3393 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1487,b,1480,a)].
% 22.17/22.35 3394 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1487,b,1481,a)].
% 22.17/22.35 3395 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1487,b,1482,a)].
% 22.17/22.35 3396 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1487,b,1483,a)].
% 22.17/22.35 3397 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1487,b,1484,a)].
% 22.17/22.35 3398 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1503,a,1487,b)].
% 22.17/22.35 3399 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1504,a,1487,b)].
% 22.17/22.35 3400 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1505,b,1487,b)].
% 22.17/22.35 3401 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1506,b,1487,b)].
% 22.17/22.35 3402 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1547,b,1515,a)].
% 22.17/22.35 3403 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1547,b,1516,a)].
% 22.17/22.35 3404 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1517,a)].
% 22.17/22.37 3405 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1518,a)].
% 22.17/22.37 3406 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1547,b,1519,a)].
% 22.17/22.37 3407 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1547,b,1520,a)].
% 22.17/22.37 3408 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1547,b,1521,a)].
% 22.17/22.37 3409 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1547,b,1522,a)].
% 22.17/22.37 3410 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1547,b,1523,a)].
% 22.17/22.37 3411 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1547,b,1524,a)].
% 22.17/22.37 3412 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1547,b,1525,a)].
% 22.17/22.37 3413 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1547,b,1526,a)].
% 22.17/22.37 3414 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1547,b,1527,a)].
% 22.17/22.37 3415 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1547,b,1528,a)].
% 22.17/22.37 3416 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1547,b,1529,a)].
% 22.17/22.37 3417 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1547,b,1530,a)].
% 22.17/22.37 3418 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1547,b,1531,a)].
% 22.17/22.37 3419 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1547,b,1532,a)].
% 22.17/22.37 3420 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1547,b,1533,a)].
% 22.17/22.37 3421 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1547,b,1534,a)].
% 22.17/22.37 3422 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1547,b,1535,a)].
% 22.17/22.37 3423 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(1547,b,1536,a)].
% 22.17/22.37 3424 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(1595,b,1581,a)].
% 22.17/22.37 3425 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1582,a)].
% 22.17/22.37 3426 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1595,b,1583,a)].
% 22.17/22.37 3427 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1595,b,1584,a)].
% 22.17/22.37 3428 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1595,b,1585,a)].
% 22.17/22.37 3429 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1595,b,1586,a)].
% 22.17/22.37 3430 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1595,b,1587,a)].
% 22.17/22.37 3431 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1595,b,1588,a)].
% 22.17/22.37 3432 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1595,b,1589,a)].
% 22.26/22.43 3433 -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1595,b,1590,a)].
% 22.26/22.43 3434 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(1595,b,1591,a)].
% 22.26/22.43 3435 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1614,a,1595,b)].
% 22.26/22.43 3436 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1615,a,1595,b)].
% 22.26/22.43 3437 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1637,a)].
% 22.26/22.43 3438 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1638,a)].
% 22.26/22.43 3439 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1660,b,1639,a)].
% 22.26/22.43 3440 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1640,a)].
% 22.26/22.43 3441 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1641,a)].
% 22.26/22.43 3442 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1660,b,1642,a)].
% 22.26/22.43 3443 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1660,b,1643,a)].
% 22.26/22.43 3444 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1660,b,1644,a)].
% 22.26/22.43 3445 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1660,b,1645,a)].
% 22.26/22.43 3446 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1660,b,1646,a)].
% 22.26/22.43 3447 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1647,a)].
% 22.26/22.43 3448 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1660,b,1648,a)].
% 22.26/22.43 3449 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1660,b,1649,a)].
% 22.26/22.43 3450 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1660,b,1650,a)].
% 22.26/22.43 3451 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1660,b,1651,a)].
% 22.26/22.43 3452 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1660,b,1652,a)].
% 22.26/22.43 3453 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1660,b,1653,a)].
% 22.26/22.43 3454 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1660,b,1654,a)].
% 22.26/22.43 3455 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1660,b,1655,a)].
% 22.26/22.43 3456 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1660,b,1656,a)].
% 22.26/22.43 3457 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1780,a,1763,b)].
% 22.26/22.43 3458 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1797,a,1763,b)].
% 22.26/22.43 3459 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1798,a,1763,b)].
% 22.26/22.44 3460 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1799,a,1763,b)].
% 22.26/22.44 3461 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1800,a,1763,b)].
% 22.26/22.44 3462 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1801,a,1763,b)].
% 22.26/22.44 3463 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1802,a,1763,b)].
% 22.26/22.44 3464 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1803,a,1763,b)].
% 22.26/22.44 3465 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1804,a,1763,b)].
% 22.26/22.44 3466 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1805,a,1763,b)].
% 22.26/22.44 3467 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1806,a,1763,b)].
% 22.26/22.44 3468 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1807,a,1763,b)].
% 22.26/22.44 3469 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1808,d,1763,b)].
% 22.26/22.44 3470 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1809,d,1763,b)].
% 22.26/22.44 3471 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1810,a,1763,b)].
% 22.26/22.44 3472 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1811,a,1763,b)].
% 22.26/22.44 3473 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1812,a,1763,b)].
% 22.26/22.44 3474 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1813,a,1763,b)].
% 22.26/22.44 3475 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1814,a,1763,b)].
% 22.26/22.44 3476 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1815,a,1763,b)].
% 22.26/22.44 3477 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1816,a,1763,b)].
% 22.26/22.44 3478 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1817,a,1763,b)].
% 22.26/22.44 3479 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1818,a,1763,b)].
% 22.26/22.44 3480 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1819,a,1763,b)].
% 22.26/22.44 3481 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1820,a,1763,b)].
% 22.26/22.44 3482 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1821,a,1763,b)].
% 22.26/22.44 3483 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1822,a,1763,b)].
% 22.26/22.44 3484 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1823,a,1763,b)].
