TSTP Solution File: SWV362-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV362-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 : Wed Jul 20 21:12:23 EDT 2022
% Result : Timeout 300.03s 299.94s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV362-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 16:39:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.83/2.06 ============================== Prover9 ===============================
% 1.83/2.06 Prover9 (32) version 2009-11A, November 2009.
% 1.83/2.06 Process 2690 was started by sandbox on n010.cluster.edu,
% 1.83/2.06 Wed Jun 15 16:39:55 2022
% 1.83/2.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2537_n010.cluster.edu".
% 1.83/2.06 ============================== end of head ===========================
% 1.83/2.06
% 1.83/2.06 ============================== INPUT =================================
% 1.83/2.06
% 1.83/2.06 % Reading from file /tmp/Prover9_2537_n010.cluster.edu
% 1.83/2.06
% 1.83/2.06 set(prolog_style_variables).
% 1.83/2.06 set(auto2).
% 1.83/2.06 % set(auto2) -> set(auto).
% 1.83/2.06 % set(auto) -> set(auto_inference).
% 1.83/2.06 % set(auto) -> set(auto_setup).
% 1.83/2.06 % set(auto_setup) -> set(predicate_elim).
% 1.83/2.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.83/2.06 % set(auto) -> set(auto_limits).
% 1.83/2.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.83/2.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.83/2.06 % set(auto) -> set(auto_denials).
% 1.83/2.06 % set(auto) -> set(auto_process).
% 1.83/2.06 % set(auto2) -> assign(new_constants, 1).
% 1.83/2.06 % set(auto2) -> assign(fold_denial_max, 3).
% 1.83/2.06 % set(auto2) -> assign(max_weight, "200.000").
% 1.83/2.06 % set(auto2) -> assign(max_hours, 1).
% 1.83/2.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.83/2.06 % set(auto2) -> assign(max_seconds, 0).
% 1.83/2.06 % set(auto2) -> assign(max_minutes, 5).
% 1.83/2.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.83/2.06 % set(auto2) -> set(sort_initial_sos).
% 1.83/2.06 % set(auto2) -> assign(sos_limit, -1).
% 1.83/2.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.83/2.06 % set(auto2) -> assign(max_megs, 400).
% 1.83/2.06 % set(auto2) -> assign(stats, some).
% 1.83/2.06 % set(auto2) -> clear(echo_input).
% 1.83/2.06 % set(auto2) -> set(quiet).
% 1.83/2.06 % set(auto2) -> clear(print_initial_clauses).
% 1.83/2.06 % set(auto2) -> clear(print_given).
% 1.83/2.06 assign(lrs_ticks,-1).
% 1.83/2.06 assign(sos_limit,10000).
% 1.83/2.06 assign(order,kbo).
% 1.83/2.06 set(lex_order_vars).
% 1.83/2.06 clear(print_given).
% 1.83/2.06
% 1.83/2.06 % formulas(sos). % not echoed (2977 formulas)
% 1.83/2.06
% 1.83/2.06 ============================== end of input ==========================
% 1.83/2.06
% 1.83/2.06 % From the command line: assign(max_seconds, 300).
% 1.83/2.06
% 1.83/2.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.83/2.06
% 1.83/2.06 % Formulas that are not ordinary clauses:
% 1.83/2.06
% 1.83/2.06 ============================== end of process non-clausal formulas ===
% 1.83/2.06
% 1.83/2.06 ============================== PROCESS INITIAL CLAUSES ===============
% 1.83/2.06
% 1.83/2.06 ============================== PREDICATE ELIMINATION =================
% 1.83/2.06 1 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 1.83/2.06 2 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 1.83/2.06 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1,a,2,a)].
% 1.83/2.06 3 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 1.83/2.06 Derived: c_lessequals(A,A,tc_nat). [resolve(3,a,2,a)].
% 1.83/2.06 4 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 1.83/2.06 Derived: c_lessequals(A,A,tc_set(B)). [resolve(4,a,2,a)].
% 1.83/2.06 5 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 1.83/2.06 Derived: -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 1.83/2.06 6 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 1.83/2.06 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 1.83/2.06 7 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 1.83/2.06 Derived: -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 1.83/2.06 8 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 1.83/2.06 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 1.83/2.06 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 1.83/2.06 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 1.83/2.08 10 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 1.83/2.08 11 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 1.83/2.08 12 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 1.83/2.08 13 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(13,b,2,a)].
% 1.83/2.08 14 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 1.83/2.08 15 -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].
% 1.83/2.08 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 1.83/2.08 16 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 1.83/2.08 17 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 1.83/2.08 Derived: -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 1.83/2.08 18 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 1.83/2.08 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 1.83/2.08 Derived: class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 1.83/2.08 Derived: class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 1.83/2.08 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 1.83/2.08 19 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 1.91/2.14 20 -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].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 1.91/2.14 21 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(21,b,2,a)].
% 1.91/2.14 22 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 1.91/2.14 23 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 1.91/2.14 24 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 1.91/2.14 25 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 1.91/2.14 26 -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].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 1.91/2.14 27 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 1.91/2.14 28 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(28,b,2,a)].
% 1.91/2.14 29 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 1.91/2.14 30 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 1.91/2.14 31 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 1.91/2.14 32 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 1.91/2.14 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 1.91/2.14 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 1.91/2.14 33 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 1.91/2.14 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(33,a,1,a)].
% 1.91/2.14 Derived: -c_less(A,A,tc_nat). [resolve(33,a,3,a)].
% 1.91/2.14 Derived: -c_less(A,A,tc_set(B)). [resolve(33,a,4,a)].
% 1.91/2.14 Derived: -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(33,a,13,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(33,a,21,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(33,a,28,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 1.93/2.16 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 1.93/2.16 34 -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].
% 1.93/2.16 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(34,a,1,a)].
% 1.93/2.16 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(34,a,3,a)].
% 1.93/2.16 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(34,a,4,a)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(34,a,8,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(34,a,9,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(34,a,10,b)].
% 1.93/2.16 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(34,a,11,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(34,a,12,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(34,a,13,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(34,a,14,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(34,a,15,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(34,a,16,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(34,a,19,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(34,a,20,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(34,a,21,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(34,a,22,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(34,a,23,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(34,a,24,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(34,a,25,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(34,a,26,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(34,a,27,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(34,a,28,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(34,a,29,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(34,a,30,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(34,a,31,b)].
% 1.93/2.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 1.93/2.17 35 -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].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(35,a,1,a)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(35,a,3,a)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(35,a,4,a)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(35,a,9,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(35,a,10,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(35,a,11,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(35,a,12,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(35,a,13,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(35,a,14,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(35,a,15,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(35,a,16,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(35,a,19,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(35,a,20,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(35,a,21,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(35,a,22,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(35,a,23,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(35,a,24,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(35,a,25,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(35,a,26,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(35,a,27,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(35,a,28,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(35,a,29,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(35,a,30,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(35,a,31,b)].
% 1.93/2.17 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 1.93/2.17 36 -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].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(36,a,1,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(36,a,3,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(36,a,4,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(36,a,8,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(36,a,9,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(36,a,10,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(36,a,11,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(36,a,12,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(36,a,13,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(36,a,14,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(36,a,15,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(36,a,16,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(36,a,19,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(36,a,20,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(36,a,21,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(36,a,22,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(36,a,23,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(36,a,24,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(36,a,25,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(36,a,26,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(36,a,27,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(36,a,28,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(36,a,29,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(36,a,30,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(36,a,31,b)].
% 1.93/2.17 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 1.93/2.17 37 -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].
% 1.93/2.18 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(37,a,1,a)].
% 1.93/2.18 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(37,a,3,a)].
% 1.93/2.18 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(37,a,4,a)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(37,a,5,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Olorder(B). [resolve(37,a,6,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(37,a,7,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(37,a,8,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(37,a,9,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(37,a,10,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(37,a,11,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(37,a,12,b)].
% 1.93/2.18 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(37,a,13,b)].
% 1.93/2.18 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__semigroup__add(B). [resolve(37,a,14,b)].
% 1.93/2.18 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__semigroup__add__imp__le(B). [resolve(37,a,15,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(37,a,16,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Orderings_Olinorder(B). [resolve(37,a,17,b)].
% 1.93/2.18 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(37,a,19,b)].
% 1.93/2.18 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(37,a,20,b)].
% 1.93/2.18 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(37,a,21,b)].
% 1.93/2.18 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(37,a,22,b)].
% 1.93/2.18 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__ring__strict(B). [resolve(37,a,23,b)].
% 1.93/2.18 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__semidom(B). [resolve(37,a,24,b)].
% 1.93/2.18 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(37,a,25,b)].
% 1.93/2.18 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(37,a,26,b)].
% 1.93/2.18 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(37,a,27,b)].
% 1.93/2.18 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(37,a,28,b)].
% 1.93/2.18 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(37,a,29,b)].
% 1.93/2.18 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(37,a,30,b)].
% 1.93/2.18 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__semiring(B). [resolve(37,a,31,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(37,a,32,b)].
% 1.93/2.18 38 -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].
% 1.93/2.18 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(38,a,1,a)].
% 1.93/2.18 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(38,a,3,a)].
% 1.93/2.18 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(38,a,4,a)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Ojoin__semilorder(C). [resolve(38,a,5,b)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(38,a,6,b)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Omeet__semilorder(C). [resolve(38,a,7,b)].
% 1.93/2.18 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(C). [resolve(38,a,8,b)].
% 1.93/2.18 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__abs(C). [resolve(38,a,9,b)].
% 1.93/2.18 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(38,a,10,b)].
% 1.93/2.18 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(38,a,11,b)].
% 1.93/2.18 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(38,a,12,b)].
% 1.93/2.18 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(38,a,13,b)].
% 1.93/2.18 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__semigroup__add(C). [resolve(38,a,14,b)].
% 1.93/2.18 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__semigroup__add__imp__le(C). [resolve(38,a,15,b)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(38,a,16,b)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(38,a,17,b)].
% 1.93/2.18 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(38,a,19,b)].
% 1.93/2.18 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(38,a,20,b)].
% 1.93/2.18 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(38,a,21,b)].
% 1.93/2.18 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(38,a,22,b)].
% 1.93/2.18 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__ring__strict(C). [resolve(38,a,23,b)].
% 1.93/2.18 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__semidom(C). [resolve(38,a,24,b)].
% 1.93/2.18 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(38,a,25,b)].
% 1.93/2.18 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(38,a,26,b)].
% 1.93/2.18 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(38,a,27,b)].
% 1.93/2.18 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(38,a,28,b)].
% 1.93/2.18 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(38,a,29,b)].
% 1.93/2.18 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(38,a,30,b)].
% 1.93/2.18 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__semiring(C). [resolve(38,a,31,b)].
% 1.93/2.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(38,a,32,b)].
% 1.93/2.18 39 -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].
% 1.93/2.18 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(39,a,1,a)].
% 1.93/2.18 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(39,a,3,a)].
% 1.93/2.18 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(39,a,4,a)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(39,a,5,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Olorder(B). [resolve(39,a,6,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Omeet__semilorder(B). [resolve(39,a,7,b)].
% 1.93/2.18 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(B). [resolve(39,a,8,b)].
% 1.93/2.18 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__abs(B). [resolve(39,a,9,b)].
% 1.93/2.18 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(39,a,10,b)].
% 1.93/2.18 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(39,a,11,b)].
% 1.93/2.18 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(39,a,12,b)].
% 1.93/2.18 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(39,a,13,b)].
% 1.93/2.18 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__semigroup__add(B). [resolve(39,a,14,b)].
% 1.93/2.18 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__semigroup__add__imp__le(B). [resolve(39,a,15,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(39,a,16,b)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Orderings_Olinorder(B). [resolve(39,a,17,b)].
% 1.93/2.18 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(39,a,19,b)].
% 1.93/2.18 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(39,a,20,b)].
% 1.93/2.18 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(39,a,21,b)].
% 1.93/2.18 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(39,a,22,b)].
% 1.93/2.18 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__ring__strict(B). [resolve(39,a,23,b)].
% 1.93/2.18 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__semidom(B). [resolve(39,a,24,b)].
% 1.93/2.18 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(39,a,25,b)].
% 1.93/2.18 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(39,a,26,b)].
% 1.93/2.18 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(39,a,27,b)].
% 1.93/2.18 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(39,a,28,b)].
% 1.93/2.19 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(39,a,29,b)].
% 1.93/2.19 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(39,a,30,b)].
% 1.93/2.19 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__semiring(B). [resolve(39,a,31,b)].
% 1.93/2.19 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(39,a,32,b)].
% 1.93/2.19 40 -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].
% 1.93/2.19 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(40,a,1,a)].
% 1.93/2.19 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(40,a,3,a)].
% 1.93/2.19 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(40,a,4,a)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Ojoin__semilorder(C). [resolve(40,a,5,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(40,a,6,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Omeet__semilorder(C). [resolve(40,a,7,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(40,a,8,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(40,a,9,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(40,a,10,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(40,a,11,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(40,a,12,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(40,a,13,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(40,a,14,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(40,a,15,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(40,a,16,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(40,a,17,b)].
% 1.93/2.19 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(40,a,19,b)].
% 1.93/2.19 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(40,a,20,b)].
% 1.93/2.19 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(40,a,21,b)].
% 1.93/2.19 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(40,a,22,b)].
% 1.93/2.19 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__ring__strict(C). [resolve(40,a,23,b)].
% 1.93/2.19 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__semidom(C). [resolve(40,a,24,b)].
% 1.93/2.19 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(40,a,25,b)].
% 1.93/2.19 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(40,a,26,b)].
% 1.93/2.19 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(40,a,27,b)].
% 1.93/2.19 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(40,a,28,b)].
% 1.93/2.19 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(40,a,29,b)].
% 1.93/2.19 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(40,a,30,b)].
% 1.93/2.19 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__semiring(C). [resolve(40,a,31,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(40,a,32,b)].
% 1.93/2.19 41 -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].
% 1.93/2.19 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(41,a,1,a)].
% 1.93/2.19 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(41,a,3,a)].
% 1.93/2.19 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(41,a,4,a)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(41,a,8,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(41,a,9,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(41,a,10,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(41,a,11,b)].
% 1.93/2.19 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(41,a,12,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(41,a,13,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(41,a,14,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(41,a,15,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(41,a,16,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(41,a,19,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(41,a,20,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(41,a,21,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(41,a,22,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(41,a,23,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(41,a,24,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(41,a,25,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(41,a,26,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(41,a,27,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(41,a,28,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(41,a,29,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(41,a,30,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(41,a,31,b)].
% 1.93/2.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 1.93/2.20 42 -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].
% 1.93/2.20 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(42,a,1,a)].
% 1.93/2.20 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(42,a,3,a)].
% 1.93/2.20 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(42,a,4,a)].
% 1.93/2.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(42,a,5,b)].
% 1.93/2.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(42,a,6,b)].
% 1.93/2.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(42,a,7,b)].
% 1.93/2.20 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(B). [resolve(42,a,8,b)].
% 1.93/2.20 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__abs(B). [resolve(42,a,9,b)].
% 1.93/2.20 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(42,a,10,b)].
% 1.93/2.20 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(42,a,11,b)].
% 1.93/2.20 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(42,a,12,b)].
% 1.93/2.20 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(42,a,13,b)].
% 1.93/2.20 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__semigroup__add(B). [resolve(42,a,14,b)].
% 1.93/2.20 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__semigroup__add__imp__le(B). [resolve(42,a,15,b)].
% 1.93/2.20 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__cancel__ab__semigroup__add(B). [resolve(42,a,16,b)].
% 1.93/2.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(42,a,17,b)].
% 1.93/2.20 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(42,a,19,b)].
% 1.93/2.20 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(42,a,20,b)].
% 1.93/2.20 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(42,a,21,b)].
% 1.93/2.20 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(42,a,22,b)].
% 1.93/2.20 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__ring__strict(B). [resolve(42,a,23,b)].
% 1.93/2.20 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__semidom(B). [resolve(42,a,24,b)].
% 1.93/2.20 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(42,a,25,b)].
% 1.93/2.20 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(42,a,26,b)].
% 1.93/2.20 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(42,a,27,b)].
% 1.93/2.20 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(42,a,28,b)].
% 1.93/2.20 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(42,a,29,b)].
% 2.34/2.60 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(42,a,30,b)].
% 2.34/2.60 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(42,a,31,b)].
% 2.34/2.60 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(42,a,32,b)].
% 2.34/2.60 43 -class_HOL_Oone(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) # label(cls_NatSimprocs_Oequation__minus__iff__1_0) # label(axiom). [assumption].
% 2.34/2.60 44 class_HOL_Oone(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_1) # label(axiom). [assumption].
% 2.34/2.60 45 class_HOL_Oone(tc_nat) # label(clsarity_nat_0) # label(axiom). [assumption].
% 2.34/2.60 46 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 2.34/2.60 47 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_0) # label(axiom). [assumption].
% 2.34/2.60 48 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.34/2.60 49 -class_Power_Orecpower(A) | class_HOL_Oone(A) # label(clsrel_Power_Orecpower_2) # label(axiom). [assumption].
% 2.34/2.60 50 -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].
% 2.34/2.60 51 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_25) # label(axiom). [assumption].
% 2.34/2.60 52 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 2.34/2.60 53 -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].
% 2.34/2.60 54 -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ofield_13) # label(axiom). [assumption].
% 2.34/2.60 55 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 2.34/2.60 56 -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__field_16) # label(axiom). [assumption].
% 2.34/2.60 57 -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__idom_13) # label(axiom). [assumption].
% 2.34/2.60 58 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 2.34/2.60 59 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 2.34/2.60 60 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 2.34/2.60 61 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(43,a,44,a)].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(43,a,45,a)].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(43,a,46,b)].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(43,a,47,b)].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(43,a,48,b)].
% 2.34/2.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(43,a,49,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(43,a,50,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(43,a,51,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(43,a,52,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(43,a,53,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(43,a,54,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(43,a,55,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(43,a,56,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(43,a,57,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(43,a,58,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(43,a,59,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(43,a,60,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(43,a,61,b)].
% 2.34/2.61 62 -class_HOL_Oone(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 # label(cls_NatSimprocs_Oequation__minus__iff__1_1) # label(axiom). [assumption].
% 2.34/2.61 63 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) # label(cls_NatSimprocs_Ole__minus__iff__1_0) # label(axiom). [assumption].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(63,a,44,a)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(63,a,45,a)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(63,a,46,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(63,a,47,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(63,a,48,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(63,a,49,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(63,a,50,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(63,a,51,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(63,a,52,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(63,a,53,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(63,a,54,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(63,a,55,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(63,a,56,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(63,a,57,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(63,a,58,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(63,a,59,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(63,a,60,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(63,a,61,b)].
% 2.34/2.61 64 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) # label(cls_NatSimprocs_Ole__minus__iff__1_1) # label(axiom). [assumption].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(64,a,44,a)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(64,a,45,a)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(64,a,46,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(64,a,47,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(64,a,48,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(64,a,49,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(64,a,50,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(64,a,51,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(64,a,52,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(64,a,53,b)].
% 2.34/2.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(64,a,54,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(64,a,55,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(64,a,56,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(64,a,57,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(64,a,58,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(64,a,59,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(64,a,60,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(64,a,61,b)].
% 2.34/2.62 65 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) # label(cls_NatSimprocs_Oless__minus__iff__1_0) # label(axiom). [assumption].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(65,a,44,a)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(65,a,45,a)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(65,a,46,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(65,a,47,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(65,a,48,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(65,a,49,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(65,a,50,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(65,a,51,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(65,a,52,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(65,a,53,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(65,a,54,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(65,a,55,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(65,a,56,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(65,a,57,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(65,a,58,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(65,a,59,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(65,a,60,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(65,a,61,b)].
% 2.34/2.62 66 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) # label(cls_NatSimprocs_Oless__minus__iff__1_1) # label(axiom). [assumption].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(66,a,44,a)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(66,a,45,a)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(66,a,46,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(66,a,47,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(66,a,48,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(66,a,49,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(66,a,50,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(66,a,51,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(66,a,52,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(66,a,53,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(66,a,54,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(66,a,55,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(66,a,56,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(66,a,57,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(66,a,58,b)].