% 22.26/22.44 3485 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1824,a,1763,b)].
% 22.56/22.76 3486 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1825,a,1763,b)].
% 22.56/22.76 3487 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1826,a,1763,b)].
% 22.56/22.76 3488 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1827,a,1763,b)].
% 22.56/22.76 3489 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1828,a,1763,b)].
% 22.56/22.76 3490 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1829,a,1763,b)].
% 22.56/22.76 3491 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1844,b,1833,b)].
% 22.56/22.76 3492 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1899,d,1833,b)].
% 22.56/22.76 3493 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 22.56/22.76 3494 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 22.56/22.76 3495 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom). [assumption].
% 22.56/22.76 3496 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 22.56/22.76 3497 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom). [assumption].
% 22.56/22.76 3498 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_2) # label(axiom). [assumption].
% 22.56/22.76 3499 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 22.56/22.76 3500 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom). [assumption].
% 22.56/22.76 3501 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 22.56/22.76 3502 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom). [assumption].
% 22.56/22.76 3503 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_43) # label(axiom). [assumption].
% 22.56/22.76 3504 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_48) # label(axiom). [assumption].
% 22.56/22.76 3505 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(26,b,1,a)].
% 22.56/22.76 3506 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(26,b,3,a)].
% 22.56/22.76 3507 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(81,b,64,b)].
% 22.56/22.76 3508 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(82,b,64,b)].
% 22.56/22.76 3509 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(147,b,131,b)].
% 22.56/22.76 3510 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(147,b,133,b)].
% 22.65/22.80 3511 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(165,a,147,b)].
% 22.65/22.80 3512 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(166,a,147,b)].
% 22.65/22.80 3513 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(171,a,147,b)].
% 22.65/22.80 3514 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(172,a,147,b)].
% 22.65/22.80 3515 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(240,a,221,b)].
% 22.65/22.80 3516 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(241,a,221,b)].
% 22.65/22.80 3517 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(247,b,221,b)].
% 22.65/22.80 3518 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(248,b,221,b)].
% 22.65/22.80 3519 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(301,b,288,a)].
% 22.65/22.80 3520 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(301,b,290,a)].
% 22.65/22.80 3521 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(322,a,301,b)].
% 22.65/22.80 3522 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(323,a,301,b)].
% 22.65/22.80 3523 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(343,b,331,b)].
% 22.65/22.80 3524 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(343,b,333,b)].
% 22.65/22.80 3525 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(343,b,334,a)].
% 22.65/22.80 3526 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,335,a)].
% 22.65/22.80 3527 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(343,b,336,a)].
% 22.65/22.80 3528 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,a,343,b)].
% 22.65/22.80 3529 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(355,a,343,b)].
% 22.65/22.80 3530 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(362,b,343,b)].
% 22.65/22.80 3531 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(363,b,343,b)].
% 22.65/22.80 3532 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(366,b,343,b)].
% 22.65/22.80 3533 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(367,b,343,b)].
% 22.65/22.80 3534 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(370,b,343,b)].
% 22.65/22.80 3535 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(371,b,343,b)].
% 22.65/22.80 3536 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(372,b,343,b)].
% 22.65/22.80 3537 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(373,b,343,b)].
% 22.65/22.80 3538 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(374,a,343,b)].
% 22.65/22.80 3539 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(375,a,343,b)].
% 22.65/22.80 3540 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(376,c,343,b)].
% 22.65/22.80 3541 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(377,c,343,b)].
% 22.65/22.80 3542 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(809,a,734,a)].
% 22.65/22.80 3543 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(809,a,741,a)].
% 22.77/22.91 3544 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1086,b,1076,a)].
% 22.77/22.91 3545 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1109,b,1099,a)].
% 22.77/22.91 3546 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint). [resolve(1324,a,1277,a)].
% 22.77/22.91 3547 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1324,a,1303,b)].
% 22.77/22.91 3548 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1324,a,1304,b)].
% 22.77/22.91 3549 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(1463,b,1434,a)].
% 22.77/22.91 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3549,a,3494,a)].
% 22.77/22.91 3550 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(1463,b,1435,a)].
% 22.77/22.91 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3550,a,3494,a)].
% 22.77/22.91 3551 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(1463,b,1436,a)].
% 22.77/22.91 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3551,a,3494,a)].
% 22.77/22.91 3552 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(1463,b,1437,a)].
% 22.77/22.91 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3552,a,3494,a)].
% 22.77/22.91 3553 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(1463,b,1438,a)].
% 22.77/22.91 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3553,a,3494,a)].
% 22.77/22.91 3554 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(1463,b,1439,a)].
% 22.77/22.91 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3554,a,3494,a)].
% 22.77/22.91 3555 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1440,a)].
% 22.77/22.91 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3555,a,3494,a)].
% 22.77/22.91 3556 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(1463,b,1441,a)].
% 22.77/22.91 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3556,a,3494,a)].
% 22.77/22.91 3557 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(1463,b,1442,a)].
% 22.77/22.91 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3557,a,3494,a)].
% 22.77/22.91 3558 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(1463,b,1443,a)].
% 22.77/22.91 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3558,a,3494,a)].
% 22.77/22.91 3559 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(1463,b,1444,a)].
% 22.77/22.91 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3559,a,3494,a)].
% 22.77/22.91 3560 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(1463,b,1445,a)].
% 22.77/22.91 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3560,a,3494,a)].
% 22.77/22.91 3561 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(1463,b,1446,a)].
% 22.77/22.91 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3561,a,3494,a)].
% 22.77/22.91 3562 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(1463,b,1447,a)].
% 22.77/22.91 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3562,a,3494,a)].
% 22.77/22.91 3563 -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(1463,b,1448,a)].
% 22.77/22.91 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3563,a,3494,a)].
% 22.77/22.91 3564 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1463,b,1450,a)].
% 22.77/22.94 3565 c_lessequals(c_HOL_Oabs(c_plus(A,B,C),C),c_plus(c_HOL_Oabs(A,C),c_HOL_Oabs(B,C),C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1466,a,1463,b)].
% 22.77/22.94 Derived: c_lessequals(c_HOL_Oabs(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint),c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3565,b,3494,a)].
% 22.77/22.94 3566 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(1497,b,1477,a)].
% 22.77/22.94 3567 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1497,b,1478,a)].
% 22.77/22.94 3568 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(1497,b,1479,a)].
% 22.77/22.94 3569 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1497,b,1480,a)].
% 22.77/22.94 3570 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(1497,b,1481,a)].
% 22.77/22.94 3571 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(1497,b,1482,a)].
% 22.77/22.94 3572 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(1497,b,1483,a)].
% 22.77/22.94 3573 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(1497,b,1484,a)].
% 22.77/22.94 3574 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(1549,b,1515,a)].
% 22.77/22.94 3575 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(1549,b,1516,a)].
% 22.77/22.94 3576 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1517,a)].
% 22.77/22.94 3577 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1518,a)].
% 22.77/22.94 3578 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(1549,b,1519,a)].
% 22.77/22.94 3579 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(1549,b,1520,a)].
% 22.77/22.94 3580 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(1549,b,1521,a)].
% 22.77/22.94 3581 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(1549,b,1522,a)].
% 22.77/22.94 3582 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(1549,b,1523,a)].
% 22.77/22.94 3583 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(1549,b,1524,a)].
% 22.77/22.94 3584 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(1549,b,1525,a)].
% 22.77/22.94 3585 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(1549,b,1526,a)].
% 22.77/22.94 3586 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(1549,b,1527,a)].
% 22.77/22.94 3587 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(1549,b,1528,a)].
% 22.77/22.94 3588 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(1549,b,1529,a)].
% 22.77/22.94 3589 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(1549,b,1530,a)].
% 22.77/22.94 3590 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(1549,b,1531,a)].
% 22.77/22.94 3591 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(1549,b,1532,a)].
% 22.77/22.94 3592 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(1549,b,1533,a)].
% 22.77/22.94 3593 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(1549,b,1534,a)].
% 22.77/22.98 3594 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1576,c,1549,b)].
% 22.77/22.98 3595 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1577,c,1549,b)].
% 22.77/22.98 3596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1578,b,1549,b)].
% 22.77/22.98 3597 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1579,b,1549,b)].
% 22.77/22.98 3598 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(1602,b,1581,a)].
% 22.77/22.98 3599 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1582,a)].
% 22.77/22.98 3600 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1602,b,1583,a)].
% 22.77/22.98 3601 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1602,b,1584,a)].
% 22.77/22.98 3602 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1602,b,1585,a)].
% 22.77/22.98 3603 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1602,b,1586,a)].
% 22.77/22.98 3604 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1602,b,1587,a)].
% 22.77/22.98 3605 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1602,b,1588,a)].
% 22.77/22.98 3606 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1602,b,1589,a)].
% 22.77/22.98 3607 -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1602,b,1590,a)].
% 22.77/22.98 3608 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(1602,b,1591,a)].
% 22.77/22.98 3609 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1614,a,1602,b)].
% 22.77/22.98 3610 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1615,a,1602,b)].
% 22.77/22.98 3611 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1637,a)].
% 22.77/22.98 3612 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1638,a)].
% 22.77/22.98 3613 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1667,b,1639,a)].
% 22.77/22.98 3614 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1640,a)].
% 22.77/22.98 3615 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1641,a)].
% 22.77/22.98 3616 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1667,b,1642,a)].
% 22.77/22.98 3617 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1667,b,1643,a)].
% 22.77/22.98 3618 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1667,b,1644,a)].
% 22.77/22.98 3619 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1667,b,1645,a)].
% 22.77/22.98 3620 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1667,b,1646,a)].
% 22.77/22.98 3621 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1647,a)].
% 22.85/23.04 3622 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1667,b,1648,a)].
% 22.85/23.04 3623 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1667,b,1649,a)].
% 22.85/23.04 3624 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1667,b,1650,a)].
% 22.85/23.04 3625 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1667,b,1651,a)].
% 22.85/23.04 3626 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1667,b,1652,a)].
% 22.85/23.04 3627 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1667,b,1653,a)].
% 22.85/23.04 3628 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1667,b,1654,a)].
% 22.85/23.04 3629 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1667,b,1655,a)].
% 22.85/23.04 3630 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1667,b,1656,a)].
% 22.85/23.04 3631 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1780,a,1769,b)].
% 22.85/23.04 3632 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1844,b,1838,b)].
% 22.85/23.04 3633 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2077,a,2062,b)].
% 22.85/23.04 3634 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2094,a,2062,b)].
% 22.85/23.04 3635 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2095,a,2062,b)].
% 22.85/23.04 3636 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2096,a,2062,b)].
% 22.85/23.04 3637 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,a,2062,b)].
% 22.85/23.04 3638 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2098,a,2062,b)].
% 22.85/23.04 3639 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2099,a,2062,b)].
% 22.85/23.04 3640 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2100,a,2062,b)].
% 22.85/23.04 3641 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2101,a,2062,b)].
% 22.85/23.04 3642 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,a,2062,b)].
% 22.85/23.04 3643 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2103,a,2062,b)].
% 22.85/23.04 3644 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2104,a,2062,b)].
% 22.85/23.04 3645 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2062,b)].
% 22.85/23.04 3646 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,d,2062,b)].
% 22.85/23.04 3647 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2107,a,2062,b)].
% 22.85/23.04 3648 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2108,a,2062,b)].
% 22.85/23.05 3649 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2109,a,2062,b)].
% 22.85/23.05 3650 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,a,2062,b)].
% 22.85/23.05 3651 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,a,2062,b)].
% 22.85/23.05 3652 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2112,a,2062,b)].