% 2.34/2.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(66,a,59,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(66,a,60,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(66,a,61,b)].
% 2.34/2.63 67 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) # label(cls_NatSimprocs_Ominus__le__iff__1_0) # label(axiom). [assumption].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(67,a,44,a)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(67,a,45,a)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(67,a,46,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(67,a,47,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(67,a,48,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(67,a,49,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(67,a,50,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(67,a,51,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(67,a,52,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(67,a,53,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(67,a,54,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(67,a,55,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(67,a,56,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(67,a,57,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(67,a,58,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(67,a,59,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(67,a,60,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(67,a,61,b)].
% 2.34/2.63 68 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) # label(cls_NatSimprocs_Ominus__le__iff__1_1) # label(axiom). [assumption].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(68,a,44,a)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(68,a,45,a)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(68,a,46,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(68,a,47,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(68,a,48,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(68,a,49,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(68,a,50,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(68,a,51,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(68,a,52,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(68,a,53,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(68,a,54,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(68,a,55,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(68,a,56,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(68,a,57,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(68,a,58,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(68,a,59,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(68,a,60,b)].
% 2.34/2.63 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(68,a,61,b)].
% 2.34/2.63 69 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) # label(cls_NatSimprocs_Ominus__less__iff__1_0) # label(axiom). [assumption].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(69,a,44,a)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(69,a,45,a)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(69,a,46,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(69,a,47,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(69,a,48,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(69,a,49,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(69,a,50,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(69,a,51,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(69,a,52,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(69,a,53,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(69,a,54,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(69,a,55,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(69,a,56,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(69,a,57,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(69,a,58,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(69,a,59,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(69,a,60,b)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(69,a,61,b)].
% 2.34/2.64 70 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) # label(cls_NatSimprocs_Ominus__less__iff__1_1) # label(axiom). [assumption].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(70,a,44,a)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(70,a,45,a)].
% 2.34/2.64 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(70,a,46,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(70,a,47,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(70,a,48,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(70,a,49,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(70,a,50,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(70,a,51,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(70,a,52,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(70,a,53,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(70,a,54,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(70,a,55,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(70,a,56,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(70,a,57,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(70,a,58,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(70,a,59,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(70,a,60,b)].
% 2.59/2.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(70,a,61,b)].
% 2.59/2.83 71 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.59/2.83 72 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.59/2.83 73 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.59/2.83 74 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.59/2.83 75 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.59/2.83 76 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 2.59/2.83 77 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_10) # label(axiom). [assumption].
% 2.59/2.83 78 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 2.59/2.83 79 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_2) # label(axiom). [assumption].
% 2.59/2.83 80 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) # label(axiom). [assumption].
% 2.59/2.83 81 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_7) # label(axiom). [assumption].
% 2.59/2.83 82 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) # label(axiom). [assumption].
% 2.59/2.83 83 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.59/2.83 84 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.59/2.83 85 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 2.59/2.83 86 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) # label(axiom). [assumption].
% 2.59/2.83 87 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 2.59/2.83 88 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 2.59/2.83 89 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_7) # label(axiom). [assumption].
% 2.59/2.83 90 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 2.59/2.83 91 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_1) # label(axiom). [assumption].
% 2.59/2.83 92 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) # label(axiom). [assumption].
% 2.59/2.83 93 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_2) # label(axiom). [assumption].
% 2.59/2.83 94 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_10) # label(axiom). [assumption].
% 2.59/2.83 95 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_4) # label(axiom). [assumption].
% 2.59/2.83 96 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 2.59/2.83 97 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 2.59/2.83 98 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.59/2.83 99 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(71,a,72,a)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(71,a,73,a)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(71,a,74,b)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(71,a,75,b)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(71,a,83,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(71,a,87,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(71,a,94,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 2.59/2.84 100 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(100,a,72,a)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(100,a,73,a)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(100,a,74,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(100,a,75,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 2.59/2.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(100,a,83,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(100,a,87,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(100,a,94,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 2.59/2.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 2.59/2.86 101 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.59/2.86 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(101,a,72,a)].
% 2.59/2.86 Derived: class_HOL_Oplus(tc_nat). [resolve(101,a,73,a)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(101,a,74,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(101,a,75,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(101,a,76,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(101,a,77,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(101,a,80,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(101,a,81,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(101,a,82,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(101,a,83,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(101,a,84,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(101,a,85,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(101,a,86,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(101,a,87,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(101,a,88,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(101,a,89,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(101,a,90,b)].
% 2.59/2.86 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(101,a,91,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(101,a,92,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(101,a,93,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(101,a,94,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(101,a,95,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(101,a,96,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(101,a,97,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 2.59/2.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(101,a,99,b)].
% 2.59/2.87 102 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(102,a,72,a)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(102,a,73,a)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(102,a,74,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(102,a,75,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(102,a,83,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(102,a,87,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(102,a,94,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 2.59/2.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 2.66/2.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 2.66/2.91 103 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.66/2.91 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(103,a,72,a)].
% 2.66/2.91 Derived: class_HOL_Otimes(tc_nat). [resolve(103,a,73,a)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(103,a,74,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(103,a,75,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(103,a,77,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(103,a,83,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(103,a,84,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(103,a,85,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(103,a,86,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(103,a,87,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(103,a,88,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(103,a,89,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(103,a,90,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(103,a,91,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(103,a,92,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(103,a,93,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(103,a,94,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(103,a,95,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(103,a,96,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(103,a,97,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 2.66/2.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 2.66/2.91 104 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.66/2.91 105 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_1) # label(axiom). [assumption].
% 2.66/2.91 106 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.66/2.91 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(106,b,101,a)].
% 2.66/2.91 107 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_3) # label(axiom). [assumption].
% 2.66/2.91 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 2.66/2.91 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 2.66/2.91 108 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__distrib__number__of_0) # label(axiom). [assumption].
% 2.66/2.91 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(108,b,72,a)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(108,b,73,a)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(108,b,74,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(108,b,75,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(108,b,76,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(108,b,77,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(108,b,78,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(108,b,79,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(108,b,80,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(108,b,81,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(108,b,82,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(108,b,83,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(108,b,84,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(108,b,85,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(108,b,86,b)].
% 2.66/2.91 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(108,b,87,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(108,b,88,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(108,b,89,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(108,b,90,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(108,b,91,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(108,b,92,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(108,b,93,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(108,b,94,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(108,b,95,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(108,b,96,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(108,b,97,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(108,b,98,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(108,b,99,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(108,b,104,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(108,b,105,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(108,b,106,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(108,b,107,b)].
% 2.66/2.92 109 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__distrib__number__of_0) # label(axiom). [assumption].
% 2.66/2.92 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(109,b,72,a)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(109,b,73,a)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(109,b,74,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A). [resolve(109,b,75,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(109,b,76,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(109,b,77,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(109,b,78,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(109,b,79,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(109,b,80,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(109,b,81,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(109,b,82,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(109,b,83,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(109,b,84,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(109,b,85,b)].
% 2.66/2.92 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(109,b,86,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(109,b,87,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(109,b,88,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(109,b,89,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(109,b,90,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(109,b,91,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(109,b,92,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(109,b,93,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(109,b,94,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(109,b,95,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(109,b,96,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(109,b,97,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(109,b,98,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(109,b,99,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(109,b,104,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(109,b,105,b)].
% 2.66/2.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(109,b,106,b)].
% 2.87/3.16 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(109,b,107,b)].
% 2.87/3.16 110 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.87/3.16 111 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.87/3.16 112 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.87/3.16 113 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.87/3.16 114 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.87/3.16 115 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_1) # label(axiom). [assumption].
% 2.87/3.16 116 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_6) # label(axiom). [assumption].
% 2.87/3.16 117 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.87/3.16 118 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.87/3.16 119 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(119,a,111,a)].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(119,a,112,a)].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(119,a,113,b)].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(119,a,114,b)].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 2.87/3.16 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 2.87/3.16 120 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.87/3.16 121 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.87/3.16 122 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_0) # label(axiom). [assumption].
% 2.87/3.16 123 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) # label(axiom). [assumption].
% 2.87/3.16 124 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_4) # label(axiom). [assumption].
% 2.87/3.16 125 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) # label(axiom). [assumption].
% 2.87/3.16 126 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.87/3.16 127 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.87/3.16 128 -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].
% 3.09/3.33 129 -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].
% 3.09/3.33 130 -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].
% 3.09/3.33 131 -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].
% 3.09/3.33 132 -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].
% 3.09/3.33 133 -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].
% 3.09/3.33 134 -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].
% 3.09/3.33 135 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(135,b,111,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(135,b,112,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(135,b,113,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(135,b,114,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 3.09/3.33 136 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(136,b,111,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(136,b,112,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(136,b,113,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(136,b,114,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 3.09/3.33 137 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 3.09/3.33 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(137,b,111,a)].
% 3.09/3.33 Derived: class_HOL_Oplus(tc_nat). [resolve(137,b,112,a)].
% 3.09/3.33 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(137,b,113,b)].
% 3.09/3.33 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(137,b,114,b)].
% 3.09/3.33 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(137,b,115,b)].
% 3.09/3.33 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(137,b,116,b)].
% 3.09/3.33 138 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(138,b,111,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(138,b,112,a)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(138,b,113,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(138,b,114,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 3.09/3.33 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 3.09/3.33 139 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 3.10/3.41 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(139,b,111,a)].
% 3.10/3.41 Derived: class_HOL_Otimes(tc_nat). [resolve(139,b,112,a)].
% 3.10/3.41 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(139,b,113,b)].
% 3.10/3.41 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(139,b,114,b)].
% 3.10/3.41 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 3.10/3.41 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(139,b,116,b)].
% 3.10/3.41 140 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(108,b,78,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(140,c,111,a)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(140,c,112,a)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(140,c,113,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(140,c,114,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(140,c,115,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(140,c,116,b)].
% 3.10/3.41 141 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(109,b,78,b)].
% 3.10/3.41 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(141,c,111,a)].
% 3.10/3.41 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(141,c,112,a)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(141,c,113,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A). [resolve(141,c,114,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(141,c,115,b)].
% 3.10/3.41 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(141,c,116,b)].
% 3.10/3.41 142 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_0) # label(axiom). [assumption].
% 3.19/3.42 143 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_12) # label(axiom). [assumption].
% 3.19/3.42 144 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat_20) # label(axiom). [assumption].
% 3.19/3.42 145 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 3.19/3.42 146 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Oab__group__add_1) # label(axiom). [assumption].
% 3.19/3.42 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(142,a,143,a)].
% 3.19/3.42 Derived: class_HOL_Ozero(tc_nat). [resolve(142,a,144,a)].
% 3.19/3.42 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(142,a,145,b)].
% 3.19/3.42 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(142,a,146,b)].
% 3.19/3.42 147 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 3.19/3.42 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(147,a,146,b)].
% 3.19/3.42 148 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_2) # label(axiom). [assumption].
% 3.19/3.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(148,a,146,b)].
% 3.19/3.42 149 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_3) # label(axiom). [assumption].
% 3.19/3.42 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(149,a,146,b)].
% 3.19/3.42 150 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(150,b,149,a)].
% 3.19/3.42 151 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(151,b,149,a)].
% 3.19/3.42 152 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(152,b,149,a)].
% 3.19/3.42 153 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 3.19/3.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(153,b,149,a)].
% 3.19/3.42 154 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_2) # label(axiom). [assumption].
% 3.19/3.43 155 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Power_Orecpower_12) # label(axiom). [assumption].
% 3.19/3.43 Derived: -class_Power_Orecpower(A) | class_HOL_Ozero(A). [resolve(155,b,142,a)].
% 3.19/3.43 156 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 3.19/3.43 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 3.19/3.43 157 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_13) # label(axiom). [assumption].
% 3.19/3.43 158 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_8) # label(axiom). [assumption].
% 3.19/3.43 159 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) # label(axiom). [assumption].
% 3.19/3.43 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 3.19/3.43 160 -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].
% 3.19/3.43 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 3.19/3.43 161 -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].
% 3.19/3.43 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 3.19/3.43 162 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ofield_23) # label(axiom). [assumption].
% 3.19/3.43 163 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 3.19/3.43 164 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 3.19/3.43 165 -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].
% 3.19/3.43 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(165,b,142,a)].
% 3.19/3.43 166 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__field_25) # label(axiom). [assumption].
% 3.19/3.43 167 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 3.19/3.43 168 -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].
% 3.19/3.43 169 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 3.19/3.43 170 -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].
% 3.19/3.43 171 -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].
% 3.19/3.43 172 -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].
% 3.19/3.43 173 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_13) # label(axiom). [assumption].
% 3.19/3.43 174 -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].
% 3.19/3.49 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A). [resolve(174,b,142,a)].
% 3.19/3.49 175 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 3.19/3.49 176 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 3.19/3.49 177 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 3.19/3.49 178 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 3.19/3.49 179 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 3.19/3.49 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 3.19/3.49 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 3.19/3.49 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 3.19/3.49 180 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_4) # label(axiom). [assumption].
% 3.19/3.49 181 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 3.19/3.49 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 3.19/3.49 182 -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].
% 3.19/3.49 183 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(B,c_0,A) = B # label(cls_OrderedGroup_Oadd__0__right_0) # label(axiom). [assumption].
% 3.19/3.49 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(183,a,143,a)].
% 3.19/3.49 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(183,a,144,a)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(183,a,145,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(183,a,146,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(183,a,154,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(183,a,155,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 3.19/3.49 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(183,a,166,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(183,a,173,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 3.27/3.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 3.27/3.50 184 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 3.27/3.50 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(184,a,143,a)].
% 3.27/3.50 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(184,a,144,a)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(184,a,145,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(184,a,146,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(184,a,154,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(184,a,155,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(184,a,166,b)].
% 3.27/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(184,a,173,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 3.49/3.73 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 3.49/3.73 185 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 3.49/3.73 186 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 3.49/3.73 187 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 3.49/3.73 188 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 3.49/3.73 189 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 3.49/3.73 190 -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].
% 3.49/3.73 191 -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].
% 3.49/3.73 192 -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].
% 3.49/3.73 193 -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].
% 3.49/3.73 194 -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].
% 3.49/3.73 195 -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].
% 3.49/3.73 196 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 3.49/3.73 197 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 3.49/3.73 198 -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].
% 3.49/3.73 199 -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].
% 3.49/3.73 200 -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].
% 3.49/3.78 201 -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].
% 3.49/3.78 202 -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].
% 3.49/3.78 203 -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].
% 3.49/3.78 204 -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].
% 3.49/3.78 205 -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].
% 3.49/3.78 206 -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].
% 3.49/3.78 207 -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].
% 3.49/3.78 208 -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].
% 3.49/3.78 209 -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].
% 3.49/3.78 210 -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].
% 3.49/3.78 211 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 3.49/3.78 212 -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].
% 3.49/3.78 213 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 3.49/3.78 214 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 3.49/3.78 215 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 3.49/3.78 216 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 3.49/3.78 217 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(217,a,196,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(217,a,197,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(217,a,198,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(217,a,200,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(217,a,201,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(217,a,202,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(217,a,203,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(217,a,204,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(217,a,205,b)].
% 3.49/3.78 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(217,a,206,b)].
% 3.67/3.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(217,a,207,b)].
% 3.67/3.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(217,a,209,b)].
% 3.67/3.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(217,a,210,b)].
% 3.67/3.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 3.67/3.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 3.67/3.94 218 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_0) # label(axiom). [assumption].
% 3.67/3.94 219 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1_3) # label(axiom). [assumption].
% 3.67/3.94 220 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_2) # label(axiom). [assumption].
% 3.67/3.94 221 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(108,b,104,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(221,c,192,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(221,c,193,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(221,c,194,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(221,c,195,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(221,c,196,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(221,c,197,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(221,c,198,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(221,c,199,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(221,c,200,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(221,c,201,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(221,c,202,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(221,c,203,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(221,c,204,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(221,c,205,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(221,c,206,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(221,c,207,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(221,c,208,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(221,c,209,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(221,c,210,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(221,c,211,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(221,c,212,b)].
% 3.67/3.94 222 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(109,b,104,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(222,c,192,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(222,c,193,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(222,c,194,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(222,c,195,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(222,c,196,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(222,c,197,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(222,c,198,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(222,c,199,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(222,c,200,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(222,c,201,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(222,c,202,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(222,c,203,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(222,c,204,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(222,c,205,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(222,c,206,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(222,c,207,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(222,c,208,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(222,c,209,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(222,c,210,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(222,c,211,b)].
% 3.67/3.94 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(222,c,212,b)].
% 3.67/3.95 223 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(223,a,186,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(223,a,187,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(223,a,188,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(223,a,189,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(223,a,196,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(223,a,200,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(223,a,207,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 3.67/3.95 224 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(224,a,186,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(224,a,187,a)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(224,a,188,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(224,a,189,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(224,a,196,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(224,a,200,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(224,a,207,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 3.67/3.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 3.67/3.95 225 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 3.67/3.95 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(225,a,186,a)].
% 3.67/3.95 Derived: class_HOL_Oplus(tc_nat). [resolve(225,a,187,a)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(225,a,188,b)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(225,a,189,b)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(225,a,190,b)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(225,a,191,b)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 3.67/3.95 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(225,a,193,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(225,a,194,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(225,a,195,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(225,a,196,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(225,a,197,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(225,a,198,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(225,a,199,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(225,a,200,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(225,a,201,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(225,a,202,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(225,a,203,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(225,a,204,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(225,a,205,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(225,a,206,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(225,a,207,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(225,a,208,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(225,a,209,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(225,a,210,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(225,a,212,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(225,a,219,b)].
% 3.67/3.96 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(225,a,220,b)].
% 3.67/3.96 226 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(226,b,186,a)].
% 3.67/3.96 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(226,b,187,a)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(226,b,188,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(226,b,189,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(226,b,200,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 3.67/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(226,b,207,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 3.82/4.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 3.82/4.06 227 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(227,b,186,a)].
% 3.82/4.06 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(227,b,187,a)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(227,b,188,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(227,b,189,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(227,b,200,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(227,b,207,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 3.82/4.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 3.82/4.06 228 -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].
% 3.82/4.06 229 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.82/4.06 230 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.98/4.25 231 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.98/4.25 232 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.98/4.25 233 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_0) # label(axiom). [assumption].
% 3.98/4.25 234 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_5) # label(axiom). [assumption].
% 3.98/4.25 235 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_3) # label(axiom). [assumption].
% 3.98/4.25 236 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_4) # label(axiom). [assumption].
% 3.98/4.25 237 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.98/4.25 238 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_6) # label(axiom). [assumption].
% 3.98/4.25 239 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.98/4.25 240 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.98/4.25 241 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) # label(axiom). [assumption].
% 3.98/4.25 242 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_3) # label(axiom). [assumption].
% 3.98/4.25 243 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) # label(axiom). [assumption].
% 3.98/4.25 244 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.98/4.25 245 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.98/4.25 246 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) # label(axiom). [assumption].
% 3.98/4.25 247 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_18) # label(axiom). [assumption].
% 3.98/4.25 248 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_15) # label(axiom). [assumption].
% 3.98/4.25 249 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_9) # label(axiom). [assumption].
% 3.98/4.25 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 3.98/4.25 250 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) # label(axiom). [assumption].
% 3.98/4.25 251 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_5) # label(axiom). [assumption].
% 3.98/4.25 252 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_0) # label(axiom). [assumption].
% 3.98/4.25 253 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 4.05/4.29 254 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 4.05/4.29 255 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 4.05/4.29 256 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 4.05/4.29 257 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 4.05/4.29 258 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(108,b,79,b)].
% 4.05/4.29 259 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(109,b,79,b)].
% 4.05/4.29 260 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 4.05/4.29 261 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 4.05/4.29 262 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(262,b,229,a)].
% 4.05/4.29 Derived: class_HOL_Ozero(tc_nat). [resolve(262,b,230,a)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(262,b,231,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(262,b,232,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(262,b,246,b)].
% 4.05/4.29 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(262,b,252,b)].
% 4.05/4.29 263 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(221,c,192,b)].