% 22.85/23.05 3653 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2113,a,2062,b)].
% 22.85/23.05 3654 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2114,a,2062,b)].
% 22.85/23.05 3655 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,a,2062,b)].
% 22.85/23.05 3656 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,a,2062,b)].
% 22.85/23.05 3657 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2117,a,2062,b)].
% 22.85/23.05 3658 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2118,a,2062,b)].
% 22.85/23.05 3659 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2119,a,2062,b)].
% 22.85/23.05 3660 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2120,a,2062,b)].
% 22.85/23.05 3661 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2121,a,2062,b)].
% 22.85/23.05 3662 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2122,a,2062,b)].
% 22.85/23.05 3663 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2123,a,2062,b)].
% 22.85/23.05 3664 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2124,a,2062,b)].
% 22.85/23.05 3665 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2125,a,2062,b)].
% 22.85/23.05 3666 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2126,a,2062,b)].
% 22.85/23.05 3667 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2127,d,2062,b)].
% 22.85/23.05 3668 -c_lessequals(A,B,C) | -c_lessequals(c_0,D,C) | c_lessequals(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2201,d,2131,b)].
% 22.85/23.05 3669 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2202,b,2131,b)].
% 22.85/23.05 3670 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2203,b,2131,b)].
% 22.85/23.05 3671 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2204,b,2131,b)].
% 22.85/23.05 3672 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2205,b,2131,b)].
% 22.85/23.05 3673 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2206,b,2131,b)].
% 22.85/23.05 3674 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2207,b,2131,b)].
% 22.85/23.05 3675 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2208,b,2131,b)].
% 22.85/23.05 3676 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2209,c,2131,b)].
% 22.85/23.05 3677 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2210,b,2131,b)].
% 22.85/23.08 3678 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2211,c,2131,b)].
% 22.85/23.08 3679 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2212,c,2131,b)].
% 22.85/23.08 3680 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2213,c,2131,b)].
% 22.85/23.08 3681 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2214,c,2131,b)].
% 22.85/23.08 3682 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2215,c,2131,b)].
% 22.85/23.08 3683 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2216,c,2131,b)].
% 22.85/23.08 3684 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2217,b,2131,b)].
% 22.85/23.08 3685 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2218,b,2131,b)].
% 22.85/23.08 3686 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2219,d,2131,b)].
% 22.85/23.08 3687 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2220,d,2131,b)].
% 22.85/23.08 3688 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2221,c,2131,b)].
% 22.85/23.08 3689 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2222,c,2131,b)].
% 22.85/23.08 3690 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2223,d,2131,b)].
% 22.85/23.08 3691 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2224,c,2131,b)].
% 22.85/23.08 3692 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2225,c,2131,b)].
% 22.85/23.08 3693 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2226,d,2131,b)].
% 22.85/23.08 3694 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2227,c,2131,b)].
% 22.85/23.08 3695 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2228,c,2131,b)].
% 22.85/23.08 3696 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2229,c,2131,b)].
% 22.85/23.08 3697 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2230,c,2131,b)].
% 22.85/23.08 3698 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2231,c,2131,b)].
% 22.85/23.08 3699 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2232,c,2131,b)].
% 22.85/23.08 3700 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2233,d,2131,b)].
% 22.85/23.08 3701 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2234,c,2131,b)].
% 22.85/23.08 3702 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2235,c,2131,b)].
% 22.85/23.08 3703 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2236,d,2131,b)].
% 22.85/23.08 3704 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2237,c,2131,b)].
% 22.99/23.19 3705 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2238,c,2131,b)].
% 22.99/23.19 3706 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,c,2131,b)].
% 22.99/23.19 3707 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,c,2131,b)].
% 22.99/23.19 3708 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_plus(D,A,C),c_plus(E,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2241,d,2131,b)].
% 22.99/23.19 3709 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3139,a,3108,b)].
% 22.99/23.19 3710 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3140,a,3108,b)].
% 22.99/23.19 3711 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3141,a,3108,b)].
% 22.99/23.19 3712 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(3142,a,3108,b)].
% 22.99/23.19 3713 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3143,a,3108,b)].
% 22.99/23.19 3714 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3144,b,3108,b)].
% 22.99/23.19 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3714,b,3503,b)].
% 22.99/23.19 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3714,b,3504,b)].
% 22.99/23.19 3715 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3145,b,3108,b)].
% 22.99/23.19 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(3715,b,3494,a)].
% 22.99/23.19 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3715,b,3503,b)].
% 22.99/23.19 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3715,b,3504,b)].
% 22.99/23.19 3716 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3152,b,3108,b)].
% 22.99/23.19 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3716,b,3494,a)].
% 22.99/23.19 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3716,b,3503,b)].
% 22.99/23.19 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3716,b,3504,b)].
% 22.99/23.19 3717 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(3153,b,3108,b)].
% 22.99/23.19 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3717,b,3494,a)].
% 22.99/23.19 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3717,b,3503,b)].
% 22.99/23.19 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3717,b,3504,b)].
% 22.99/23.19 3718 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3161,a,3108,b)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(3718,c,3494,a)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3718,c,3503,b)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3718,c,3504,b)].
% 22.99/23.19 3719 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3162,a,3108,b)].
% 22.99/23.19 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3719,c,3494,a)].
% 22.99/23.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3719,c,3503,b)].
% 22.99/23.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3719,c,3504,b)].
% 22.99/23.19 3720 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3163,a,3108,b)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3720,c,3494,a)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3720,c,3503,b)].
% 22.99/23.19 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3720,c,3504,b)].
% 22.99/23.19 3721 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3164,a,3108,b)].
% 22.99/23.19 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3721,c,3494,a)].
% 22.99/23.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3721,c,3503,b)].
% 22.99/23.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3721,c,3504,b)].
% 22.99/23.19 3722 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3165,a,3108,b)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(3722,c,3494,a)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3722,c,3503,b)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3722,c,3504,b)].