% 4.05/4.29 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(263,c,229,a)].
% 4.05/4.29 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(263,c,230,a)].
% 4.05/4.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(263,c,231,b)].
% 4.05/4.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A). [resolve(263,c,232,b)].
% 4.05/4.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(263,c,233,b)].
% 4.05/4.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(263,c,234,b)].
% 4.05/4.31 264 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(222,c,192,b)].
% 4.05/4.31 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(264,c,229,a)].
% 4.05/4.31 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(264,c,230,a)].
% 4.05/4.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(264,c,231,b)].
% 4.05/4.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A). [resolve(264,c,232,b)].
% 4.05/4.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(264,c,233,b)].
% 4.05/4.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(264,c,234,b)].
% 4.05/4.31 265 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(265,b,229,a)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(265,b,230,a)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(265,b,231,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(265,b,232,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 4.05/4.31 266 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(266,b,229,a)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(266,b,230,a)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(266,b,231,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(266,b,232,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 4.05/4.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 4.05/4.31 267 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 4.05/4.31 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(267,b,229,a)].
% 4.05/4.31 Derived: class_HOL_Oplus(tc_nat). [resolve(267,b,230,a)].
% 4.05/4.31 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(267,b,231,b)].
% 4.05/4.31 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(267,b,232,b)].
% 4.05/4.31 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(267,b,233,b)].
% 4.05/4.31 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(267,b,234,b)].
% 4.05/4.31 268 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 4.05/4.31 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(268,b,229,a)].
% 4.05/4.31 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(268,b,230,a)].
% 4.05/4.31 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(268,b,231,b)].
% 4.16/4.39 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(268,b,232,b)].
% 4.16/4.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 4.16/4.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 4.16/4.39 269 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 4.16/4.39 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(269,b,229,a)].
% 4.16/4.39 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(269,b,230,a)].
% 4.16/4.39 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(269,b,231,b)].
% 4.16/4.39 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(269,b,232,b)].
% 4.16/4.39 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 4.16/4.39 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 4.16/4.39 270 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 4.16/4.39 271 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 4.16/4.39 272 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 4.16/4.39 273 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 4.16/4.39 274 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 4.16/4.39 275 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 4.16/4.39 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 4.16/4.39 276 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 4.16/4.39 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 4.16/4.39 277 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 4.16/4.39 278 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom). [assumption].
% 4.16/4.39 279 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom). [assumption].
% 4.16/4.39 280 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom). [assumption].
% 4.16/4.39 281 -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].
% 4.16/4.39 282 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom). [assumption].
% 4.16/4.39 283 -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].
% 4.16/4.39 284 -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].
% 4.16/4.39 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 4.16/4.39 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(284,b,276,a)].
% 4.23/4.44 285 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 4.23/4.44 286 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom). [assumption].
% 4.23/4.44 287 -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].
% 4.23/4.44 288 -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].
% 4.23/4.44 289 -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].
% 4.23/4.44 290 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 4.23/4.44 291 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 4.23/4.44 292 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom). [assumption].
% 4.23/4.44 293 -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].
% 4.23/4.44 294 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom). [assumption].
% 4.23/4.44 295 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom). [assumption].
% 4.23/4.44 296 -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].
% 4.23/4.44 297 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom). [assumption].
% 4.23/4.44 298 -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].
% 4.23/4.44 299 -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].
% 4.23/4.44 300 -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].
% 4.23/4.44 301 -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].
% 4.23/4.44 302 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom). [assumption].
% 4.23/4.44 303 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 4.23/4.44 304 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom). [assumption].
% 4.23/4.44 305 -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].
% 4.23/4.44 306 -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].
% 4.23/4.44 307 -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].
% 4.23/4.45 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(307,a,271,a)].
% 4.23/4.45 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(307,a,272,a)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(307,a,273,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(307,a,274,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(307,a,275,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(307,a,278,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(307,a,279,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(307,a,280,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(307,a,281,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(307,a,282,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(307,a,283,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(307,a,284,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(307,a,285,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(307,a,286,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(307,a,287,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(307,a,288,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(307,a,289,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(307,a,292,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(307,a,293,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(307,a,294,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(307,a,295,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(307,a,296,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(307,a,297,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(307,a,298,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(307,a,299,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(307,a,300,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(307,a,301,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(307,a,302,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(307,a,304,b)].
% 4.23/4.45 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(307,a,305,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(307,a,306,b)].
% 4.23/4.46 308 -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].
% 4.23/4.46 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(308,a,271,a)].
% 4.23/4.46 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(308,a,272,a)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(308,a,273,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(308,a,274,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(308,a,275,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(308,a,278,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(308,a,279,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(308,a,280,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(308,a,281,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(308,a,282,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(308,a,283,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(308,a,284,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(308,a,285,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(308,a,286,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(308,a,287,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(308,a,288,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(308,a,289,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(308,a,292,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(308,a,293,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(308,a,294,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(308,a,295,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(308,a,296,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(308,a,297,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(308,a,298,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(308,a,299,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(308,a,300,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(308,a,301,b)].
% 4.23/4.46 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(308,a,302,b)].
% 4.48/4.71 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 4.48/4.71 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(308,a,304,b)].
% 4.48/4.71 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(308,a,305,b)].
% 4.48/4.71 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(308,a,306,b)].
% 4.48/4.71 309 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 4.48/4.71 310 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 4.48/4.71 311 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 4.48/4.71 312 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 4.48/4.71 313 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 4.48/4.71 314 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 4.48/4.71 315 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 4.48/4.71 316 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 4.48/4.71 317 -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].
% 4.48/4.71 318 -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].
% 4.48/4.71 319 -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].
% 4.48/4.71 320 -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].
% 4.48/4.71 321 -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].
% 4.48/4.71 322 -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].
% 4.48/4.71 323 -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].
% 4.48/4.71 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 4.48/4.71 324 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 4.48/4.71 325 -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].
% 4.48/4.71 326 -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].
% 4.48/4.71 327 -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].
% 4.67/4.94 328 -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].
% 4.67/4.94 329 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 4.67/4.94 330 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 4.67/4.94 331 -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].
% 4.67/4.94 332 -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].
% 4.67/4.94 333 -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].
% 4.67/4.94 334 -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].
% 4.67/4.94 335 -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].
% 4.67/4.94 336 -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].
% 4.67/4.94 337 -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].
% 4.67/4.94 338 -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].
% 4.67/4.94 339 -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].
% 4.67/4.94 340 -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].
% 4.67/4.94 341 -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].
% 4.67/4.94 342 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 4.67/4.94 343 -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].
% 4.67/4.94 344 -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].
% 4.67/4.94 345 -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].
% 4.67/4.94 346 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(346,b,310,a)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(346,b,311,a)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(346,b,312,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(346,b,313,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(346,b,321,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(346,b,324,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(346,b,329,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(346,b,333,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(346,b,340,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 4.67/4.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 4.67/4.94 347 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(347,b,310,a)].
% 4.67/4.94 Derived: class_HOL_Oplus(tc_nat). [resolve(347,b,311,a)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(347,b,312,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(347,b,313,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(347,b,316,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(347,b,317,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(347,b,318,b)].
% 4.67/4.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(347,b,319,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(347,b,320,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(347,b,321,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(347,b,322,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(347,b,324,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(347,b,325,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(347,b,326,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(347,b,327,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(347,b,328,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(347,b,329,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(347,b,330,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(347,b,331,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(347,b,332,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(347,b,333,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(347,b,334,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(347,b,335,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(347,b,336,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(347,b,337,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(347,b,338,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(347,b,339,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(347,b,340,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(347,b,341,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(347,b,343,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 4.82/5.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(347,b,345,b)].
% 4.82/5.03 348 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(307,a,275,b)].
% 4.82/5.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(348,c,310,a)].
% 4.82/5.03 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(348,c,311,a)].
% 4.82/5.03 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(348,c,312,b)].
% 4.82/5.03 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(348,c,313,b)].
% 4.82/5.03 349 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(308,a,275,b)].
% 4.82/5.03 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(349,c,310,a)].
% 4.82/5.03 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(349,c,311,a)].
% 4.82/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(349,c,312,b)].
% 4.82/5.03 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(349,c,313,b)].
% 4.82/5.03 350 -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].
% 4.82/5.03 351 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 4.82/5.03 352 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 4.82/5.04 353 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 4.82/5.04 354 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 4.82/5.04 355 -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].
% 4.82/5.04 356 -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].
% 4.82/5.04 357 -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].
% 4.82/5.04 358 -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].
% 4.82/5.04 359 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 4.82/5.04 360 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 4.82/5.04 361 -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].
% 4.82/5.04 362 -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].
% 4.82/5.04 363 -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].
% 4.82/5.04 364 -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].
% 4.82/5.04 365 -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].
% 4.82/5.04 366 -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].
% 4.82/5.04 367 -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].
% 4.82/5.04 368 -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].
% 4.82/5.04 369 -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].
% 4.82/5.04 370 -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].
% 4.82/5.04 371 -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].
% 4.82/5.04 372 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 4.82/5.04 373 -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].
% 4.82/5.04 374 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 4.82/5.04 375 -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].
% 4.93/5.13 376 -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].
% 4.93/5.13 377 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 4.93/5.13 378 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 4.93/5.13 379 -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].
% 4.93/5.13 380 -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].
% 4.93/5.13 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(380,a,351,a)].
% 4.93/5.13 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(380,a,352,a)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(380,a,353,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(380,a,354,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(380,a,363,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(380,a,370,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 4.93/5.13 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 4.93/5.13 381 -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].
% 4.93/5.13 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(381,a,351,a)].
% 4.93/5.13 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(381,a,352,a)].
% 4.93/5.13 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(381,a,353,b)].
% 4.93/5.13 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(381,a,354,b)].
% 4.93/5.13 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 4.93/5.13 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 4.93/5.13 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(381,a,363,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(381,a,370,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 5.05/5.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 5.05/5.26 382 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(108,b,105,b)].
% 5.05/5.26 383 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(109,b,105,b)].
% 5.05/5.26 384 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 5.05/5.26 385 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 5.05/5.26 386 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(386,b,359,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(386,b,363,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 5.05/5.26 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(386,b,370,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 5.08/5.29 387 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 5.08/5.29 388 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 5.08/5.29 389 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(307,a,305,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(389,c,354,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(389,c,355,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(389,c,356,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(389,c,357,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(389,c,358,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(389,c,361,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(389,c,362,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(389,c,363,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(389,c,364,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(389,c,365,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(389,c,366,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(389,c,367,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(389,c,368,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(389,c,369,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(389,c,370,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(389,c,371,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(389,c,373,b)].
% 5.08/5.29 390 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Osemiring__0__cancel(C). [resolve(308,a,305,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(390,c,354,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(390,c,355,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(390,c,356,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(390,c,357,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(390,c,358,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(390,c,361,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(390,c,362,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(390,c,363,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(390,c,364,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(390,c,365,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(390,c,366,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(390,c,367,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(390,c,368,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(390,c,369,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(390,c,370,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(390,c,371,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 5.08/5.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(390,c,373,b)].
% 5.08/5.29 391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(391,b,351,a)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(391,b,352,a)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(391,b,353,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(391,b,354,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(391,b,359,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(391,b,363,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 5.08/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 5.15/5.39 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(391,b,370,b)].
% 5.15/5.39 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 5.15/5.39 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 5.15/5.39 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 5.15/5.39 392 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(392,b,351,a)].
% 5.15/5.39 Derived: class_HOL_Oplus(tc_nat). [resolve(392,b,352,a)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(392,b,353,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(392,b,354,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(392,b,355,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(392,b,356,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(392,b,357,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(392,b,358,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(392,b,359,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(392,b,360,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(392,b,361,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(392,b,362,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(392,b,363,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(392,b,364,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(392,b,365,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(392,b,366,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(392,b,367,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(392,b,368,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(392,b,369,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(392,b,370,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(392,b,371,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 5.15/5.39 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(392,b,373,b)].
% 5.15/5.39 393 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 5.15/5.39 394 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 5.15/5.39 395 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 5.15/5.39 396 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 5.15/5.39 397 -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].
% 5.15/5.39 398 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 5.15/5.39 399 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 5.15/5.39 400 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 5.15/5.39 401 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 5.21/5.44 402 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 5.21/5.44 403 -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].
% 5.21/5.44 404 -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].
% 5.21/5.44 405 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 5.21/5.44 406 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 5.21/5.44 407 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 5.21/5.44 408 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 5.21/5.44 409 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 5.21/5.44 410 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(410,a,394,a)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(410,a,395,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(410,a,401,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(410,a,404,b)].
% 5.21/5.44 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 5.21/5.44 411 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 5.21/5.44 412 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 5.21/5.44 413 -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].
% 5.21/5.44 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(413,b,394,a)].
% 5.21/5.44 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(413,b,395,b)].
% 5.21/5.44 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(A). [resolve(413,b,396,b)].
% 5.21/5.45 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(413,b,397,b)].
% 5.21/5.45 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(413,b,398,b)].
% 5.21/5.45 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(413,b,399,b)].
% 5.21/5.45 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(413,b,400,b)].
% 5.21/5.45 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(413,b,401,b)].
% 5.21/5.45 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(413,b,402,b)].
% 5.21/5.45 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__ring__strict(A). [resolve(413,b,403,b)].
% 5.21/5.45 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_Opordered__comm__ring(A). [resolve(413,b,404,b)].
% 5.21/5.45 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_Opordered__ring(A). [resolve(413,b,405,b)].
% 5.21/5.45 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_Oring__1(A). [resolve(413,b,412,b)].
% 5.21/5.45 414 -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].
% 5.21/5.45 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(414,b,394,a)].
% 5.21/5.45 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(414,b,395,b)].
% 5.21/5.45 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(414,b,396,b)].
% 5.21/5.45 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(414,b,397,b)].
% 5.25/5.48 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(414,b,398,b)].
% 5.25/5.48 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(414,b,399,b)].
% 5.25/5.48 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(414,b,400,b)].
% 5.25/5.48 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(414,b,401,b)].
% 5.25/5.48 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(414,b,402,b)].
% 5.25/5.48 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__ring__strict(A). [resolve(414,b,403,b)].
% 5.25/5.48 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_Opordered__comm__ring(A). [resolve(414,b,404,b)].
% 5.25/5.48 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_Opordered__ring(A). [resolve(414,b,405,b)].
% 5.25/5.48 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_Oring__1(A). [resolve(414,b,412,b)].
% 5.25/5.48 415 -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].
% 5.25/5.48 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(415,a,394,a)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(415,a,395,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ocomm__ring(B). [resolve(415,a,396,b)].
% 5.25/5.48 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(415,a,397,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(415,a,398,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(415,a,399,b)].
% 5.25/5.48 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(415,a,400,b)].
% 5.25/5.48 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(415,a,401,b)].
% 5.25/5.48 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(415,a,402,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(415,a,403,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(415,a,404,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(415,a,405,b)].
% 5.25/5.48 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oring__1(B). [resolve(415,a,412,b)].
% 5.35/5.57 416 -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].
% 5.35/5.57 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(416,a,394,a)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(416,a,395,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring(B). [resolve(416,a,396,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(416,a,397,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(416,a,398,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(416,a,399,b)].
% 5.35/5.57 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(416,a,400,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(416,a,401,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(416,a,402,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(416,a,403,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(416,a,404,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(416,a,405,b)].
% 5.35/5.57 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oring__1(B). [resolve(416,a,412,b)].
% 5.35/5.57 417 -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].
% 5.35/5.57 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(417,a,394,a)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(417,a,395,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(417,a,396,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(417,a,397,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(417,a,398,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(417,a,399,b)].
% 5.35/5.57 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(417,a,400,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(417,a,401,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(417,a,402,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(417,a,403,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(417,a,404,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(417,a,405,b)].
% 5.35/5.57 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(417,a,412,b)].
% 5.35/5.57 418 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 5.35/5.57 419 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 5.39/5.61 420 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 5.39/5.61 421 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(421,b,398,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(421,b,401,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(421,b,404,b)].
% 5.39/5.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 5.39/5.61 422 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(422,b,398,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(422,b,399,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(422,b,400,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(422,b,401,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(422,b,402,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(422,b,403,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(422,b,404,b)].
% 5.39/5.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(422,b,405,b)].
% 5.39/5.61 423 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(108,b,98,b)].
% 5.39/5.61 424 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(109,b,98,b)].
% 5.39/5.61 425 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 5.39/5.61 426 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 5.39/5.61 427 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(427,b,398,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(427,b,399,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(427,b,400,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(427,b,401,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(427,b,402,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(427,b,403,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(427,b,404,b)].
% 5.39/5.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(427,b,405,b)].
% 5.39/5.61 428 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(221,c,211,b)].
% 5.39/5.61 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(428,c,398,b)].
% 5.39/5.61 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(428,c,399,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(428,c,400,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(428,c,401,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(428,c,402,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(428,c,403,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(428,c,404,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(428,c,405,b)].
% 5.39/5.62 429 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(222,c,211,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(429,c,398,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(429,c,399,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(429,c,400,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(429,c,401,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(429,c,402,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(429,c,403,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(429,c,404,b)].
% 5.39/5.62 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(429,c,405,b)].
% 5.39/5.62 430 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 5.39/5.62 431 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 5.46/5.66 432 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 5.46/5.66 433 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(433,b,401,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(433,b,404,b)].
% 5.46/5.66 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 5.46/5.66 434 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(434,b,401,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(434,b,404,b)].
% 5.46/5.66 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 5.46/5.66 435 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 5.46/5.66 436 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 5.46/5.66 437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 5.46/5.66 438 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 5.46/5.66 439 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 5.46/5.66 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(439,b,394,a)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(439,b,395,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(439,b,401,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(439,b,404,b)].
% 5.46/5.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 5.46/5.66 440 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 5.46/5.66 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(440,b,394,a)].
% 5.46/5.66 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(440,b,395,b)].
% 5.46/5.66 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 5.46/5.66 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 5.46/5.66 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(440,b,401,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(440,b,404,b)].
% 5.46/5.67 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 5.46/5.67 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(441,b,394,a)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(441,b,395,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(441,b,398,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(441,b,401,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(441,b,404,b)].
% 5.46/5.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 5.46/5.67 442 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 5.46/5.67 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(442,c,394,a)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(442,c,395,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(442,c,396,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(442,c,397,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(442,c,400,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(442,c,401,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(442,c,402,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(442,c,403,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(442,c,404,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(442,c,405,b)].
% 5.46/5.67 443 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 5.46/5.67 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(443,c,394,a)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(443,c,395,b)].
% 5.46/5.67 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(443,c,396,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(443,c,397,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(443,c,400,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(443,c,401,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(443,c,402,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(443,c,403,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(443,c,404,b)].
% 5.83/6.08 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(443,c,405,b)].
% 5.83/6.08 444 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(444,b,394,a)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(444,b,395,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(444,b,398,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(444,b,401,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(444,b,404,b)].
% 5.83/6.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 5.83/6.08 445 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(445,b,394,a)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(445,b,395,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(445,b,396,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(445,b,397,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(445,b,398,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(445,b,399,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(445,b,400,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(445,b,401,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(445,b,402,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(445,b,403,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(445,b,404,b)].
% 5.83/6.08 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(445,b,405,b)].
% 5.83/6.08 446 -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].
% 5.83/6.08 447 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 6.04/6.25 448 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 6.04/6.25 449 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 6.04/6.25 450 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 6.04/6.25 451 -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].
% 6.04/6.25 452 -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].
% 6.04/6.25 453 -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].
% 6.04/6.25 454 -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].
% 6.04/6.25 455 -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].
% 6.04/6.25 456 -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].
% 6.04/6.25 457 -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].
% 6.04/6.25 458 -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].
% 6.04/6.25 459 -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].
% 6.04/6.25 460 -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].
% 6.04/6.25 461 -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].
% 6.04/6.25 462 -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].
% 6.04/6.25 463 -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].
% 6.04/6.25 464 -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].
% 6.04/6.25 465 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 6.04/6.25 466 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 6.04/6.25 467 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 6.04/6.25 468 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 6.04/6.25 469 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(108,b,80,b)].
% 6.04/6.25 470 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(109,b,80,b)].
% 6.04/6.25 471 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 6.04/6.31 472 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 6.04/6.31 473 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 6.04/6.31 474 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(221,c,193,b)].
% 6.04/6.31 475 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(222,c,193,b)].
% 6.04/6.31 476 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 6.04/6.31 477 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 6.04/6.31 478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 6.04/6.31 479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 6.04/6.31 480 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 6.04/6.31 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(480,b,447,a)].
% 6.04/6.31 Derived: class_HOL_Ozero(tc_nat). [resolve(480,b,448,a)].
% 6.04/6.31 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,449,b)].
% 6.04/6.31 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(480,b,450,b)].
% 6.04/6.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 6.04/6.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 6.04/6.31 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(480,b,463,b)].
% 6.04/6.31 481 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(307,a,288,b)].
% 6.04/6.31 482 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(308,a,288,b)].
% 6.04/6.31 483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 6.04/6.31 484 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 6.04/6.31 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(484,b,448,a)].
% 6.04/6.31 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(484,b,450,b)].
% 6.04/6.31 485 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 6.04/6.31 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(485,b,448,a)].
% 6.04/6.31 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(485,b,450,b)].
% 6.04/6.31 486 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 6.04/6.31 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(486,b,448,a)].
% 6.04/6.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(486,b,450,b)].
% 6.04/6.31 487 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(389,c,357,b)].
% 6.04/6.31 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(487,c,448,a)].
% 6.04/6.31 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(487,c,450,b)].
% 6.04/6.31 488 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(390,c,357,b)].
% 6.04/6.31 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(488,c,448,a)].
% 6.04/6.31 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(488,c,450,b)].
% 6.04/6.31 489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 6.04/6.31 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(489,b,448,a)].
% 6.04/6.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(489,b,450,b)].
% 6.33/6.56 490 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 6.33/6.56 491 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 6.33/6.56 492 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 6.33/6.56 493 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 6.33/6.56 494 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 6.33/6.56 495 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 6.33/6.56 496 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 6.33/6.56 497 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 6.33/6.56 498 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 6.33/6.56 499 -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].
% 6.33/6.56 500 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 6.33/6.56 501 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 6.33/6.56 502 -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].
% 6.33/6.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(502,b,494,a)].
% 6.33/6.56 503 -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].
% 6.33/6.56 504 -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].
% 6.33/6.56 505 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 6.33/6.56 506 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 6.33/6.56 507 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 6.33/6.56 508 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 6.33/6.56 509 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(108,b,76,b)].
% 6.33/6.56 510 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(109,b,76,b)].
% 6.33/6.56 511 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(511,b,491,a)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(511,b,492,b)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(511,b,500,b)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 6.33/6.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(511,b,504,b)].
% 6.33/6.60 512 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 6.33/6.60 513 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 6.33/6.60 514 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 6.33/6.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(514,b,491,a)].
% 6.33/6.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(514,b,492,b)].
% 6.33/6.60 515 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 6.33/6.60 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(515,b,491,a)].
% 6.33/6.60 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(515,b,492,b)].
% 6.33/6.60 516 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(140,c,115,b)].
% 6.33/6.60 517 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(141,c,115,b)].
% 6.33/6.60 518 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 6.33/6.60 519 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 6.33/6.60 520 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 6.33/6.60 521 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 6.33/6.60 522 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 6.33/6.60 523 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 6.33/6.60 524 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 6.33/6.60 525 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 6.33/6.60 526 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(263,c,233,b)].
% 6.33/6.60 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(526,c,491,a)].
% 6.33/6.60 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(526,c,492,b)].
% 6.33/6.60 527 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(264,c,233,b)].
% 6.33/6.60 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(527,c,491,a)].
% 6.33/6.60 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(527,c,492,b)].
% 6.33/6.60 528 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 6.33/6.60 529 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 6.33/6.60 530 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 6.33/6.60 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(530,b,491,a)].
% 6.42/6.63 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(530,b,492,b)].
% 6.42/6.63 531 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 6.42/6.63 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(531,b,491,a)].
% 6.42/6.63 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(531,b,492,b)].
% 6.42/6.63 532 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(307,a,286,b)].
% 6.42/6.63 533 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(308,a,286,b)].
% 6.42/6.63 534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 6.42/6.63 535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 6.42/6.63 536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 6.42/6.63 537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(389,c,355,b)].
% 6.42/6.63 538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(390,c,355,b)].
% 6.42/6.63 539 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 6.42/6.63 540 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 6.42/6.63 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(540,b,491,a)].
% 6.42/6.63 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(540,b,492,b)].
% 6.42/6.63 541 -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(A). [resolve(413,b,396,b)].
% 6.42/6.63 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(541,c,491,a)].
% 6.42/6.63 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(541,c,492,b)].
% 6.42/6.63 542 -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(A). [resolve(414,b,396,b)].
% 6.42/6.63 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(542,c,491,a)].
% 6.42/6.63 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A). [resolve(542,c,492,b)].
% 6.42/6.63 543 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ocomm__ring(B). [resolve(415,a,396,b)].
% 6.42/6.63 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(543,b,491,a)].
% 6.42/6.63 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(543,b,492,b)].
% 6.42/6.63 544 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring(B). [resolve(416,a,396,b)].
% 6.42/6.63 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(544,b,491,a)].
% 6.42/6.63 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(544,b,492,b)].
% 6.42/6.63 545 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ocomm__ring(C). [resolve(417,a,396,b)].
% 6.42/6.63 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(545,b,491,a)].
% 6.51/6.72 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(545,b,492,b)].
% 6.51/6.72 546 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 6.51/6.72 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(546,b,491,a)].
% 6.51/6.72 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(546,b,492,b)].
% 6.51/6.72 547 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 6.51/6.72 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(547,b,491,a)].
% 6.51/6.72 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(547,b,492,b)].
% 6.51/6.72 548 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 6.51/6.72 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(548,b,491,a)].
% 6.51/6.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(548,b,492,b)].
% 6.51/6.72 549 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(442,c,396,b)].
% 6.51/6.72 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(549,c,491,a)].
% 6.51/6.72 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(549,c,492,b)].
% 6.51/6.72 550 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(443,c,396,b)].
% 6.51/6.72 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(550,c,491,a)].
% 6.51/6.72 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(550,c,492,b)].
% 6.51/6.72 551 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 6.51/6.72 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(551,b,491,a)].
% 6.51/6.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(551,b,492,b)].
% 6.51/6.72 552 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(552,b,491,a)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(552,b,492,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(552,b,500,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(552,b,501,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(552,b,502,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(552,b,503,b)].
% 6.51/6.72 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(552,b,504,b)].
% 6.51/6.72 553 -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].
% 6.51/6.72 554 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 6.51/6.72 555 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 6.51/6.72 556 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 6.51/6.72 557 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 6.51/6.72 558 -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].
% 6.51/6.72 559 -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].
% 6.51/6.72 560 -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].
% 6.51/6.72 561 -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].
% 6.64/6.85 562 -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].
% 6.64/6.85 563 -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].
% 6.64/6.85 564 -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].
% 6.64/6.85 565 -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].
% 6.64/6.85 566 -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].
% 6.64/6.85 567 -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].
% 6.64/6.85 568 -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].
% 6.64/6.85 569 -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].
% 6.64/6.85 Derived: c_0 != c_1. [resolve(569,a,554,a)].
% 6.64/6.85 570 -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].
% 6.64/6.85 Derived: c_1 != c_0. [resolve(570,a,554,a)].
% 6.64/6.85 571 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(43,a,50,b)].
% 6.64/6.85 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(571,d,554,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(571,d,555,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(571,d,556,b)].
% 6.64/6.85 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(571,d,557,b)].
% 6.64/6.85 572 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(63,a,50,b)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(572,d,554,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(572,d,555,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(572,d,556,b)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(572,d,557,b)].
% 6.64/6.85 573 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(64,a,50,b)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(573,d,554,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(573,d,555,a)].
% 6.64/6.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(573,d,556,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(573,d,557,b)].
% 6.64/6.86 574 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(65,a,50,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(574,d,554,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(574,d,555,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(574,d,556,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(574,d,557,b)].
% 6.64/6.86 575 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(66,a,50,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(575,d,554,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(575,d,555,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(575,d,556,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(575,d,557,b)].
% 6.64/6.86 576 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(67,a,50,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(576,d,554,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(576,d,555,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(576,d,556,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(576,d,557,b)].
% 6.64/6.86 577 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(68,a,50,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(577,d,554,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(577,d,555,a)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(577,d,556,b)].
% 6.64/6.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(577,d,557,b)].
% 6.64/6.86 578 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(69,a,50,b)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(578,d,554,a)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(578,d,555,a)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(578,d,556,b)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(578,d,557,b)].
% 6.83/7.03 579 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(70,a,50,b)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(579,d,554,a)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(579,d,555,a)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(579,d,556,b)].
% 6.83/7.03 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(579,d,557,b)].
% 6.83/7.03 580 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 6.83/7.03 581 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 6.83/7.03 582 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 6.83/7.03 583 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 6.83/7.03 584 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 6.83/7.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 6.83/7.03 585 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 6.83/7.03 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 6.83/7.03 586 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 6.83/7.03 587 -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].
% 6.83/7.03 588 -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].
% 6.83/7.03 589 -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].
% 6.83/7.03 590 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 6.83/7.03 591 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 6.83/7.03 592 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 6.83/7.03 593 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 6.91/7.16 594 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 6.91/7.16 595 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 6.91/7.16 596 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 6.91/7.16 597 -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].
% 6.91/7.16 598 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 6.91/7.16 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(598,a,581,a)].
% 6.91/7.16 Derived: c_times(c_1,A,tc_nat) = A. [resolve(598,a,582,a)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(598,a,583,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(598,a,586,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(598,a,592,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 6.91/7.16 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 6.91/7.16 599 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 6.91/7.16 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(599,a,581,a)].
% 6.91/7.16 Derived: c_times(A,c_1,tc_nat) = A. [resolve(599,a,582,a)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(599,a,583,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(599,a,586,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(599,a,592,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 6.91/7.16 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 6.91/7.16 600 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(43,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(600,d,584,b)].
% 7.13/7.36 601 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(63,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(601,d,584,b)].
% 7.13/7.36 602 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(64,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(602,d,584,b)].
% 7.13/7.36 603 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(65,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(603,d,584,b)].
% 7.13/7.36 604 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(66,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(604,d,584,b)].
% 7.13/7.36 605 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(67,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(605,d,584,b)].
% 7.13/7.36 606 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(68,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(606,d,584,b)].
% 7.13/7.36 607 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(69,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(607,d,584,b)].
% 7.13/7.36 608 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Omonoid__mult(A). [resolve(70,a,48,b)].
% 7.13/7.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(608,d,584,b)].
% 7.13/7.36 609 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 7.13/7.36 610 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_24) # label(axiom). [assumption].
% 7.13/7.36 611 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat_24) # label(axiom). [assumption].
% 7.13/7.36 612 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 7.13/7.36 613 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_2) # label(axiom). [assumption].
% 7.13/7.36 614 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_3) # label(axiom). [assumption].
% 7.35/7.60 615 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Power_Orecpower_16) # label(axiom). [assumption].
% 7.35/7.60 616 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_21) # label(axiom). [assumption].
% 7.35/7.60 617 -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].
% 7.35/7.60 618 -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].
% 7.35/7.60 619 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_8) # label(axiom). [assumption].
% 7.35/7.60 620 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 7.35/7.60 621 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_11) # label(axiom). [assumption].
% 7.35/7.60 622 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_8) # label(axiom). [assumption].
% 7.35/7.60 623 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 7.35/7.60 624 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(43,a,47,b)].
% 7.35/7.60 625 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(63,a,47,b)].
% 7.35/7.60 626 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(64,a,47,b)].
% 7.35/7.60 627 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(65,a,47,b)].
% 7.35/7.60 628 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(66,a,47,b)].
% 7.35/7.60 629 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(67,a,47,b)].
% 7.35/7.60 630 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(68,a,47,b)].
% 7.35/7.60 631 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(69,a,47,b)].
% 7.35/7.60 632 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(70,a,47,b)].
% 7.35/7.60 633 class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(633,b,610,a)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(633,b,611,a)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(633,b,612,b)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(633,b,615,b)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 7.35/7.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 7.35/7.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(633,b,619,b)].
% 7.35/7.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 7.35/7.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(633,b,621,b)].
% 7.35/7.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 7.35/7.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 7.35/7.61 634 class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(634,b,610,a)].
% 7.35/7.61 Derived: class_HOL_Otimes(tc_nat). [resolve(634,b,611,a)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(634,b,612,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(634,b,615,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(634,b,616,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(634,b,619,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(634,b,620,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(634,b,621,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(634,b,622,b)].
% 7.35/7.61 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(634,b,623,b)].
% 7.35/7.61 635 c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 7.35/7.61 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(635,b,610,a)].
% 7.35/7.61 Derived: c_times(c_1,A,tc_nat) = A. [resolve(635,b,611,a)].
% 7.35/7.61 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(635,b,612,b)].
% 7.35/7.61 636 c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 7.35/7.61 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(636,b,610,a)].
% 7.35/7.61 Derived: c_times(A,c_1,tc_nat) = A. [resolve(636,b,611,a)].
% 7.35/7.61 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(636,b,612,b)].
% 7.35/7.61 637 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(600,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(637,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(637,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(637,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(637,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(637,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(637,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(637,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(637,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(637,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(637,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(637,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(637,d,623,b)].
% 7.35/7.61 638 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(601,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(638,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(638,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(638,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(638,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(638,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(638,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(638,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(638,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(638,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(638,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(638,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(638,d,623,b)].
% 7.35/7.61 639 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(602,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(639,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(639,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(639,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(639,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(639,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(639,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(639,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(639,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(639,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(639,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(639,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(639,d,623,b)].
% 7.35/7.61 640 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(603,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(640,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(640,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(640,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(640,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(640,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(640,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(640,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(640,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(640,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(640,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(640,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(640,d,623,b)].
% 7.35/7.61 641 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(604,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(641,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(641,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(641,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(641,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(641,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(641,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(641,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(641,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(641,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(641,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(641,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(641,d,623,b)].
% 7.35/7.61 642 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(605,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(642,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(642,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(642,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(642,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(642,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(642,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(642,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(642,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(642,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(642,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(642,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(642,d,623,b)].
% 7.35/7.61 643 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(606,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(643,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(643,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(643,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(643,d,615,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(643,d,616,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(643,d,617,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(643,d,618,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(643,d,619,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(643,d,620,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(643,d,621,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(643,d,622,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(643,d,623,b)].
% 7.35/7.61 644 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(607,d,584,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(644,d,610,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(644,d,611,a)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(644,d,612,b)].
% 7.35/7.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(644,d,615,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(644,d,616,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(644,d,617,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(644,d,618,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(644,d,619,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(644,d,620,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(644,d,621,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(644,d,622,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(644,d,623,b)].
% 7.51/7.71 645 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(608,d,584,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(645,d,610,a)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(645,d,611,a)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(645,d,612,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(645,d,615,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(645,d,616,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(645,d,617,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(645,d,618,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(645,d,619,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(645,d,620,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(645,d,621,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(645,d,622,b)].
% 7.51/7.71 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(645,d,623,b)].
% 7.51/7.71 646 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 7.65/7.86 647 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 7.65/7.86 648 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 7.65/7.86 649 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 7.65/7.86 650 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 7.65/7.86 651 -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].
% 7.65/7.86 652 -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].
% 7.65/7.86 653 -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].
% 7.65/7.86 654 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 7.65/7.86 655 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 7.65/7.86 656 -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].
% 7.65/7.86 657 -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].
% 7.65/7.86 658 -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].
% 7.65/7.86 659 -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].
% 7.65/7.86 660 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 7.65/7.86 661 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 7.65/7.86 662 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 7.65/7.86 663 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 7.65/7.86 664 -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].
% 7.65/7.86 665 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(43,a,60,b)].
% 7.65/7.86 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(665,d,659,b)].
% 7.65/7.86 666 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(63,a,60,b)].
% 7.65/7.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(666,d,659,b)].
% 7.65/7.86 667 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(64,a,60,b)].
% 7.65/7.86 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(667,d,659,b)].
% 7.65/7.86 668 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(65,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(668,d,659,b)].
% 7.81/8.00 669 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(66,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(669,d,659,b)].
% 7.81/8.00 670 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(67,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(670,d,659,b)].
% 7.81/8.00 671 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(68,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(671,d,659,b)].
% 7.81/8.00 672 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(69,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(672,d,659,b)].
% 7.81/8.00 673 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(70,a,60,b)].
% 7.81/8.00 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(673,d,659,b)].
% 7.81/8.00 674 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(108,b,106,b)].
% 7.81/8.00 675 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(109,b,106,b)].
% 7.81/8.00 676 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 7.81/8.00 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 7.81/8.00 677 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 7.81/8.00 678 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 7.81/8.00 679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 7.81/8.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 7.81/8.00 680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 7.81/8.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 7.81/8.00 681 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 7.81/8.00 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(681,b,650,b)].
% 7.81/8.00 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 7.81/8.00 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 7.81/8.00 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 7.81/8.00 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 7.91/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 7.91/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(681,b,656,b)].
% 7.91/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 7.91/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 7.91/8.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 7.91/8.11 682 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(682,b,650,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(682,b,656,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 7.91/8.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 7.91/8.11 683 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 7.91/8.11 684 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 7.91/8.11 685 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 7.91/8.11 686 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 7.91/8.11 687 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 7.91/8.11 688 -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].
% 7.91/8.11 689 -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].
% 7.91/8.11 690 -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].
% 7.91/8.11 691 -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].
% 7.91/8.11 692 -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].
% 7.91/8.11 693 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 7.91/8.11 694 -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].
% 7.91/8.11 695 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 7.91/8.11 696 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 7.91/8.11 697 -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].
% 7.91/8.11 698 -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].
% 8.10/8.29 699 -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].
% 8.10/8.29 700 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(43,a,52,b)].
% 8.10/8.29 701 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(63,a,52,b)].
% 8.10/8.29 702 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(64,a,52,b)].
% 8.10/8.29 703 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(65,a,52,b)].
% 8.10/8.29 704 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(66,a,52,b)].
% 8.10/8.29 705 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(67,a,52,b)].
% 8.10/8.29 706 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(68,a,52,b)].
% 8.10/8.29 707 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(69,a,52,b)].
% 8.10/8.29 708 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(70,a,52,b)].
% 8.10/8.29 709 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 8.10/8.29 710 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 8.10/8.29 711 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 8.10/8.29 712 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 8.10/8.29 713 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(108,b,81,b)].
% 8.10/8.29 714 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(109,b,81,b)].
% 8.10/8.29 715 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 8.10/8.29 716 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 8.10/8.29 717 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 8.10/8.29 718 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(221,c,194,b)].
% 8.10/8.29 719 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(222,c,194,b)].
% 8.10/8.29 720 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 8.10/8.29 721 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 8.10/8.29 722 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 8.10/8.29 723 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 8.17/8.36 724 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 8.17/8.36 725 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 8.17/8.36 726 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 8.17/8.36 727 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 8.17/8.36 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(727,b,684,a)].
% 8.17/8.36 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(727,b,685,a)].
% 8.17/8.36 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(727,b,686,b)].
% 8.17/8.36 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(727,b,687,b)].
% 8.17/8.36 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 8.17/8.36 728 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 8.17/8.36 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(728,b,684,a)].
% 8.17/8.36 Derived: class_HOL_Otimes(tc_nat). [resolve(728,b,685,a)].
% 8.17/8.36 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,686,b)].
% 8.17/8.36 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(728,b,687,b)].
% 8.17/8.36 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(728,b,688,b)].
% 8.17/8.36 729 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(637,d,617,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(729,d,684,a)].
% 8.17/8.36 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(729,d,685,a)].
% 8.17/8.36 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(729,d,686,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(729,d,687,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(729,d,688,b)].
% 8.17/8.36 730 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(638,d,617,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(730,d,684,a)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(730,d,685,a)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(730,d,686,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(730,d,687,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(730,d,688,b)].