% 22.99/23.19 3723 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3166,a,3108,b)].
% 22.99/23.19 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3723,c,3494,a)].
% 22.99/23.19 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3723,c,3503,b)].
% 22.99/23.19 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3723,c,3504,b)].
% 22.99/23.19 3724 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3167,a,3108,b)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3724,c,3494,a)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3724,c,3503,b)].
% 22.99/23.19 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3724,c,3504,b)].
% 22.99/23.19 3725 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3168,a,3108,b)].
% 22.99/23.19 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3725,c,3494,a)].
% 22.99/23.19 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3725,c,3503,b)].
% 22.99/23.19 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3725,c,3504,b)].
% 22.99/23.19 3726 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3203,a,3108,b)].
% 22.99/23.19 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3726,b,3494,a)].
% 22.99/23.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3726,b,3503,b)].
% 22.99/23.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3726,b,3504,b)].
% 22.99/23.19 3727 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3204,a,3108,b)].
% 22.99/23.19 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(3727,b,3494,a)].
% 22.99/23.20 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3727,b,3503,b)].
% 22.99/23.20 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3727,b,3504,b)].
% 22.99/23.20 3728 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3205,e,3108,b)].
% 22.99/23.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3728,e,3494,a)].
% 22.99/23.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3728,e,3503,b)].
% 22.99/23.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,C,A) | c_lessequals(c_0,c_plus(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3728,e,3504,b)].
% 22.99/23.20 3729 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3241,b,3108,b)].
% 22.99/23.20 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3729,b,3494,a)].
% 22.99/23.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3729,b,3503,b)].
% 22.99/23.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3729,b,3504,b)].
% 22.99/23.20 3730 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3242,b,3108,b)].
% 22.99/23.20 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(3730,b,3494,a)].
% 22.99/23.20 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3730,b,3503,b)].
% 22.99/23.20 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3504,b)].
% 22.99/23.20 3731 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3243,b,3108,b)].
% 22.99/23.20 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(3731,b,3494,a)].
% 22.99/23.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3731,b,3503,b)].
% 22.99/23.20 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3731,b,3504,b)].
% 22.99/23.20 3732 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3244,b,3108,b)].
% 22.99/23.20 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(3732,b,3494,a)].
% 22.99/23.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3732,b,3503,b)].
% 22.99/23.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3732,b,3504,b)].
% 22.99/23.20 3733 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(3245,b,3108,b)].
% 22.99/23.20 Derived: c_times(A,c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,B,tc_IntDef_Oint),c_times(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3733,b,3494,a)].
% 22.99/23.20 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3733,b,3503,b)].
% 22.99/23.20 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3733,b,3504,b)].
% 22.99/23.20 3734 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(3246,b,3108,b)].
% 22.99/23.20 Derived: c_times(c_plus(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) = c_plus(c_times(A,C,tc_IntDef_Oint),c_times(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3734,b,3494,a)].
% 22.99/23.20 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3734,b,3503,b)].
% 22.99/23.20 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3734,b,3504,b)].
% 22.99/23.20 3735 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3299,a,3255,b)].
% 23.69/23.82 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3735,b,3494,a)].
% 23.69/23.82 3736 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) # label(axiom). [assumption].
% 23.69/23.82 3737 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom). [assumption].
% 23.69/23.82 3738 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) # label(axiom). [assumption].
% 23.69/23.82 3739 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Ofield_32) # label(axiom). [assumption].
% 23.69/23.82 3740 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oidom_30) # label(axiom). [assumption].
% 23.69/23.82 3741 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__field_31) # label(axiom). [assumption].
% 23.69/23.82 3742 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__idom_56) # label(axiom). [assumption].
% 23.69/23.82 3743 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint). [resolve(1329,a,1277,a)].
% 23.69/23.82 3744 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1329,a,1303,b)].
% 23.69/23.82 3745 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1329,a,1304,b)].
% 23.69/23.82 3746 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 23.69/23.82 3747 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 23.69/23.82 3748 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 23.69/23.82 Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A). [resolve(3746,a,3748,b)].
% 23.69/23.82 3749 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 23.69/23.82 3750 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 23.69/23.82 3751 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom). [assumption].
% 23.69/23.82 3752 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 23.69/23.82 3753 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom). [assumption].
% 23.69/23.82 3754 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 23.69/23.82 3755 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom). [assumption].
% 23.69/23.82 3756 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 23.69/23.82 3757 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom). [assumption].
% 23.69/23.82 3758 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 23.69/23.82 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3758,a,3748,b)].
% 23.69/23.82 3759 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 23.69/23.82 3760 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 23.69/23.82 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A). [resolve(3760,b,3746,a)].
% 23.69/23.84 3761 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(25,b,1,a)].
% 23.69/23.84 3762 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(25,b,3,a)].
% 23.69/23.84 3763 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(81,b,63,b)].
% 23.69/23.84 3764 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(82,b,63,b)].
% 23.69/23.84 3765 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(124,b,108,a)].
% 23.69/23.84 3766 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(124,b,111,a)].
% 23.69/23.84 3767 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(146,b,131,b)].
% 23.69/23.84 3768 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(146,b,133,b)].
% 23.69/23.84 3769 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(165,a,146,b)].
% 23.69/23.84 3770 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(166,a,146,b)].
% 23.69/23.84 3771 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(171,a,146,b)].
% 23.69/23.84 3772 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(172,a,146,b)].
% 23.69/23.84 3773 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(201,b,190,b)].
% 23.69/23.84 3774 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(202,b,190,b)].
% 23.69/23.84 3775 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(240,a,220,b)].
% 23.69/23.84 3776 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(241,a,220,b)].
% 23.69/23.84 3777 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(247,b,220,b)].
% 23.69/23.84 3778 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(248,b,220,b)].
% 23.69/23.84 3779 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(300,b,288,a)].