% 8.17/8.36 731 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(639,d,617,b)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(731,d,684,a)].
% 8.17/8.36 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(731,d,685,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(731,d,686,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(731,d,687,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(731,d,688,b)].
% 8.17/8.37 732 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(640,d,617,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(732,d,684,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(732,d,685,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(732,d,686,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(732,d,687,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(732,d,688,b)].
% 8.17/8.37 733 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(641,d,617,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(733,d,684,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(733,d,685,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(733,d,686,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(733,d,687,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(733,d,688,b)].
% 8.17/8.37 734 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(642,d,617,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(734,d,684,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(734,d,685,a)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(734,d,686,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(734,d,687,b)].
% 8.17/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(734,d,688,b)].
% 8.17/8.37 735 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(643,d,617,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(735,d,684,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(735,d,685,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(735,d,686,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(735,d,687,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(735,d,688,b)].
% 8.20/8.37 736 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(644,d,617,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(736,d,684,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(736,d,685,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(736,d,686,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(736,d,687,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(736,d,688,b)].
% 8.20/8.37 737 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(645,d,617,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(737,d,684,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(737,d,685,a)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(737,d,686,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(737,d,687,b)].
% 8.20/8.37 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(737,d,688,b)].
% 8.20/8.37 738 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(738,b,684,a)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(738,b,685,a)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(738,b,686,b)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(738,b,687,b)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 8.20/8.37 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(738,b,695,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(738,b,697,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 8.26/8.46 739 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(739,b,684,a)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(739,b,685,a)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(739,b,686,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(739,b,687,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(739,b,695,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(739,b,697,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 8.26/8.46 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 8.26/8.46 740 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 8.26/8.46 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(740,b,684,a)].
% 8.26/8.46 Derived: c_times(c_1,A,tc_nat) = A. [resolve(740,b,685,a)].
% 8.26/8.46 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(740,b,686,b)].
% 8.26/8.46 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(740,b,687,b)].
% 8.26/8.46 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 8.26/8.46 741 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 8.26/8.46 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(741,b,684,a)].
% 8.26/8.46 Derived: c_times(A,c_1,tc_nat) = A. [resolve(741,b,685,a)].
% 8.26/8.46 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(741,b,686,b)].
% 8.26/8.46 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(741,b,687,b)].
% 8.26/8.46 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 8.26/8.46 742 -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].
% 8.26/8.46 743 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 8.26/8.46 744 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 8.26/8.46 745 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 8.26/8.46 746 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 8.26/8.46 747 -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].
% 8.26/8.46 748 -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].
% 8.26/8.46 749 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 8.41/8.63 750 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 8.41/8.63 751 -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].
% 8.41/8.63 752 -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].
% 8.41/8.63 753 -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].
% 8.41/8.63 754 -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].
% 8.41/8.63 755 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 8.41/8.63 756 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 8.41/8.63 757 -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].
% 8.41/8.63 758 -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].
% 8.41/8.63 759 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(43,a,61,b)].
% 8.41/8.63 760 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(63,a,61,b)].
% 8.41/8.63 761 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(64,a,61,b)].
% 8.41/8.63 762 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(65,a,61,b)].
% 8.41/8.63 763 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(66,a,61,b)].
% 8.41/8.63 764 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(67,a,61,b)].
% 8.41/8.63 765 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(68,a,61,b)].
% 8.41/8.63 766 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(69,a,61,b)].
% 8.41/8.63 767 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(70,a,61,b)].
% 8.41/8.63 768 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 8.41/8.63 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 8.41/8.63 769 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 8.41/8.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 8.41/8.63 770 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(108,b,107,b)].
% 8.41/8.63 771 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(109,b,107,b)].
% 8.64/8.82 772 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 8.64/8.82 773 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 8.64/8.82 774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 8.64/8.82 775 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 8.64/8.82 776 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(307,a,306,b)].
% 8.64/8.82 777 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Osemiring__1__cancel(C). [resolve(308,a,306,b)].
% 8.64/8.82 778 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 8.64/8.82 779 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 8.64/8.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 8.64/8.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 8.64/8.82 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 8.64/8.82 780 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 8.64/8.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 8.64/8.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 8.64/8.82 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 8.64/8.82 781 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 8.64/8.82 782 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 8.64/8.82 783 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(783,b,743,a)].
% 8.64/8.82 Derived: class_HOL_Ozero(tc_nat). [resolve(783,b,744,a)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(783,b,745,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(783,b,746,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(783,b,749,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(783,b,750,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(783,b,751,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(783,b,752,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(783,b,753,b)].
% 8.64/8.82 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 8.64/8.82 784 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 8.64/8.82 785 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 8.64/8.82 786 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 8.64/8.82 787 -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].
% 8.64/8.82 788 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 8.64/8.82 789 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 8.64/8.82 790 -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].
% 8.78/8.98 791 -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].
% 8.78/8.98 792 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 8.78/8.98 793 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 8.78/8.98 794 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 8.78/8.98 795 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 8.78/8.98 796 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 8.78/8.98 797 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(43,a,59,b)].
% 8.78/8.98 798 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(63,a,59,b)].
% 8.78/8.98 799 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(64,a,59,b)].
% 8.78/8.98 800 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(65,a,59,b)].
% 8.78/8.98 801 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(66,a,59,b)].
% 8.78/8.98 802 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(67,a,59,b)].
% 8.78/8.98 803 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(68,a,59,b)].
% 8.78/8.98 804 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(69,a,59,b)].
% 8.78/8.98 805 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(70,a,59,b)].
% 8.78/8.98 806 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 8.78/8.98 807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 8.78/8.98 808 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 8.78/8.98 809 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 8.78/8.98 810 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(108,b,99,b)].
% 8.78/8.98 811 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(109,b,99,b)].
% 8.78/8.98 812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 8.78/8.98 813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 8.78/8.98 814 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 8.78/8.98 815 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(221,c,212,b)].
% 8.78/8.98 816 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(222,c,212,b)].
% 8.82/9.02 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 8.82/9.02 818 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 8.82/9.02 819 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 8.82/9.02 820 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 8.82/9.02 821 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(307,a,304,b)].
% 8.82/9.02 822 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(308,a,304,b)].
% 8.82/9.02 823 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 8.82/9.02 824 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 8.82/9.02 825 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 8.82/9.02 826 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 8.82/9.02 827 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(389,c,373,b)].
% 8.82/9.02 828 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(390,c,373,b)].
% 8.82/9.02 829 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 8.82/9.02 830 -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_Oring__1(A). [resolve(413,b,412,b)].
% 8.82/9.02 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(830,c,787,b)].
% 8.82/9.02 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(830,c,788,b)].
% 8.82/9.02 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(830,c,789,b)].
% 8.82/9.02 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(830,c,790,b)].
% 8.82/9.02 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(830,c,791,b)].
% 8.82/9.02 831 -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_Oring__1(A). [resolve(414,b,412,b)].
% 8.82/9.02 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(831,c,787,b)].
% 8.82/9.02 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(831,c,788,b)].
% 8.82/9.02 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(831,c,789,b)].
% 8.82/9.02 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(831,c,790,b)].
% 8.87/9.07 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(831,c,791,b)].
% 8.87/9.07 832 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oring__1(B). [resolve(415,a,412,b)].
% 8.87/9.07 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(832,b,787,b)].
% 8.87/9.07 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(832,b,788,b)].
% 8.87/9.07 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(832,b,789,b)].
% 8.87/9.07 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(832,b,790,b)].
% 8.87/9.07 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(832,b,791,b)].
% 8.87/9.07 833 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oring__1(B). [resolve(416,a,412,b)].
% 8.87/9.07 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(833,b,787,b)].
% 8.87/9.07 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(833,b,788,b)].
% 8.87/9.07 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(833,b,789,b)].
% 8.87/9.07 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(833,b,790,b)].
% 8.87/9.07 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(833,b,791,b)].
% 8.87/9.07 834 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oring__1(C). [resolve(417,a,412,b)].
% 8.87/9.07 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(834,b,787,b)].
% 8.87/9.07 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(834,b,788,b)].
% 8.87/9.07 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(834,b,789,b)].
% 8.87/9.07 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(834,b,790,b)].
% 8.87/9.07 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(834,b,791,b)].
% 8.87/9.07 835 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 8.87/9.07 836 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 8.87/9.07 837 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(665,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(837,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(837,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(837,d,790,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(837,d,791,b)].
% 8.87/9.07 838 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(666,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(838,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(838,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(838,d,790,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(838,d,791,b)].
% 8.87/9.07 839 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(667,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(839,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(839,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(839,d,790,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(839,d,791,b)].
% 8.87/9.07 840 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(668,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(840,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(840,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(840,d,790,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(840,d,791,b)].
% 8.87/9.07 841 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(669,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(841,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(841,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(841,d,790,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(841,d,791,b)].
% 8.87/9.07 842 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(670,d,659,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(842,d,788,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(842,d,789,b)].
% 8.87/9.07 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(842,d,790,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(842,d,791,b)].
% 8.87/9.09 843 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(671,d,659,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(843,d,788,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(843,d,789,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(843,d,790,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(843,d,791,b)].
% 8.87/9.09 844 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(672,d,659,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(844,d,788,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(844,d,789,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(844,d,790,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(844,d,791,b)].
% 8.87/9.09 845 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(673,d,659,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(845,d,788,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(845,d,789,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(845,d,790,b)].
% 8.87/9.09 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(845,d,791,b)].
% 8.87/9.09 846 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 8.87/9.09 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 8.87/9.09 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 8.87/9.09 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(846,b,790,b)].
% 8.87/9.09 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 8.87/9.09 847 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 8.87/9.09 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 8.87/9.09 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 8.87/9.09 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(847,b,790,b)].
% 8.87/9.09 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 8.87/9.09 848 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(848,b,785,a)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(848,b,786,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(848,b,788,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(848,b,790,b)].
% 9.00/9.17 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 9.00/9.17 849 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(849,b,785,a)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(849,b,786,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(849,b,787,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(849,b,788,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(849,b,789,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(849,b,790,b)].
% 9.00/9.17 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(849,b,791,b)].
% 9.00/9.17 850 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 9.00/9.17 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(850,b,785,a)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(850,b,786,b)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(850,b,790,b)].
% 9.00/9.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 9.00/9.17 851 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 9.00/9.17 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(851,b,785,a)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(851,b,786,b)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(851,b,790,b)].
% 9.00/9.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 9.00/9.17 852 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(852,b,785,a)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(852,b,786,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(852,b,788,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(852,b,789,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(852,b,790,b)].
% 9.00/9.17 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(852,b,791,b)].
% 9.00/9.17 853 -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].
% 9.00/9.17 854 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 9.00/9.17 855 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 9.00/9.20 856 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 9.00/9.20 857 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 9.00/9.20 858 -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].
% 9.00/9.20 859 -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].
% 9.00/9.20 860 -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].
% 9.00/9.20 861 -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].
% 9.00/9.20 862 -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].
% 9.00/9.20 863 -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].
% 9.00/9.20 864 -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].
% 9.00/9.20 865 -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].
% 9.00/9.20 866 -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].
% 9.00/9.20 867 -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].
% 9.00/9.20 868 -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].
% 9.00/9.20 869 -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].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(869,a,854,a)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(869,a,855,a)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(869,a,856,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(869,a,857,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(869,a,866,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 9.00/9.20 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 9.00/9.20 870 -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].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(870,a,854,a)].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(870,a,855,a)].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(870,a,856,b)].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(870,a,857,b)].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 9.00/9.20 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 9.00/9.22 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 9.00/9.22 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(870,a,866,b)].
% 9.00/9.22 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 9.00/9.22 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 9.00/9.22 871 -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].
% 9.00/9.22 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(871,a,854,a)].
% 9.00/9.22 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(871,a,855,a)].
% 9.00/9.22 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_Numeral_Onumber__ring(B). [resolve(871,a,856,b)].
% 9.00/9.22 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_Power_Orecpower(B). [resolve(871,a,857,b)].
% 9.00/9.22 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_Ocomm__ring__1(B). [resolve(871,a,858,b)].
% 9.00/9.22 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(871,a,864,b)].
% 9.00/9.22 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_Oidom(B). [resolve(871,a,865,b)].
% 9.00/9.22 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(871,a,866,b)].
% 9.00/9.22 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(871,a,867,b)].
% 9.00/9.22 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__semidom(B). [resolve(871,a,868,b)].
% 9.00/9.22 872 -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].
% 9.00/9.22 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(872,a,854,a)].
% 9.00/9.22 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(872,a,855,a)].
% 9.00/9.22 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_Numeral_Onumber__ring(B). [resolve(872,a,856,b)].
% 9.00/9.22 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_Power_Orecpower(B). [resolve(872,a,857,b)].
% 9.00/9.22 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_Ocomm__ring__1(B). [resolve(872,a,858,b)].
% 9.00/9.22 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(872,a,864,b)].
% 9.00/9.22 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_Oidom(B). [resolve(872,a,865,b)].
% 9.00/9.22 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(872,a,866,b)].
% 9.00/9.22 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(872,a,867,b)].
% 9.00/9.22 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__semidom(B). [resolve(872,a,868,b)].
% 9.00/9.24 873 -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].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(873,a,854,a)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(873,a,855,a)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(873,a,856,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Power_Orecpower(B). [resolve(873,a,857,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(873,a,858,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(873,a,866,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(873,a,867,b)].
% 9.00/9.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(873,a,868,b)].
% 9.00/9.24 874 -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].
% 9.00/9.24 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(874,a,854,a)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(874,a,855,a)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Numeral_Onumber__ring(B). [resolve(874,a,856,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Power_Orecpower(B). [resolve(874,a,857,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(874,a,858,b)].
% 9.00/9.24 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(874,a,864,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oidom(B). [resolve(874,a,865,b)].
% 9.00/9.24 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(874,a,866,b)].
% 9.00/9.24 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(874,a,867,b)].
% 9.00/9.24 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__semidom(B). [resolve(874,a,868,b)].
% 9.00/9.24 875 -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].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(875,a,854,a)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(875,a,855,a)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(875,a,856,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Power_Orecpower(A). [resolve(875,a,857,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 9.00/9.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(875,a,866,b)].
% 9.00/9.25 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 9.00/9.25 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 9.00/9.25 876 -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].
% 9.00/9.25 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(876,a,854,a)].
% 9.00/9.25 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(876,a,855,a)].
% 9.00/9.25 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_Numeral_Onumber__ring(C). [resolve(876,a,856,b)].
% 9.00/9.25 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_Power_Orecpower(C). [resolve(876,a,857,b)].
% 9.00/9.25 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_Ocomm__ring__1(C). [resolve(876,a,858,b)].
% 9.00/9.25 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(876,a,864,b)].
% 9.00/9.25 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_Oidom(C). [resolve(876,a,865,b)].
% 9.00/9.25 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(876,a,866,b)].
% 9.00/9.25 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(876,a,867,b)].
% 9.00/9.25 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__semidom(C). [resolve(876,a,868,b)].
% 9.00/9.25 877 -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].
% 9.00/9.25 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(877,a,854,a)].
% 9.00/9.25 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(877,a,855,a)].
% 9.00/9.25 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_Numeral_Onumber__ring(C). [resolve(877,a,856,b)].
% 9.00/9.25 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_Power_Orecpower(C). [resolve(877,a,857,b)].
% 9.00/9.25 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_Ocomm__ring__1(C). [resolve(877,a,858,b)].
% 9.00/9.25 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(877,a,864,b)].
% 9.00/9.25 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_Oidom(C). [resolve(877,a,865,b)].
% 9.00/9.25 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(877,a,866,b)].
% 9.00/9.25 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(877,a,867,b)].
% 9.18/9.38 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__semidom(C). [resolve(877,a,868,b)].
% 9.18/9.38 878 -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].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(878,a,854,a)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(878,a,855,a)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(878,a,856,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Power_Orecpower(A). [resolve(878,a,857,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(878,a,866,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 9.18/9.38 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 9.18/9.38 879 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(43,a,53,b)].
% 9.18/9.38 880 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(63,a,53,b)].
% 9.18/9.38 881 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(64,a,53,b)].
% 9.18/9.38 882 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(65,a,53,b)].
% 9.18/9.38 883 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(66,a,53,b)].
% 9.18/9.38 884 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(67,a,53,b)].
% 9.18/9.38 885 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(68,a,53,b)].
% 9.18/9.38 886 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(69,a,53,b)].
% 9.18/9.38 887 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(70,a,53,b)].
% 9.18/9.38 888 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 9.18/9.38 889 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 9.18/9.38 890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 9.18/9.38 891 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 9.18/9.38 892 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(108,b,82,b)].
% 9.18/9.38 893 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(109,b,82,b)].
% 9.18/9.38 894 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 9.27/9.47 895 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 9.27/9.47 896 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 9.27/9.47 897 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(221,c,195,b)].
% 9.27/9.47 898 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(222,c,195,b)].
% 9.27/9.47 899 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 9.27/9.47 900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 9.27/9.47 901 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 9.27/9.47 902 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 9.27/9.47 903 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 9.27/9.47 904 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(307,a,289,b)].
% 9.27/9.47 905 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(308,a,289,b)].
% 9.27/9.47 906 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 9.27/9.47 907 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 9.27/9.47 908 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 9.27/9.47 909 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 9.27/9.47 910 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(389,c,358,b)].
% 9.27/9.47 911 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C). [resolve(390,c,358,b)].
% 9.27/9.47 912 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 9.27/9.47 913 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 9.27/9.47 914 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 9.27/9.47 915 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 9.27/9.47 916 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 9.27/9.47 917 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(637,d,618,b)].
% 9.27/9.47 918 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(638,d,618,b)].
% 9.27/9.47 919 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(639,d,618,b)].
% 9.27/9.47 920 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(640,d,618,b)].
% 9.27/9.47 921 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(641,d,618,b)].
% 9.27/9.47 922 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(642,d,618,b)].
% 9.27/9.47 923 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(643,d,618,b)].
% 9.75/9.91 924 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(644,d,618,b)].
% 9.75/9.91 925 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(645,d,618,b)].
% 9.75/9.91 926 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 9.75/9.91 927 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 9.75/9.91 928 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(928,b,854,a)].
% 9.75/9.91 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(928,b,855,a)].
% 9.75/9.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(928,b,856,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(928,b,857,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 9.75/9.91 929 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(929,b,854,a)].
% 9.75/9.91 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(929,b,855,a)].
% 9.75/9.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(929,b,856,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(929,b,857,b)].
% 9.75/9.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 9.75/9.91 930 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 9.75/9.91 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(930,b,855,a)].
% 9.75/9.91 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(930,b,857,b)].
% 9.75/9.91 931 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 9.75/9.91 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(931,b,855,a)].
% 9.75/9.91 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(931,b,857,b)].
% 9.75/9.91 932 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 9.75/9.91 Derived: class_HOL_Ozero(tc_nat). [resolve(932,b,855,a)].
% 9.75/9.91 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(932,b,857,b)].
% 9.75/9.91 933 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_11) # label(axiom). [assumption].
% 9.75/9.91 934 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_30) # label(axiom). [assumption].
% 9.75/9.91 935 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 9.75/9.91 936 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_14) # label(axiom). [assumption].
% 9.75/9.91 937 -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].
% 9.75/9.91 938 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_18) # label(axiom). [assumption].
% 9.75/9.91 939 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_2) # label(axiom). [assumption].
% 9.75/9.91 940 -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].
% 9.75/9.91 941 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Ofield_0) # label(axiom). [assumption].
% 9.76/9.93 942 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 9.76/9.93 943 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_3) # label(axiom). [assumption].
% 9.76/9.93 944 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_0) # label(axiom). [assumption].
% 9.76/9.93 945 -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_OInts,A) # label(cls_IntDef_OInts__0_0) # label(axiom). [assumption].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(945,a,934,a)].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(945,a,935,b)].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(945,a,943,b)].
% 9.76/9.93 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 9.76/9.93 946 -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_OInts,A) # label(cls_IntDef_OInts__1_0) # label(axiom). [assumption].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(946,a,934,a)].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(946,a,935,b)].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(946,a,943,b)].
% 9.76/9.93 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 9.76/9.93 947 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__add_0) # label(axiom). [assumption].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(947,a,934,a)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Numeral_Onumber__ring(B). [resolve(947,a,935,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(947,a,941,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(947,a,942,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(947,a,943,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(947,a,944,b)].
% 9.76/9.93 948 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__diff_0) # label(axiom). [assumption].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_minus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(948,a,934,a)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Numeral_Onumber__ring(B). [resolve(948,a,935,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(948,a,941,b)].
% 9.76/9.93 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(948,a,942,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(948,a,943,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(948,a,944,b)].
% 9.76/9.94 949 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__minus_0) # label(axiom). [assumption].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_uminus(A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(949,a,934,a)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Numeral_Onumber__ring(B). [resolve(949,a,935,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(949,a,941,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(949,a,942,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(949,a,943,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(949,a,944,b)].
% 9.76/9.94 950 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__mult_0) # label(axiom). [assumption].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(950,a,934,a)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Numeral_Onumber__ring(B). [resolve(950,a,935,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(950,a,941,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(950,a,942,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(950,a,943,b)].
% 9.76/9.94 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(950,a,944,b)].
% 9.76/9.94 951 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_1,A) = c_1 # label(cls_IntDef_Oof__int__1_0) # label(axiom). [assumption].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(951,a,934,a)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(951,a,935,b)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(951,a,943,b)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 9.76/9.94 952 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__add_0) # label(axiom). [assumption].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(952,a,934,a)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(952,a,935,b)].
% 9.76/9.94 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(952,a,941,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(952,a,942,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(952,a,943,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(952,a,944,b)].
% 9.76/9.95 953 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__diff_0) # label(axiom). [assumption].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(953,a,934,a)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(953,a,935,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(953,a,941,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(953,a,942,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(953,a,943,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(953,a,944,b)].
% 9.76/9.95 954 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A) # label(cls_IntDef_Oof__int__int__eq_0) # label(axiom). [assumption].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(954,a,934,a)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Numeral_Onumber__ring(B). [resolve(954,a,935,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(954,a,941,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oidom(B). [resolve(954,a,942,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(954,a,943,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(954,a,944,b)].
% 9.76/9.95 955 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A) # label(cls_IntDef_Oof__int__minus_0) # label(axiom). [assumption].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(955,a,934,a)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Numeral_Onumber__ring(B). [resolve(955,a,935,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(955,a,941,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(955,a,942,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(955,a,943,b)].
% 9.76/9.95 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(955,a,944,b)].
% 9.76/9.97 956 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__mult_0) # label(axiom). [assumption].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(956,a,934,a)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(956,a,935,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(956,a,941,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(956,a,942,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(956,a,943,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(956,a,944,b)].
% 9.76/9.97 957 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A) # label(cls_IntDef_Oof__int__of__nat__eq_0) # label(axiom). [assumption].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(957,a,934,a)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Numeral_Onumber__ring(B). [resolve(957,a,935,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(957,a,941,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oidom(B). [resolve(957,a,942,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(957,a,943,b)].
% 9.76/9.97 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(957,a,944,b)].
% 9.76/9.97 958 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__diff_0) # label(axiom). [assumption].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),tc_IntDef_Oint) = c_minus(c_NatArith_Oof__nat(B,tc_IntDef_Oint),c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(958,a,934,a)].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Numeral_Onumber__ring(C). [resolve(958,a,935,b)].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(958,a,941,b)].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(958,a,942,b)].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(958,a,943,b)].
% 9.76/9.97 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(958,a,944,b)].
% 9.76/9.97 959 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) # label(cls_NatBin_Opower__minus__even_0) # label(axiom). [assumption].
% 9.76/9.99 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(c_uminus(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint) = c_Nat_Opower(A,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint). [resolve(959,b,934,a)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Numeral_Onumber__ring(A). [resolve(959,b,935,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Ofield(A). [resolve(959,b,941,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oidom(A). [resolve(959,b,942,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(959,b,943,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(959,b,944,b)].
% 9.76/9.99 960 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 # label(cls_Parity_Ominus__one__even__power_0) # label(axiom). [assumption].
% 9.76/9.99 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(960,b,934,a)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(960,b,935,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(960,b,941,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(960,b,942,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(960,b,943,b)].
% 9.76/9.99 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(960,b,944,b)].
% 9.76/10.00 961 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) # label(cls_Parity_Ominus__one__odd__power_0) # label(axiom). [assumption].
% 9.76/10.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint). [resolve(961,b,934,a)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(961,b,935,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(961,b,941,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(961,b,942,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(961,b,943,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(961,b,944,b)].
% 9.76/10.00 962 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) # label(cls_Parity_Opower__minus__even_0) # label(axiom). [assumption].
% 9.76/10.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Nat_Opower(B,A,tc_IntDef_Oint). [resolve(962,b,934,a)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Numeral_Onumber__ring(A). [resolve(962,b,935,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Ofield(A). [resolve(962,b,941,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oidom(A). [resolve(962,b,942,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(962,b,943,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(962,b,944,b)].
% 9.76/10.00 963 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) # label(cls_Parity_Opower__minus__odd_0) # label(axiom). [assumption].
% 9.76/10.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_Nat_Opower(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(963,b,934,a)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(963,b,935,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(963,b,941,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(963,b,942,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(963,b,943,b)].
% 9.76/10.00 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(963,b,944,b)].
% 9.93/10.11 964 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(43,a,51,b)].
% 9.93/10.11 965 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(63,a,51,b)].
% 9.93/10.11 966 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(64,a,51,b)].
% 9.93/10.11 967 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(65,a,51,b)].
% 9.93/10.11 968 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(66,a,51,b)].
% 9.93/10.11 969 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(67,a,51,b)].
% 9.93/10.11 970 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(68,a,51,b)].
% 9.93/10.11 971 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(69,a,51,b)].
% 9.93/10.11 972 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(70,a,51,b)].
% 9.93/10.11 973 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 9.93/10.11 974 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 9.93/10.11 975 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 9.93/10.11 976 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(108,b,77,b)].
% 9.93/10.11 977 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(109,b,77,b)].
% 9.93/10.11 978 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 9.93/10.11 979 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 9.93/10.11 980 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 9.93/10.11 981 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 9.93/10.11 982 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(140,c,116,b)].
% 9.93/10.11 983 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(141,c,116,b)].
% 9.93/10.11 984 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 9.93/10.11 985 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 9.93/10.11 986 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 9.93/10.11 987 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 9.93/10.11 988 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 9.93/10.11 989 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 9.93/10.11 990 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 10.02/10.18 991 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 10.02/10.18 992 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(263,c,234,b)].
% 10.02/10.18 993 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(264,c,234,b)].
% 10.02/10.18 994 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 10.02/10.18 995 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 10.02/10.18 996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 10.02/10.18 997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 10.02/10.18 998 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(307,a,287,b)].
% 10.02/10.18 999 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(308,a,287,b)].
% 10.02/10.18 1000 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 10.02/10.18 1001 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 10.02/10.18 1002 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 10.02/10.18 1003 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(389,c,356,b)].
% 10.02/10.18 1004 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(390,c,356,b)].
% 10.02/10.18 1005 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 10.02/10.18 1006 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 10.02/10.18 1007 -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(413,b,397,b)].
% 10.02/10.18 1008 -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(414,b,397,b)].
% 10.02/10.18 1009 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(415,a,397,b)].
% 10.02/10.18 1010 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(416,a,397,b)].
% 10.02/10.18 1011 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(417,a,397,b)].
% 10.02/10.18 1012 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 10.02/10.18 1013 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 10.02/10.18 1014 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 10.02/10.18 1015 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(442,c,397,b)].
% 10.02/10.18 1016 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C). [resolve(443,c,397,b)].
% 10.02/10.18 1017 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 10.02/10.18 1018 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 10.02/10.18 1019 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 10.02/10.18 1020 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 10.02/10.18 1021 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 10.02/10.18 1022 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(637,d,616,b)].
% 10.02/10.20 1023 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(638,d,616,b)].
% 10.02/10.20 1024 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(639,d,616,b)].
% 10.02/10.20 1025 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(640,d,616,b)].
% 10.02/10.20 1026 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(641,d,616,b)].
% 10.02/10.20 1027 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(642,d,616,b)].
% 10.02/10.20 1028 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(643,d,616,b)].
% 10.02/10.20 1029 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(644,d,616,b)].
% 10.02/10.20 1030 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(645,d,616,b)].
% 10.02/10.20 1031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 10.02/10.20 1032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 10.02/10.20 1033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 10.02/10.20 1034 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(729,d,688,b)].
% 10.02/10.20 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(1034,d,934,a)].
% 10.02/10.20 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1034,d,935,b)].
% 10.02/10.20 1035 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(730,d,688,b)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1035,d,934,a)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(1035,d,935,b)].
% 10.02/10.20 1036 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(731,d,688,b)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1036,d,934,a)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(1036,d,935,b)].
% 10.02/10.20 1037 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(732,d,688,b)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1037,d,934,a)].
% 10.02/10.20 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(1037,d,935,b)].
% 10.05/10.21 1038 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(733,d,688,b)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1038,d,934,a)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(1038,d,935,b)].
% 10.05/10.21 1039 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(734,d,688,b)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1039,d,934,a)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(1039,d,935,b)].
% 10.05/10.21 1040 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(735,d,688,b)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1040,d,934,a)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1040,d,935,b)].
% 10.05/10.21 1041 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(736,d,688,b)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1041,d,934,a)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Numeral_Onumber__ring(A). [resolve(1041,d,935,b)].
% 10.05/10.21 1042 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(737,d,688,b)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1042,d,934,a)].
% 10.05/10.21 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1042,d,935,b)].
% 10.05/10.21 1043 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 10.05/10.21 1044 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 10.05/10.21 1045 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 10.05/10.21 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1045,b,934,a)].
% 10.05/10.21 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1045,b,935,b)].
% 10.05/10.21 1046 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 10.05/10.21 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1046,b,934,a)].
% 10.05/10.21 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1046,b,935,b)].
% 10.05/10.21 1047 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 10.05/10.21 1048 -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(830,c,787,b)].
% 10.06/10.22 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(1048,c,934,a)].
% 10.06/10.22 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(1048,c,935,b)].
% 10.06/10.22 1049 -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(831,c,787,b)].
% 10.06/10.22 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(1049,c,934,a)].
% 10.06/10.22 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(1049,c,935,b)].
% 10.06/10.22 1050 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(832,b,787,b)].
% 10.06/10.22 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(1050,b,934,a)].
% 10.06/10.22 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B). [resolve(1050,b,935,b)].
% 10.06/10.22 1051 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(833,b,787,b)].
% 10.06/10.22 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(1051,b,934,a)].
% 10.06/10.22 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B). [resolve(1051,b,935,b)].
% 10.06/10.22 1052 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(834,b,787,b)].
% 10.06/10.22 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(1052,b,934,a)].
% 10.06/10.22 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(1052,b,935,b)].
% 10.06/10.22 1053 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 10.06/10.22 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1053,b,934,a)].
% 10.06/10.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(1053,b,935,b)].
% 10.06/10.22 1054 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 10.06/10.22 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1054,b,934,a)].
% 10.06/10.22 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1054,b,935,b)].
% 10.06/10.22 1055 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 10.06/10.22 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1055,b,934,a)].
% 10.06/10.22 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1055,b,935,b)].
% 10.06/10.22 1056 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 10.06/10.22 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1056,b,934,a)].
% 10.06/10.22 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(1056,b,935,b)].
% 10.06/10.22 1057 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 10.06/10.22 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1057,b,934,a)].
% 10.06/10.22 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1057,b,935,b)].
% 10.06/10.22 1058 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 10.06/10.24 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1058,b,934,a)].
% 10.06/10.24 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1058,b,935,b)].
% 10.06/10.24 1059 -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_Ocomm__ring__1(B). [resolve(871,a,858,b)].
% 10.06/10.24 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(1059,d,934,a)].
% 10.06/10.24 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_Numeral_Onumber__ring(B). [resolve(1059,d,935,b)].
% 10.06/10.24 1060 -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_Ocomm__ring__1(B). [resolve(872,a,858,b)].
% 10.06/10.24 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(1060,d,934,a)].
% 10.06/10.24 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_Numeral_Onumber__ring(B). [resolve(1060,d,935,b)].
% 10.06/10.24 1061 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(873,a,858,b)].
% 10.06/10.24 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1061,b,934,a)].
% 10.06/10.24 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(1061,b,935,b)].
% 10.06/10.24 1062 c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(874,a,858,b)].
% 10.06/10.24 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(1062,b,934,a)].
% 10.06/10.24 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Numeral_Onumber__ring(B). [resolve(1062,b,935,b)].
% 10.06/10.24 1063 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 10.06/10.24 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1063,b,934,a)].
% 10.06/10.24 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(1063,b,935,b)].
% 10.06/10.24 1064 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_Ocomm__ring__1(C). [resolve(876,a,858,b)].
% 10.06/10.24 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(1064,b,934,a)].
% 10.06/10.24 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_Numeral_Onumber__ring(C). [resolve(1064,b,935,b)].
% 10.06/10.24 1065 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_Ocomm__ring__1(C). [resolve(877,a,858,b)].
% 10.06/10.24 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(1065,b,934,a)].
% 10.06/10.24 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_Numeral_Onumber__ring(C). [resolve(1065,b,935,b)].
% 10.06/10.24 1066 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 10.06/10.24 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1066,b,934,a)].
% 10.06/10.24 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1066,b,935,b)].
% 10.06/10.24 1067 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 10.06/10.24 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1067,b,934,a)].
% 10.06/10.24 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1067,b,935,b)].
% 10.06/10.24 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1067,b,941,b)].
% 10.06/10.24 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1067,b,943,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 10.17/10.33 1068 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1068,b,934,a)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1068,b,935,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1068,b,941,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1068,b,943,b)].
% 10.17/10.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 10.17/10.33 1069 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 10.17/10.33 1070 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 10.17/10.33 1071 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 10.17/10.33 1072 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 10.17/10.33 1073 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 10.17/10.33 1074 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 10.17/10.33 1075 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 10.17/10.33 1076 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 10.17/10.33 1077 -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].
% 10.17/10.33 1078 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 10.17/10.33 1079 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 10.17/10.33 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 10.17/10.33 1080 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) # label(axiom). [assumption].
% 10.17/10.33 1081 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 10.17/10.33 1082 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 10.17/10.33 1083 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_20) # label(axiom). [assumption].
% 10.17/10.33 1084 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 10.17/10.33 1085 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_13) # label(axiom). [assumption].
% 10.17/10.33 1086 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 10.25/10.43 1087 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1087,a,1070,a)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1087,a,1071,a)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1087,a,1081,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 10.25/10.43 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 10.25/10.43 1088 -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 10.25/10.43 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1088,a,1070,a)].
% 10.25/10.43 Derived: c_lessequals(A,A,tc_nat). [resolve(1088,a,1071,a)].
% 10.25/10.43 Derived: c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 10.25/10.43 1089 class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 10.25/10.43 Derived: class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 10.25/10.43 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 10.25/10.43 1090 -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 10.25/10.43 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1090,b,1070,a)].
% 10.25/10.43 Derived: -c_less(A,A,tc_nat). [resolve(1090,b,1071,a)].
% 10.25/10.43 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 10.25/10.43 1091 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 10.25/10.43 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1091,c,1070,a)].
% 10.25/10.43 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1091,c,1071,a)].
% 10.25/10.43 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 10.25/10.43 1092 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 10.25/10.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1092,b,1070,a)].
% 10.25/10.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1092,b,1071,a)].
% 10.25/10.45 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 10.25/10.45 1093 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1093,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1093,c,1071,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 10.25/10.45 1094 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(37,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1094,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1094,c,1071,a)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Olorder(B). [resolve(1094,c,1072,b)].
% 10.25/10.45 1095 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Omeet__semilorder(C). [resolve(38,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1095,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1095,c,1071,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(1095,c,1072,b)].
% 10.25/10.45 1096 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Omeet__semilorder(B). [resolve(39,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1096,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1096,c,1071,a)].
% 10.25/10.45 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Olorder(B). [resolve(1096,c,1072,b)].
% 10.25/10.45 1097 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Omeet__semilorder(C). [resolve(40,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1097,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1097,c,1071,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(1097,c,1072,b)].
% 10.25/10.45 1098 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1098,c,1070,a)].
% 10.25/10.45 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1098,c,1071,a)].
% 10.46/10.69 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 10.46/10.69 1099 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(42,a,7,b)].
% 10.46/10.69 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1099,b,1070,a)].
% 10.46/10.69 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1099,b,1071,a)].
% 10.46/10.69 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1099,b,1072,b)].
% 10.46/10.69 1100 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 10.46/10.69 1101 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 10.46/10.69 1102 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 10.46/10.69 1103 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 10.46/10.69 1104 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 10.46/10.69 1105 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 10.46/10.69 1106 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 10.46/10.69 1107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 10.46/10.69 1108 -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].
% 10.46/10.69 1109 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 10.46/10.69 1110 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 10.46/10.69 1111 -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].
% 10.46/10.69 1112 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 10.46/10.69 1113 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 10.46/10.69 1114 -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].
% 10.46/10.69 1115 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 10.46/10.69 1116 -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].
% 10.46/10.69 1117 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 10.46/10.69 1118 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 10.46/10.69 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1118,a,1101,a)].
% 10.46/10.69 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1118,a,1102,a)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1118,a,1112,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 10.88/11.03 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 10.88/11.03 1119 -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 10.88/11.03 1120 class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 10.88/11.03 1121 -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 10.88/11.03 1122 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 10.88/11.03 1123 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 10.88/11.03 1124 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 10.88/11.03 1125 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(37,a,5,b)].
% 10.88/11.03 1126 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Ojoin__semilorder(C). [resolve(38,a,5,b)].
% 10.88/11.03 1127 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(39,a,5,b)].
% 10.88/11.03 1128 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Ojoin__semilorder(C). [resolve(40,a,5,b)].
% 10.88/11.03 1129 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 10.88/11.03 1130 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(42,a,5,b)].
% 10.88/11.03 1131 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 10.88/11.03 1132 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 10.88/11.03 1133 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 10.88/11.03 1134 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 10.88/11.03 1135 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 10.88/11.03 1136 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 11.09/11.28 1137 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 11.09/11.28 1138 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 11.09/11.28 1139 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 11.09/11.28 1140 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 11.09/11.28 1141 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) # label(axiom). [assumption].
% 11.09/11.28 1142 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 11.09/11.28 1143 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 11.09/11.28 1144 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 11.09/11.28 1145 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 11.09/11.28 1146 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 11.09/11.28 1147 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 11.09/11.28 1148 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 11.09/11.28 1149 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 11.09/11.28 1150 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 11.09/11.28 1151 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 11.09/11.28 1152 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 11.09/11.28 1153 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 11.09/11.28 1154 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Olorder(B). [resolve(37,a,6,b)].
% 11.09/11.28 1155 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(38,a,6,b)].
% 11.09/11.28 1156 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Olorder(B). [resolve(39,a,6,b)].
% 11.09/11.28 1157 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(40,a,6,b)].
% 11.09/11.28 1158 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 11.09/11.28 1159 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(42,a,6,b)].
% 11.09/11.28 1160 c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 11.09/11.28 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1160,b,1132,a)].
% 11.09/11.28 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1160,b,1133,a)].
% 11.09/11.28 1161 c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 11.09/11.28 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1161,b,1132,a)].
% 11.09/11.28 Derived: c_lessequals(A,A,tc_nat). [resolve(1161,b,1133,a)].
% 11.09/11.28 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 11.09/11.28 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 11.09/11.28 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1161,b,1142,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 11.09/11.29 Derived: c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 11.09/11.29 1162 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 11.09/11.29 Derived: class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 11.09/11.29 Derived: class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 11.09/11.29 1163 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 11.09/11.29 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1163,b,1132,a)].
% 11.09/11.29 Derived: -c_less(A,A,tc_nat). [resolve(1163,b,1133,a)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1163,b,1142,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 11.09/11.29 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 11.09/11.29 1164 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 11.09/11.29 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1164,c,1132,a)].