% 23.69/23.84 3780 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(300,b,290,a)].
% 23.69/23.84 3781 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(322,a,300,b)].
% 23.69/23.84 3782 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(323,a,300,b)].
% 23.69/23.84 3783 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A). [resolve(342,b,331,b)].
% 23.69/23.84 3784 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A). [resolve(342,b,333,b)].
% 23.69/23.84 3785 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A). [resolve(342,b,334,a)].
% 23.69/23.84 3786 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,335,a)].
% 23.69/23.84 3787 -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A). [resolve(342,b,336,a)].
% 23.69/23.84 3788 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,a,342,b)].
% 23.69/23.84 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3788,b,3748,b)].
% 23.69/23.84 3789 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A). [resolve(355,a,342,b)].
% 23.69/23.84 Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3789,b,3748,b)].
% 23.69/23.84 3790 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(366,b,342,b)].
% 23.69/23.84 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3790,b,3748,b)].
% 23.69/23.86 3791 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(367,b,342,b)].
% 23.69/23.86 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3748,b)].
% 23.69/23.86 3792 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(370,b,342,b)].
% 23.69/23.86 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3792,b,3748,b)].
% 23.69/23.86 3793 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(371,b,342,b)].
% 23.69/23.86 3794 c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Oidom(D). [resolve(372,b,342,b)].
% 23.69/23.86 Derived: c_times(A,c_plus(B,C,D),D) = c_plus(c_times(A,B,D),c_times(A,C,D),D) | -class_Ring__and__Field_Ofield(D). [resolve(3794,b,3748,b)].
% 23.69/23.86 3795 c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(373,b,342,b)].
% 23.69/23.86 Derived: c_times(c_plus(A,B,C),D,C) = c_plus(c_times(A,D,C),c_times(B,D,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3795,b,3748,b)].
% 23.69/23.86 3796 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(374,a,342,b)].
% 23.69/23.86 3797 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(375,a,342,b)].
% 23.69/23.86 3798 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(376,c,342,b)].
% 23.69/23.86 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3798,c,3748,b)].
% 23.69/23.86 3799 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(377,c,342,b)].
% 23.69/23.86 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3799,c,3748,b)].
% 23.69/23.86 3800 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(479,b,435,b)].
% 23.69/23.86 3801 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(480,b,435,b)].
% 23.69/23.86 3802 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(517,a,511,b)].
% 23.69/23.86 3803 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(524,a,511,b)].
% 23.69/23.86 3804 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(525,a,511,b)].
% 23.69/23.86 3805 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(571,b,549,b)].
% 23.69/23.86 3806 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(572,b,549,b)].
% 23.69/23.86 3807 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(654,a,618,b)].
% 23.69/23.86 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3807,c,3748,b)].
% 23.69/23.86 3808 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(655,a,618,b)].
% 23.69/23.86 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3808,c,3748,b)].
% 23.69/23.86 3809 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(656,a,618,b)].
% 23.69/23.86 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3809,b,3748,b)].
% 23.69/23.86 3810 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(657,a,618,b)].
% 23.69/23.86 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3810,b,3748,b)].
% 23.69/23.86 3811 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(658,a,618,b)].
% 23.69/23.86 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3811,b,3748,b)].
% 23.69/23.86 3812 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A). [resolve(659,b,618,b)].
% 23.69/23.86 Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A). [resolve(3812,b,3748,b)].
% 25.70/25.82 3813 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(660,b,618,b)].
% 25.70/25.82 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3813,b,3748,b)].
% 25.70/25.82 3814 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(661,b,618,b)].
% 25.70/25.82 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3814,b,3748,b)].
% 25.70/25.82 3815 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(663,b,618,b)].
% 25.70/25.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3815,b,3748,b)].
% 25.70/25.82 3816 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(664,b,618,b)].
% 25.70/25.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3816,b,3748,b)].
% 25.70/25.82 3817 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(666,b,618,b)].
% 25.70/25.82 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(3817,b,3748,b)].
% 25.70/25.82 3818 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(667,b,618,b)].
% 25.70/25.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(3818,b,3748,b)].
% 25.70/25.82 3819 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(694,b,668,a)].
% 25.70/25.82 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3819,a,3748,b)].
% 25.70/25.82 3820 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(694,b,670,a)].
% 25.70/25.82 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3820,a,3748,b)].
% 25.70/25.82 3821 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(694,b,671,a)].
% 25.70/25.82 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3821,a,3748,b)].
% 25.70/25.82 3822 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(694,b,672,a)].
% 25.70/25.82 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3822,a,3748,b)].
% 25.70/25.82 3823 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(694,b,673,a)].
% 25.70/25.82 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3823,a,3748,b)].
% 25.70/25.82 3824 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(694,b,674,a)].
% 25.70/25.82 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Ofield(B). [resolve(3824,a,3748,b)].
% 25.70/25.82 3825 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(694,b,675,a)].
% 25.70/25.82 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3825,a,3748,b)].
% 25.70/25.82 3826 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(694,b,676,a)].
% 25.70/25.82 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3826,a,3748,b)].
% 25.70/25.82 3827 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(694,b,677,a)].
% 25.70/25.82 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3827,a,3748,b)].
% 25.70/25.82 3828 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(694,b,678,a)].
% 25.70/25.82 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3828,a,3748,b)].
% 25.70/25.82 3829 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(826,a,734,a)].
% 25.70/25.82 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3829,a,3748,b)].
% 25.70/25.82 3830 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(903,b,832,a)].
% 25.70/25.82 3831 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 25.70/25.82 3832 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(903,b,833,a)].
% 25.70/25.82 3833 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(903,b,834,a)].
% 25.70/25.82 3834 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(903,b,835,a)].
% 25.70/25.82 3835 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,836,a)].
% 25.70/25.82 3836 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,837,a)].
% 25.70/25.82 3837 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(903,b,838,a)].
% 25.70/25.82 3838 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,839,a)].