% 11.09/11.29 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1164,c,1133,a)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1164,c,1134,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1164,c,1135,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1164,c,1136,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1164,c,1137,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1164,c,1138,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1164,c,1140,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1164,c,1141,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1164,c,1142,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1164,c,1143,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1164,c,1144,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1164,c,1145,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1164,c,1146,b)].
% 11.09/11.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 11.09/11.29 1165 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1165,b,1132,a)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1165,b,1133,a)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1165,b,1135,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1165,b,1136,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1165,b,1137,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1165,b,1138,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1165,b,1140,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1165,b,1141,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1165,b,1142,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1165,b,1143,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1165,b,1144,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1165,b,1145,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1165,b,1146,b)].
% 11.09/11.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 11.09/11.29 1166 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1166,c,1132,a)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1166,c,1133,a)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1166,c,1134,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1166,c,1135,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1166,c,1136,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1166,c,1137,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1166,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1166,c,1140,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1166,c,1141,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1166,c,1142,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1166,c,1143,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1166,c,1144,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1166,c,1145,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1166,c,1146,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 11.09/11.29 1167 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_LOrder_Olorder(B). [resolve(1094,c,1072,b)].
% 11.09/11.29 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(1167,c,1132,a)].
% 11.09/11.29 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(1167,c,1133,a)].
% 11.09/11.29 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(B). [resolve(1167,c,1134,b)].
% 11.09/11.29 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__abs(B). [resolve(1167,c,1135,b)].
% 11.09/11.29 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(1167,c,1136,b)].
% 11.09/11.29 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(1167,c,1137,b)].
% 11.09/11.29 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(1167,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Orderings_Olinorder(B). [resolve(1167,c,1139,b)].
% 11.09/11.29 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(1167,c,1140,b)].
% 11.09/11.29 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(1167,c,1141,b)].
% 11.09/11.29 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(1167,c,1142,b)].
% 11.09/11.29 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(1167,c,1143,b)].
% 11.09/11.29 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__ring__strict(B). [resolve(1167,c,1144,b)].
% 11.09/11.29 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__semidom(B). [resolve(1167,c,1145,b)].
% 11.09/11.29 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(1167,c,1146,b)].
% 11.09/11.29 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1167,c,1147,b)].
% 11.09/11.29 1168 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(1095,c,1072,b)].
% 11.09/11.29 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(1168,c,1132,a)].
% 11.09/11.29 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(1168,c,1133,a)].
% 11.09/11.29 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(C). [resolve(1168,c,1134,b)].
% 11.09/11.29 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__abs(C). [resolve(1168,c,1135,b)].
% 11.09/11.29 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(1168,c,1136,b)].
% 11.09/11.29 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(1168,c,1137,b)].
% 11.09/11.29 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(1168,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(1168,c,1139,b)].
% 11.09/11.29 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(1168,c,1140,b)].
% 11.09/11.29 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(1168,c,1141,b)].
% 11.09/11.29 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(1168,c,1142,b)].
% 11.09/11.29 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(1168,c,1143,b)].
% 11.09/11.29 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__ring__strict(C). [resolve(1168,c,1144,b)].
% 11.09/11.29 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__semidom(C). [resolve(1168,c,1145,b)].
% 11.09/11.29 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(1168,c,1146,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1168,c,1147,b)].
% 11.09/11.29 1169 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_LOrder_Olorder(B). [resolve(1096,c,1072,b)].
% 11.09/11.29 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(1169,c,1132,a)].
% 11.09/11.29 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(1169,c,1133,a)].
% 11.09/11.29 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(B). [resolve(1169,c,1134,b)].
% 11.09/11.29 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__abs(B). [resolve(1169,c,1135,b)].
% 11.09/11.29 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(1169,c,1136,b)].
% 11.09/11.29 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(1169,c,1137,b)].
% 11.09/11.29 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(1169,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Orderings_Olinorder(B). [resolve(1169,c,1139,b)].
% 11.09/11.29 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(1169,c,1140,b)].
% 11.09/11.29 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(1169,c,1141,b)].
% 11.09/11.29 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(1169,c,1142,b)].
% 11.09/11.29 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(1169,c,1143,b)].
% 11.09/11.29 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__ring__strict(B). [resolve(1169,c,1144,b)].
% 11.09/11.29 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__semidom(B). [resolve(1169,c,1145,b)].
% 11.09/11.29 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(1169,c,1146,b)].
% 11.09/11.29 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1169,c,1147,b)].
% 11.09/11.29 1170 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_LOrder_Olorder(C). [resolve(1097,c,1072,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1170,c,1132,a)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1170,c,1133,a)].
% 11.09/11.29 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(C). [resolve(1170,c,1134,b)].
% 11.09/11.29 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__abs(C). [resolve(1170,c,1135,b)].
% 11.09/11.29 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(1170,c,1136,b)].
% 11.09/11.29 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(1170,c,1137,b)].
% 11.09/11.29 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(1170,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(1170,c,1139,b)].
% 11.09/11.29 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(1170,c,1140,b)].
% 11.09/11.29 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(1170,c,1141,b)].
% 11.09/11.29 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(1170,c,1142,b)].
% 11.09/11.29 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(1170,c,1143,b)].
% 11.09/11.29 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__ring__strict(C). [resolve(1170,c,1144,b)].
% 11.09/11.29 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__semidom(C). [resolve(1170,c,1145,b)].
% 11.09/11.29 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(1170,c,1146,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1170,c,1147,b)].
% 11.09/11.29 1171 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1171,c,1132,a)].
% 11.09/11.29 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1171,c,1133,a)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1171,c,1134,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1171,c,1135,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1171,c,1136,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1171,c,1137,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1171,c,1138,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 11.09/11.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1171,c,1140,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1171,c,1141,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1171,c,1142,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1171,c,1143,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1171,c,1144,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1171,c,1145,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1171,c,1146,b)].
% 11.09/11.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 11.09/11.30 1172 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1099,b,1072,b)].
% 11.09/11.30 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(1172,b,1132,a)].
% 11.09/11.30 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(1172,b,1133,a)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1172,b,1134,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1172,b,1135,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1172,b,1136,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1172,b,1137,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1172,b,1138,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1172,b,1139,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1172,b,1140,b)].
% 11.09/11.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1172,b,1141,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1172,b,1142,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1172,b,1143,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1172,b,1144,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1172,b,1145,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1172,b,1146,b)].
% 11.25/11.40 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1172,b,1147,b)].
% 11.25/11.40 1173 c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 11.25/11.40 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1173,b,1132,a)].
% 11.25/11.40 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1173,b,1133,a)].
% 11.25/11.40 1174 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 11.25/11.40 1175 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 11.25/11.40 1176 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 11.25/11.40 1177 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 11.25/11.40 1178 -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].
% 11.25/11.40 1179 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 11.25/11.40 1180 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 11.25/11.40 1181 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 11.25/11.40 1182 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 11.25/11.40 1183 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 11.25/11.40 1184 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 11.25/11.40 1185 -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].
% 11.25/11.40 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(1185,a,1175,a)].
% 11.25/11.40 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(1185,a,1176,a)].
% 11.25/11.40 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1185,a,1177,b)].
% 11.25/11.40 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(1185,a,1178,b)].
% 11.25/11.41 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(1185,a,1179,b)].
% 11.25/11.41 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(1185,a,1180,b)].
% 11.25/11.41 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__ring__strict(C). [resolve(1185,a,1181,b)].
% 11.25/11.41 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__semidom(C). [resolve(1185,a,1182,b)].
% 11.25/11.41 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__semiring__strict(C). [resolve(1185,a,1183,b)].
% 11.25/11.41 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_Wellfounded__Recursion_Owellorder(C). [resolve(1185,a,1184,b)].
% 11.25/11.41 1186 -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].
% 11.25/11.41 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(1186,a,1175,a)].
% 11.25/11.41 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(1186,a,1176,a)].
% 11.25/11.41 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1186,a,1177,b)].
% 11.25/11.41 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(1186,a,1178,b)].
% 11.25/11.41 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(1186,a,1179,b)].
% 11.25/11.41 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(1186,a,1180,b)].
% 11.25/11.41 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__ring__strict(B). [resolve(1186,a,1181,b)].
% 11.25/11.41 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__semidom(B). [resolve(1186,a,1182,b)].
% 11.25/11.41 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__semiring__strict(B). [resolve(1186,a,1183,b)].
% 11.25/11.41 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_Wellfounded__Recursion_Owellorder(B). [resolve(1186,a,1184,b)].
% 11.25/11.41 1187 -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].
% 11.25/11.41 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(1187,a,1175,a)].
% 11.25/11.41 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(1187,a,1176,a)].
% 11.25/11.41 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1187,a,1177,b)].
% 11.25/11.42 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(1187,a,1178,b)].
% 11.25/11.42 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(1187,a,1179,b)].
% 11.25/11.42 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(1187,a,1180,b)].
% 11.25/11.42 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__ring__strict(B). [resolve(1187,a,1181,b)].
% 11.25/11.42 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__semidom(B). [resolve(1187,a,1182,b)].
% 11.25/11.42 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__semiring__strict(B). [resolve(1187,a,1183,b)].
% 11.25/11.42 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_Wellfounded__Recursion_Owellorder(B). [resolve(1187,a,1184,b)].
% 11.25/11.42 1188 -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].
% 11.25/11.42 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(1188,a,1175,a)].
% 11.25/11.42 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(1188,a,1176,a)].
% 11.25/11.42 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1188,a,1177,b)].
% 11.25/11.42 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(1188,a,1178,b)].
% 11.25/11.42 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(1188,a,1179,b)].
% 11.25/11.42 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(1188,a,1180,b)].
% 11.25/11.42 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__ring__strict(C). [resolve(1188,a,1181,b)].
% 11.25/11.42 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__semidom(C). [resolve(1188,a,1182,b)].
% 11.25/11.42 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__semiring__strict(C). [resolve(1188,a,1183,b)].
% 11.25/11.43 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_Wellfounded__Recursion_Owellorder(C). [resolve(1188,a,1184,b)].
% 11.25/11.43 1189 -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].
% 11.25/11.43 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(1189,a,1175,a)].
% 11.25/11.43 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(1189,a,1176,a)].
% 11.25/11.43 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1189,a,1177,b)].
% 11.25/11.43 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(1189,a,1178,b)].
% 11.25/11.43 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(1189,a,1179,b)].
% 11.25/11.43 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(1189,a,1180,b)].
% 11.25/11.43 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__ring__strict(B). [resolve(1189,a,1181,b)].
% 11.25/11.43 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__semidom(B). [resolve(1189,a,1182,b)].
% 11.25/11.43 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__semiring__strict(B). [resolve(1189,a,1183,b)].
% 11.25/11.43 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_Wellfounded__Recursion_Owellorder(B). [resolve(1189,a,1184,b)].
% 11.25/11.43 1190 -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].
% 11.25/11.43 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(1190,a,1175,a)].
% 11.25/11.43 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(1190,a,1176,a)].
% 11.25/11.43 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1190,a,1177,b)].
% 11.25/11.43 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(1190,a,1178,b)].
% 11.25/11.43 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(1190,a,1179,b)].
% 11.25/11.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1190,a,1180,b)].
% 11.25/11.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1190,a,1181,b)].
% 11.25/11.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1190,a,1182,b)].
% 11.25/11.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1190,a,1183,b)].
% 11.25/11.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1190,a,1184,b)].
% 11.25/11.44 1191 -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].
% 11.25/11.44 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(1191,a,1175,a)].
% 11.25/11.44 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(1191,a,1176,a)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1191,a,1177,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1191,a,1178,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1191,a,1179,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1191,a,1180,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1191,a,1181,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1191,a,1182,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1191,a,1183,b)].
% 11.25/11.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1191,a,1184,b)].
% 11.25/11.44 1192 -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].
% 11.25/11.44 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(1192,a,1175,a)].
% 11.25/11.45 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(1192,a,1176,a)].
% 11.25/11.45 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1192,a,1177,b)].
% 11.25/11.45 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(1192,a,1178,b)].
% 11.25/11.45 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(1192,a,1179,b)].
% 11.25/11.45 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(1192,a,1180,b)].
% 11.25/11.45 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__ring__strict(B). [resolve(1192,a,1181,b)].
% 11.25/11.45 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__semidom(B). [resolve(1192,a,1182,b)].
% 11.25/11.45 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__semiring__strict(B). [resolve(1192,a,1183,b)].
% 11.25/11.45 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_Wellfounded__Recursion_Owellorder(B). [resolve(1192,a,1184,b)].
% 11.25/11.45 1193 -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].
% 11.25/11.45 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(1193,a,1175,a)].
% 11.25/11.45 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(1193,a,1176,a)].
% 11.25/11.45 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1193,a,1177,b)].
% 11.25/11.45 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(1193,a,1178,b)].
% 11.25/11.45 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(1193,a,1179,b)].
% 11.25/11.45 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(1193,a,1180,b)].
% 11.25/11.45 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__ring__strict(B). [resolve(1193,a,1181,b)].
% 11.25/11.46 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__semidom(B). [resolve(1193,a,1182,b)].
% 11.25/11.46 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__semiring__strict(B). [resolve(1193,a,1183,b)].
% 11.25/11.46 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_Wellfounded__Recursion_Owellorder(B). [resolve(1193,a,1184,b)].
% 11.25/11.46 1194 -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].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1194,a,1175,a)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1194,a,1176,a)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1194,a,1177,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1194,a,1178,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1194,a,1179,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1194,a,1180,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1194,a,1181,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1194,a,1182,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1194,a,1183,b)].
% 11.25/11.46 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 11.25/11.46 1195 -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].
% 11.25/11.46 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(1195,a,1175,a)].
% 11.25/11.46 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(1195,a,1176,a)].
% 11.25/11.46 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1195,a,1177,b)].
% 11.25/11.46 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(1195,a,1178,b)].
% 11.25/11.46 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(1195,a,1179,b)].
% 11.25/11.46 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(1195,a,1180,b)].
% 11.25/11.46 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__ring__strict(C). [resolve(1195,a,1181,b)].
% 11.33/11.47 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__semidom(C). [resolve(1195,a,1182,b)].
% 11.33/11.47 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__semiring__strict(C). [resolve(1195,a,1183,b)].
% 11.33/11.47 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_Wellfounded__Recursion_Owellorder(C). [resolve(1195,a,1184,b)].
% 11.33/11.47 1196 -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].
% 11.33/11.47 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(1196,a,1175,a)].
% 11.33/11.47 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(1196,a,1176,a)].
% 11.33/11.47 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1196,a,1177,b)].
% 11.33/11.47 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(1196,a,1178,b)].
% 11.33/11.47 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(1196,a,1179,b)].
% 11.33/11.47 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(1196,a,1180,b)].
% 11.33/11.47 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__ring__strict(B). [resolve(1196,a,1181,b)].
% 11.33/11.47 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__semidom(B). [resolve(1196,a,1182,b)].
% 11.33/11.47 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__semiring__strict(B). [resolve(1196,a,1183,b)].
% 11.33/11.47 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_Wellfounded__Recursion_Owellorder(B). [resolve(1196,a,1184,b)].
% 11.33/11.47 1197 -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].
% 11.33/11.47 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(1197,a,1175,a)].
% 11.33/11.47 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(1197,a,1176,a)].
% 11.33/11.47 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1197,a,1177,b)].
% 11.33/11.48 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(1197,a,1178,b)].
% 11.33/11.48 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(1197,a,1179,b)].
% 11.33/11.48 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(1197,a,1180,b)].
% 11.33/11.48 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__ring__strict(B). [resolve(1197,a,1181,b)].
% 11.33/11.49 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__semidom(B). [resolve(1197,a,1182,b)].
% 11.33/11.49 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__semiring__strict(B). [resolve(1197,a,1183,b)].
% 11.33/11.49 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_Wellfounded__Recursion_Owellorder(B). [resolve(1197,a,1184,b)].
% 11.33/11.49 1198 -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].
% 11.33/11.49 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(1198,a,1175,a)].
% 11.33/11.49 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(1198,a,1176,a)].
% 11.33/11.49 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1198,a,1177,b)].
% 11.33/11.49 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(1198,a,1178,b)].
% 11.33/11.49 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__field(C). [resolve(1198,a,1179,b)].
% 11.33/11.49 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__idom(C). [resolve(1198,a,1180,b)].
% 11.33/11.49 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__ring__strict(C). [resolve(1198,a,1181,b)].
% 11.33/11.49 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__semidom(C). [resolve(1198,a,1182,b)].
% 11.33/11.49 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__semiring__strict(C). [resolve(1198,a,1183,b)].
% 11.33/11.49 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_Wellfounded__Recursion_Owellorder(C). [resolve(1198,a,1184,b)].
% 11.35/11.49 1199 -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].
% 11.35/11.49 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(1199,a,1175,a)].
% 11.35/11.49 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(1199,a,1176,a)].
% 11.35/11.49 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1199,a,1177,b)].
% 11.35/11.49 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(1199,a,1178,b)].
% 11.35/11.49 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__field(B). [resolve(1199,a,1179,b)].
% 11.35/11.49 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__idom(B). [resolve(1199,a,1180,b)].
% 11.35/11.49 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__ring__strict(B). [resolve(1199,a,1181,b)].
% 11.35/11.49 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__semidom(B). [resolve(1199,a,1182,b)].
% 11.35/11.49 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__semiring__strict(B). [resolve(1199,a,1183,b)].
% 11.35/11.49 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_Wellfounded__Recursion_Owellorder(B). [resolve(1199,a,1184,b)].
% 11.35/11.49 1200 -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].
% 11.35/11.49 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(1200,a,1175,a)].
% 11.35/11.49 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(1200,a,1176,a)].
% 11.35/11.49 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1200,a,1177,b)].
% 11.35/11.49 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(1200,a,1178,b)].
% 11.35/11.49 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__field(B). [resolve(1200,a,1179,b)].
% 11.35/11.51 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(1200,a,1180,b)].
% 11.35/11.51 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__ring__strict(B). [resolve(1200,a,1181,b)].
% 11.35/11.51 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__semidom(B). [resolve(1200,a,1182,b)].
% 11.35/11.51 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__semiring__strict(B). [resolve(1200,a,1183,b)].
% 11.35/11.51 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_Wellfounded__Recursion_Owellorder(B). [resolve(1200,a,1184,b)].
% 11.35/11.51 1201 -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].
% 11.35/11.51 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(1201,a,1175,a)].
% 11.35/11.51 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(1201,a,1176,a)].
% 11.35/11.51 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1201,a,1177,b)].
% 11.35/11.51 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(1201,a,1178,b)].
% 11.35/11.51 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(1201,a,1179,b)].
% 11.35/11.51 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(1201,a,1180,b)].
% 11.35/11.51 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__ring__strict(B). [resolve(1201,a,1181,b)].
% 11.35/11.51 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__semidom(B). [resolve(1201,a,1182,b)].
% 11.35/11.51 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__semiring__strict(B). [resolve(1201,a,1183,b)].
% 11.35/11.51 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_Wellfounded__Recursion_Owellorder(B). [resolve(1201,a,1184,b)].
% 11.35/11.51 1202 -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].
% 11.35/11.51 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(1202,a,1175,a)].
% 11.35/11.51 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(1202,a,1176,a)].
% 11.35/11.51 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1202,a,1177,b)].
% 11.35/11.52 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(1202,a,1178,b)].
% 11.35/11.52 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(1202,a,1179,b)].
% 11.35/11.52 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(1202,a,1180,b)].
% 11.35/11.52 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__ring__strict(B). [resolve(1202,a,1181,b)].
% 11.35/11.52 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__semidom(B). [resolve(1202,a,1182,b)].
% 11.35/11.52 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__semiring__strict(B). [resolve(1202,a,1183,b)].
% 11.35/11.52 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_Wellfounded__Recursion_Owellorder(B). [resolve(1202,a,1184,b)].
% 11.35/11.52 1203 -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].
% 11.35/11.52 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(1203,a,1175,a)].
% 11.35/11.52 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(1203,a,1176,a)].