% 25.70/25.82 3839 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(903,b,840,a)].
% 25.70/25.82 3840 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,841,a)].
% 25.70/25.82 3841 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(903,b,842,a)].
% 25.70/25.82 3842 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,843,a)].
% 25.70/25.82 3843 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,844,a)].
% 25.70/25.82 3844 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(903,b,845,a)].
% 25.70/25.82 3845 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,846,a)].
% 25.70/25.82 3846 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(903,b,847,a)].
% 25.70/25.82 3847 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(903,b,848,a)].
% 25.70/25.82 3848 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(903,b,849,a)].
% 25.70/25.82 3849 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(903,b,850,a)].
% 25.70/25.82 3850 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(903,b,851,a)].
% 25.70/25.83 3851 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(903,b,852,a)].
% 25.70/25.83 3852 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(903,b,853,a)].
% 25.70/25.83 3853 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(903,b,854,a)].
% 25.70/25.83 3854 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(903,b,855,b)].
% 25.70/25.83 3855 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(903,b,856,b)].
% 25.70/25.83 3856 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(903,b,857,a)].
% 25.70/25.83 3857 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(903,b,858,a)].
% 25.70/25.83 3858 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(903,b,859,a)].
% 25.70/25.83 3859 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(903,b,860,a)].
% 25.70/25.83 3860 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(903,b,861,a)].
% 25.70/25.83 3861 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(903,b,862,a)].
% 25.70/25.83 3862 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(903,b,863,a)].
% 25.70/25.83 3863 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(903,b,864,a)].
% 25.70/25.83 3864 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(903,b,865,a)].
% 25.70/25.83 3865 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(903,b,866,a)].
% 25.70/25.83 3866 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(903,b,867,a)].
% 25.70/25.83 3867 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(903,b,868,a)].
% 25.70/25.83 3868 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(903,b,869,a)].
% 25.70/25.83 3869 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(903,b,870,a)].
% 25.70/25.83 3870 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(903,b,871,a)].
% 25.70/25.83 3871 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(903,b,872,a)].
% 25.70/25.83 3872 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(903,b,873,a)].
% 25.70/25.83 3873 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(903,b,874,a)].
% 25.70/25.83 3874 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(903,b,875,a)].
% 25.70/25.83 3875 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(903,b,876,a)].
% 25.70/25.83 3876 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(903,b,877,a)].
% 25.70/25.83 3877 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(903,b,878,a)].
% 25.79/25.92 3878 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(903,b,879,a)].
% 25.79/25.92 3879 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(903,b,880,a)].
% 25.79/25.92 3880 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(903,b,881,a)].
% 25.79/25.92 3881 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(903,b,882,a)].
% 25.79/25.92 3882 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(903,b,883,a)].
% 25.79/25.92 3883 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(903,b,884,a)].
% 25.79/25.92 3884 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(903,b,885,a)].
% 25.79/25.92 3885 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(903,b,886,a)].
% 25.79/25.92 3886 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(903,b,887,a)].
% 25.79/25.92 3887 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(903,b,888,a)].
% 25.79/25.92 3888 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(903,b,889,a)].
% 25.79/25.92 3889 c_lessequals(A,c_Orderings_Omax(A,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(904,a,903,b)].
% 25.79/25.92 3890 c_lessequals(A,c_Orderings_Omax(B,A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(905,a,903,b)].
% 25.79/25.92 3891 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(1093,b,1076,a)].
% 25.79/25.92 3892 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(1116,b,1099,a)].
% 25.79/25.92 3893 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(1613,b,1581,a)].
% 25.79/25.92 3894 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1582,a)].
% 25.79/25.92 3895 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(1613,b,1583,a)].
% 25.79/25.92 3896 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(1613,b,1584,a)].
% 25.79/25.92 3897 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(1613,b,1585,a)].
% 25.79/25.92 3898 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(1613,b,1586,a)].
% 25.79/25.92 3899 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(1613,b,1587,a)].
% 25.79/25.92 3900 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(1613,b,1588,a)].
% 25.79/25.92 3901 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(1613,b,1589,a)].
% 25.79/25.92 3902 -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(1613,b,1590,a)].
% 27.78/27.90 3903 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(1613,b,1591,a)].
% 27.78/27.90 3904 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_lessequals(D,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1614,a,1613,b)].
% 27.78/27.90 3905 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1615,a,1613,b)].
% 27.78/27.90 3906 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1637,a)].
% 27.78/27.90 3907 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1638,a)].
% 27.78/27.90 3908 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1678,b,1639,a)].
% 27.78/27.90 3909 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1640,a)].
% 27.78/27.90 3910 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1641,a)].
% 27.78/27.90 3911 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1678,b,1642,a)].
% 27.78/27.90 3912 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1678,b,1643,a)].
% 27.78/27.90 3913 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1678,b,1644,a)].
% 27.78/27.90 3914 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1678,b,1645,a)].
% 27.78/27.90 3915 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1678,b,1646,a)].
% 27.78/27.90 3916 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1647,a)].
% 27.78/27.90 3917 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1678,b,1648,a)].
% 27.78/27.90 3918 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1678,b,1649,a)].
% 27.78/27.90 3919 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1678,b,1650,a)].
% 27.78/27.90 3920 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1678,b,1651,a)].
% 27.78/27.90 3921 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1678,b,1652,a)].
% 27.78/27.90 3922 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1678,b,1653,a)].
% 27.78/27.90 3923 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1678,b,1654,a)].
% 27.78/27.90 3924 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1678,b,1655,a)].
% 27.78/27.90 3925 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1678,b,1656,a)].
% 27.78/27.90
% 27.78/27.90 ============================== end predicate elimination =============
% 27.78/27.90
% 27.78/27.90 Auto_denials: (non-Horn, no changes).
% 27.78/27.90
% 27.78/27.90 Term ordering decisions:
% 27.78/27.90 Function symbol KB weights: tc_IntDef_Oint=1. tc_nat=1. c_0=1. c_emptyset=1. c_1=1. c_Finite__Set_OFinites=1. c_List_Olist_ONil=1. c_IntDef_ONats=1. c_Numeral_OPls=1. c_Numeral_Obit_OB1=1. c_Numeral_Obit_OB0=1. c_UNIV=1. c_Numeral_OMin=1. tc_List_Onibble=1. c_Relation_OId=1. c_IntDef_OInts=1. 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. c_Numeral_Onumber__of=1. c_uminus=1. tc_fun=1. c_NatArith_Oof__nat=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. c_SetInterval_OlessThan=1. tc_prod=1. c_Finite__Set_OMax=1. c_Finite__Set_OMin=1. c_SetInterval_OgreaterThan=1. c_HOL_Oabs=1. c_Numeral_OBit=1. tc_Datatype__Universe_Onode=1. c_Nat_Osize=1. c_Numeral_Obin__add=1. c_List_Oset=1. c_HOL_Oinverse=1. c_IntDef_Oof__int=1. c_List_Orev=1. c_OrderedGroup_Onprt=1. c_OrderedGroup_Opprt=1. c_Union=1. c_List_Olists=1. c_Transitive__Closure_Ortrancl=1. c_Finite__Set_Ocard=1. c_Inter=1. c_List_Oremdups=1. c_List_Oupt=1. c_List_Olast=1. c_List_Oconcat=1. c_List_Olistrel=1. c_List_Olex=1. c_Pow=1. c_Datatype_Ooption_OSome=1. c_Numeral_Obin__mult=1. c_Relation_Odiag=1. tc_sum=1. c_Binomial_Obinomial=1. c_List_Olexord=1. c_List_Orotate1=1. c_List_Obutlast=1. c_List_Ohd=1. c_List_Otl=1. c_Transitive__Closure_Otrancl=1. c_Datatype_Oo2s=1. c_List_Ochar_OChar=1. c_IntDiv_Oadjust=1. c_List_Olistset=1. c_Main_OIdE__1=1. c_Main_OInter__UNIV__conv__1__1=1. c_Main_OInter__UNIV__conv__2__1=1. c_Main_ONil__eq__concat__conv__1=1. c_Main_OUnion__empty__conv__1=1. c_Main_Oconcat__eq__Nil__conv__1=1. c_Main_Oempty__Union__conv__1=1. c_Main_Ofinite__Union__1=1. c_Datatype_Othe=1. c_Fun_Oid=1. c_List_Olenlex=1. c_Main_Oall__not__in__conv__1=1. c_Main_Olexord__Nil__left__1=1. c_Main_Olexord__Nil__left__2=1. c_Main_Omod__eq__0D__dest__1=1. c_Main_Onot__None__eq__1=1. c_Main_Onot__Some__eq__1=1. c_Main_Ozmod__eq__0D__dest__1=1. c_Set_Ocontents=1. tc_set=1. tc_List_Olist=1. c_Suc=1. c_Numeral_Obin__minus=1. c_IntDef_Oint=1. c_IntDef_Onat=1. c_GCD_Ogcd=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Numeral_Obin__pred=1. c_IntDiv_OnegateSnd=1. c_Numeral_Obin__succ=1. c_IntDef_OAbs__Integ=1. tc_Datatype_Ooption=1. v_f=1. v_g=1. c_IntDef_ORep__Integ=1. v_a=1. v_b=1. v_xa=1. c_times=1. c_plus=1. c_SetInterval_OatLeastLessThan=1. c_minus=1. c_insert=1. c_Orderings_Omax=1. c_divide=1. c_Orderings_Omin=1. c_Nat_Opower=1. c_SetInterval_OatLeastAtMost=1. c_List_Olist_OCons=1. c_SetInterval_OgreaterThanAtMost=1. c_Divides_Oop_Amod=1. c_append=1. c_SetInterval_OgreaterThanLessThan=1. c_div=1. c_inter=1. c_union=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=1. c_Main_OMax__le__iff__1=1. c_Main_OMax__less__iff__1=1. c_Main_OMin__ge__iff__1=1. c_Main_OMin__gr__iff__1=1. c_List_Onth=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_Datatype__Universe_OIn0=1. c_Datatype__Universe_OIn1=1. c_Relation_ODomain=1. c_Relation_Oconverse=1. c_List_Orotate=1. c_Relation_ORange=1. c_fst=1. c_snd=1. c_List_Oremove1=1. c_List_Osublist=1. c_SetsAndFunctions_Oelt__set__plus=1. c_SetsAndFunctions_Oelt__set__times=1. c_Sum__Type_OInl=1. c_Sum__Type_OInr=1. c_List_Olist__inter=1. c_Datatype__Universe_OAtom=1. c_Datatype__Universe_OLeaf=1. c_Datatype__Universe_ONumb=1. c_Equiv__Relations_Oquotient=1. c_List_Oitrev=1. c_Main_OdiagE__1=1. c_Main_OInterI__1=1. c_Main_OInter__iff__1=1. c_Main_OUnionE__1=1. c_Main_OUnion__iff__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Datatype_Ounit_Ounit__case=1. c_Datatype_Ounit_Ounit__rec=1. c_List_Olexn=1. c_List_Oset__Cons=1. c_Main_Osurj__pair__1=1. c_Main_Osurj__pair__2=1. c_Pair=1. c_Relation_OImage=1. c_Datatype__Universe_Ontrunc=1. c_Datatype__Universe_OScons=1. c_List_Ozip=1. c_List_Olist__update=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Datatype__Universe_Odprod=1. c_Datatype__Universe_Ouprod=1. c_Main_OPlusE__1=1. c_Main_OPlusE__2=1. c_Main_OdsumE__1=1. c_Main_OdsumE__2=1. c_Main_OdsumE__3=1. c_Main_OdsumE__4=Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------