% 11.35/11.52 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1203,a,1177,b)].
% 11.35/11.52 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(1203,a,1178,b)].
% 11.35/11.52 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(1203,a,1179,b)].
% 11.35/11.52 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(1203,a,1180,b)].
% 11.35/11.52 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__ring__strict(C). [resolve(1203,a,1181,b)].
% 11.35/11.52 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__semidom(C). [resolve(1203,a,1182,b)].
% 11.35/11.52 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__semiring__strict(C). [resolve(1203,a,1183,b)].
% 11.35/11.52 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_Wellfounded__Recursion_Owellorder(C). [resolve(1203,a,1184,b)].
% 11.35/11.52 1204 -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].
% 11.35/11.52 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1204,a,1175,a)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1204,a,1176,a)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1204,a,1177,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1204,a,1178,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1204,a,1179,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1204,a,1180,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1204,a,1181,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1204,a,1182,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1204,a,1183,b)].
% 11.38/11.53 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 11.38/11.53 1205 -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].
% 11.38/11.53 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(1205,a,1175,a)].
% 11.38/11.53 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(1205,a,1176,a)].
% 11.38/11.53 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1205,a,1177,b)].
% 11.38/11.53 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(1205,a,1178,b)].
% 11.38/11.53 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(1205,a,1179,b)].
% 11.38/11.53 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(1205,a,1180,b)].
% 11.38/11.53 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__ring__strict(B). [resolve(1205,a,1181,b)].
% 11.38/11.53 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__semidom(B). [resolve(1205,a,1182,b)].
% 11.38/11.53 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__semiring__strict(B). [resolve(1205,a,1183,b)].
% 11.38/11.53 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_Wellfounded__Recursion_Owellorder(B). [resolve(1205,a,1184,b)].
% 11.38/11.53 1206 -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].
% 11.38/11.53 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(1206,a,1175,a)].
% 11.38/11.54 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(1206,a,1176,a)].
% 11.38/11.54 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1206,a,1177,b)].
% 11.38/11.54 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(1206,a,1178,b)].
% 11.38/11.54 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(1206,a,1179,b)].
% 11.38/11.54 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(1206,a,1180,b)].
% 11.38/11.54 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__ring__strict(C). [resolve(1206,a,1181,b)].
% 11.38/11.54 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__semidom(C). [resolve(1206,a,1182,b)].
% 11.38/11.54 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__semiring__strict(C). [resolve(1206,a,1183,b)].
% 11.38/11.54 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_Wellfounded__Recursion_Owellorder(C). [resolve(1206,a,1184,b)].
% 11.38/11.54 1207 -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].
% 11.38/11.54 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(1207,a,1175,a)].
% 11.38/11.54 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(1207,a,1176,a)].
% 11.38/11.54 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1207,a,1177,b)].
% 11.38/11.54 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(1207,a,1178,b)].
% 11.38/11.54 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(1207,a,1179,b)].
% 11.38/11.54 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(1207,a,1180,b)].
% 11.38/11.54 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__ring__strict(C). [resolve(1207,a,1181,b)].
% 11.38/11.54 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__semidom(C). [resolve(1207,a,1182,b)].
% 11.38/11.54 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__semiring__strict(C). [resolve(1207,a,1183,b)].
% 11.40/11.58 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_Wellfounded__Recursion_Owellorder(C). [resolve(1207,a,1184,b)].
% 11.40/11.58 1208 -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].
% 11.40/11.58 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(1208,b,1175,a)].
% 11.40/11.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(1208,b,1176,a)].
% 11.40/11.58 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1208,b,1177,b)].
% 11.40/11.58 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(1208,b,1178,b)].
% 11.40/11.58 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(1208,b,1179,b)].
% 11.40/11.58 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(1208,b,1180,b)].
% 11.40/11.58 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__ring__strict(A). [resolve(1208,b,1181,b)].
% 11.40/11.58 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__semidom(A). [resolve(1208,b,1182,b)].
% 11.40/11.58 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__semiring__strict(A). [resolve(1208,b,1183,b)].
% 11.40/11.58 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_Wellfounded__Recursion_Owellorder(A). [resolve(1208,b,1184,b)].
% 11.40/11.58 1209 -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].
% 11.40/11.58 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(1209,b,1175,a)].
% 11.40/11.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(1209,b,1176,a)].
% 11.40/11.58 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1209,b,1177,b)].
% 11.40/11.58 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(1209,b,1178,b)].
% 11.40/11.58 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(1209,b,1179,b)].
% 11.40/11.58 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(1209,b,1180,b)].
% 11.40/11.58 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__ring__strict(A). [resolve(1209,b,1181,b)].
% 11.40/11.58 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__semidom(A). [resolve(1209,b,1182,b)].
% 11.40/11.58 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__semiring__strict(A). [resolve(1209,b,1183,b)].
% 11.40/11.59 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_Wellfounded__Recursion_Owellorder(A). [resolve(1209,b,1184,b)].
% 11.40/11.59 1210 -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].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1210,a,1175,a)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1210,a,1176,a)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1210,a,1177,b)].
% 11.40/11.59 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(1210,a,1178,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1210,a,1179,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1210,a,1180,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1210,a,1181,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1210,a,1182,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1210,a,1183,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1210,a,1184,b)].
% 11.40/11.59 1211 -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].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1211,a,1175,a)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1211,a,1176,a)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1211,a,1177,b)].
% 11.40/11.59 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(1211,a,1178,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1211,a,1179,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1211,a,1180,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1211,a,1181,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1211,a,1182,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1211,a,1183,b)].
% 11.40/11.59 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1211,a,1184,b)].
% 11.40/11.59 1212 -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].
% 11.40/11.59 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(1212,a,1175,a)].
% 11.40/11.59 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(1212,a,1176,a)].
% 11.40/11.59 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1212,a,1177,b)].
% 11.40/11.59 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(1212,a,1178,b)].
% 11.40/11.60 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(1212,a,1179,b)].
% 11.40/11.60 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(1212,a,1180,b)].
% 11.40/11.60 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__ring__strict(C). [resolve(1212,a,1181,b)].
% 11.40/11.60 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__semidom(C). [resolve(1212,a,1182,b)].
% 11.40/11.60 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__semiring__strict(C). [resolve(1212,a,1183,b)].
% 11.40/11.60 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1212,a,1184,b)].
% 11.40/11.60 1213 -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].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1213,a,1175,a)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1213,a,1176,a)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1213,a,1177,b)].
% 11.40/11.60 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(1213,a,1178,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1213,a,1179,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1213,a,1180,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1213,a,1181,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1213,a,1182,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1213,a,1183,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1213,a,1184,b)].
% 11.40/11.60 1214 -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].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1214,a,1175,a)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1214,a,1176,a)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1214,a,1177,b)].
% 11.40/11.60 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(1214,a,1178,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1214,a,1179,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1214,a,1180,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1214,a,1181,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1214,a,1182,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1214,a,1183,b)].
% 11.40/11.60 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1214,a,1184,b)].
% 11.40/11.61 1215 -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].
% 11.40/11.61 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(1215,a,1175,a)].
% 11.40/11.61 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(1215,a,1176,a)].
% 11.40/11.61 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1215,a,1177,b)].
% 11.40/11.61 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(1215,a,1178,b)].
% 11.40/11.61 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(1215,a,1179,b)].
% 11.40/11.61 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(1215,a,1180,b)].
% 11.40/11.61 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__ring__strict(C). [resolve(1215,a,1181,b)].
% 11.40/11.61 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__semidom(C). [resolve(1215,a,1182,b)].
% 11.40/11.61 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__semiring__strict(C). [resolve(1215,a,1183,b)].
% 11.40/11.61 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1215,a,1184,b)].
% 11.40/11.61 1216 -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].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1216,a,1175,a)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1216,a,1176,a)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1216,a,1177,b)].
% 11.40/11.61 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(1216,a,1178,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1216,a,1179,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1216,a,1180,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1216,a,1181,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1216,a,1182,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1216,a,1183,b)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1216,a,1184,b)].
% 11.40/11.61 1217 -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].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1217,a,1175,a)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1217,a,1176,a)].
% 11.40/11.61 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1217,a,1177,b)].
% 11.40/11.61 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(1217,a,1178,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1217,a,1179,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1217,a,1180,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1217,a,1181,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1217,a,1182,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1217,a,1183,b)].
% 11.48/11.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1217,a,1184,b)].
% 11.48/11.62 1218 -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].
% 11.48/11.62 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(1218,a,1175,a)].
% 11.48/11.62 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(1218,a,1176,a)].
% 11.48/11.62 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1218,a,1177,b)].
% 11.48/11.62 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(1218,a,1178,b)].
% 11.48/11.62 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(1218,a,1179,b)].
% 11.48/11.62 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(1218,a,1180,b)].
% 11.48/11.62 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__ring__strict(C). [resolve(1218,a,1181,b)].
% 11.48/11.62 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__semidom(C). [resolve(1218,a,1182,b)].
% 11.48/11.62 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__semiring__strict(C). [resolve(1218,a,1183,b)].
% 11.48/11.62 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1218,a,1184,b)].
% 11.48/11.62 1219 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1219,a,1175,a)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1219,a,1176,a)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1219,a,1179,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 11.48/11.62 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 11.48/11.64 1220 -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].
% 11.48/11.64 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(1220,a,1175,a)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(1220,a,1176,a)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1220,a,1177,b)].
% 11.48/11.64 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(1220,a,1178,b)].
% 11.48/11.64 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(1220,a,1179,b)].
% 11.48/11.64 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(1220,a,1180,b)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1220,a,1181,b)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1220,a,1182,b)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1220,a,1183,b)].
% 11.48/11.64 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1220,a,1184,b)].
% 11.48/11.64 1221 -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].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1221,a,1175,a)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1221,a,1176,a)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1221,a,1177,b)].
% 11.48/11.64 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(1221,a,1178,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1221,a,1179,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1221,a,1180,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1221,a,1181,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1221,a,1182,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1221,a,1183,b)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1221,a,1184,b)].
% 11.48/11.64 1222 -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].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1222,a,1175,a)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1222,a,1176,a)].
% 11.48/11.64 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1222,a,1177,b)].
% 11.48/11.65 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(1222,a,1178,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1222,a,1179,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1222,a,1180,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1222,a,1181,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1222,a,1182,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1222,a,1183,b)].
% 11.48/11.65 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1222,a,1184,b)].
% 11.48/11.65 1223 -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].
% 11.48/11.65 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(1223,a,1175,a)].
% 11.48/11.65 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(1223,a,1176,a)].
% 11.48/11.65 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1223,a,1177,b)].
% 11.48/11.65 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(1223,a,1178,b)].
% 11.48/11.65 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(1223,a,1179,b)].
% 11.48/11.65 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(1223,a,1180,b)].
% 11.48/11.65 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__ring__strict(C). [resolve(1223,a,1181,b)].
% 11.48/11.65 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__semidom(C). [resolve(1223,a,1182,b)].
% 11.48/11.65 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__semiring__strict(C). [resolve(1223,a,1183,b)].
% 11.48/11.65 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1223,a,1184,b)].
% 11.48/11.65 1224 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1224,a,1175,a)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1224,a,1176,a)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1224,a,1179,b)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 11.48/11.65 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 11.48/11.67 1225 -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].
% 11.48/11.67 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(1225,a,1175,a)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(1225,a,1176,a)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1225,a,1177,b)].
% 11.48/11.67 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(1225,a,1178,b)].
% 11.48/11.67 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(1225,a,1179,b)].
% 11.48/11.67 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(1225,a,1180,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1225,a,1181,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1225,a,1182,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1225,a,1183,b)].
% 11.48/11.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1225,a,1184,b)].
% 11.48/11.67 1226 -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].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1226,a,1175,a)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1226,a,1176,a)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1226,a,1177,b)].
% 11.48/11.67 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(1226,a,1178,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1226,a,1179,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1180,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1226,a,1181,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1226,a,1182,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1226,a,1183,b)].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1226,a,1184,b)].
% 11.48/11.67 1227 -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].
% 11.48/11.67 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1227,a,1175,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1227,a,1176,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1227,a,1177,b)].
% 11.55/11.68 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(1227,a,1178,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1227,a,1179,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1227,a,1180,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1227,a,1181,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1227,a,1182,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1227,a,1183,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1227,a,1184,b)].
% 11.55/11.68 1228 -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].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1228,a,1175,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1228,a,1176,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1228,a,1177,b)].
% 11.55/11.68 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(1228,a,1178,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1228,a,1179,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1228,a,1180,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1228,a,1181,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1228,a,1182,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1228,a,1183,b)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1228,a,1184,b)].
% 11.55/11.68 1229 -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].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1229,a,1175,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1229,a,1176,a)].
% 11.55/11.68 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1229,a,1177,b)].
% 11.55/11.69 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(1229,a,1178,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1229,a,1179,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1229,a,1180,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1229,a,1181,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1229,a,1182,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1229,a,1183,b)].
% 11.55/11.69 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1229,a,1184,b)].
% 11.55/11.69 1230 -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].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1230,a,1175,a)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1230,a,1176,a)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1230,a,1177,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1230,a,1178,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1230,a,1179,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1230,a,1180,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1230,a,1181,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1230,a,1182,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1230,a,1183,b)].
% 11.55/11.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 11.55/11.69 1231 -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].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1231,a,1175,a)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1231,a,1176,a)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1231,a,1177,b)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1231,a,1178,b)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1231,a,1179,b)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1231,a,1180,b)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1231,a,1181,b)].
% 11.55/11.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1231,a,1182,b)].
% 11.55/11.70 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1231,a,1183,b)].
% 11.55/11.70 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 11.55/11.70 1232 -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].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1232,a,1175,a)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1232,a,1176,a)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1232,a,1177,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1232,a,1178,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1232,a,1179,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1232,a,1180,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1232,a,1181,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1232,a,1182,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1232,a,1183,b)].
% 11.55/11.70 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 11.55/11.70 1233 -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].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1233,a,1175,a)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1233,a,1176,a)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1233,a,1177,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1233,a,1178,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1233,a,1179,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1233,a,1180,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1233,a,1181,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1233,a,1182,b)].
% 11.55/11.70 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1233,a,1183,b)].
% 11.55/11.71 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1233,a,1184,b)].
% 11.55/11.71 1234 -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].
% 11.55/11.71 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(1234,a,1175,a)].
% 11.55/11.71 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(1234,a,1176,a)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1234,a,1177,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1234,a,1178,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1234,a,1179,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1234,a,1180,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1234,a,1181,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1234,a,1182,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1234,a,1183,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1234,a,1184,b)].
% 11.55/11.71 1235 -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].
% 11.55/11.71 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(1235,a,1175,a)].
% 11.55/11.71 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(1235,a,1176,a)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1235,a,1177,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1235,a,1178,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1235,a,1179,b)].
% 11.55/11.71 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1235,a,1180,b)].
% 11.55/11.72 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__ring__strict(C). [resolve(1235,a,1181,b)].
% 11.55/11.72 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__semidom(C). [resolve(1235,a,1182,b)].
% 11.55/11.72 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__semiring__strict(C). [resolve(1235,a,1183,b)].
% 11.55/11.72 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_Wellfounded__Recursion_Owellorder(C). [resolve(1235,a,1184,b)].
% 11.55/11.72 1236 -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].
% 11.55/11.72 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(1236,a,1175,a)].
% 11.55/11.72 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(1236,a,1176,a)].
% 11.55/11.72 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1236,a,1177,b)].
% 11.55/11.72 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(1236,a,1178,b)].
% 11.55/11.72 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(1236,a,1179,b)].
% 11.55/11.72 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(1236,a,1180,b)].
% 11.55/11.72 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__ring__strict(C). [resolve(1236,a,1181,b)].
% 11.55/11.72 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__semidom(C). [resolve(1236,a,1182,b)].
% 11.55/11.72 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__semiring__strict(C). [resolve(1236,a,1183,b)].
% 11.55/11.72 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_Wellfounded__Recursion_Owellorder(C). [resolve(1236,a,1184,b)].
% 11.55/11.72 1237 -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].
% 11.55/11.72 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(1237,a,1175,a)].
% 11.55/11.73 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(1237,a,1176,a)].
% 11.55/11.73 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1237,a,1177,b)].
% 11.55/11.73 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(1237,a,1178,b)].
% 11.55/11.73 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(1237,a,1179,b)].
% 11.55/11.73 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(1237,a,1180,b)].
% 11.55/11.73 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__ring__strict(C). [resolve(1237,a,1181,b)].
% 11.55/11.73 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__semidom(C). [resolve(1237,a,1182,b)].
% 11.55/11.73 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__semiring__strict(C). [resolve(1237,a,1183,b)].
% 11.55/11.73 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_Wellfounded__Recursion_Owellorder(C). [resolve(1237,a,1184,b)].
% 11.55/11.73 1238 -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].
% 11.55/11.73 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(1238,a,1175,a)].
% 11.55/11.73 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(1238,a,1176,a)].
% 11.55/11.73 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1238,a,1177,b)].
% 11.55/11.73 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(1238,a,1178,b)].
% 11.55/11.73 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(1238,a,1179,b)].
% 11.55/11.73 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(1238,a,1180,b)].
% 11.55/11.73 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__ring__strict(C). [resolve(1238,a,1181,b)].
% 11.55/11.73 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__semidom(C). [resolve(1238,a,1182,b)].
% 11.55/11.73 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__semiring__strict(C). [resolve(1238,a,1183,b)].
% 11.55/11.74 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1238,a,1184,b)].
% 11.55/11.74 1239 -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].
% 11.55/11.74 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(1239,a,1175,a)].
% 11.55/11.74 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(1239,a,1176,a)].
% 11.55/11.74 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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1239,a,1177,b)].
% 11.55/11.74 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(1239,a,1178,b)].
% 11.55/11.74 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(1239,a,1179,b)].
% 11.55/11.74 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(1239,a,1180,b)].
% 11.55/11.74 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__ring__strict(C). [resolve(1239,a,1181,b)].
% 11.55/11.74 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__semidom(C). [resolve(1239,a,1182,b)].
% 11.55/11.74 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__semiring__strict(C). [resolve(1239,a,1183,b)].
% 11.55/11.74 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_Wellfounded__Recursion_Owellorder(C). [resolve(1239,a,1184,b)].
% 11.55/11.74 1240 -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].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1240,a,1175,a)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1240,a,1176,a)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1240,a,1177,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1240,a,1178,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1240,a,1179,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1240,a,1180,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1240,a,1181,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1240,a,1182,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1240,a,1183,b)].
% 11.55/11.74 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 11.55/11.74 1241 -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].
% 11.55/11.74 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(1241,a,1175,a)].
% 11.55/11.74 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(1241,a,1176,a)].
% 11.55/11.74 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1241,a,1177,b)].
% 11.55/11.74 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(1241,a,1178,b)].
% 11.55/11.74 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(1241,a,1179,b)].
% 11.55/11.74 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(1241,a,1180,b)].
% 11.55/11.74 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__ring__strict(B). [resolve(1241,a,1181,b)].
% 11.55/11.74 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__semidom(B). [resolve(1241,a,1182,b)].
% 11.55/11.74 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__semiring__strict(B). [resolve(1241,a,1183,b)].
% 11.55/11.74 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1241,a,1184,b)].
% 11.55/11.74 1242 -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].
% 11.55/11.74 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(1242,a,1175,a)].
% 11.55/11.74 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(1242,a,1176,a)].
% 11.55/11.74 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1242,a,1177,b)].
% 11.55/11.74 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(1242,a,1178,b)].
% 11.55/11.74 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(1242,a,1179,b)].
% 11.55/11.74 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(1242,a,1180,b)].
% 11.55/11.74 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__ring__strict(C). [resolve(1242,a,1181,b)].
% 11.80/11.97 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__semidom(C). [resolve(1242,a,1182,b)].
% 11.80/11.97 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__semiring__strict(C). [resolve(1242,a,1183,b)].
% 11.80/11.97 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1242,a,1184,b)].
% 11.80/11.97 1243 -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 11.80/11.97 1244 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 11.80/11.97 1245 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 11.80/11.97 1246 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 11.80/11.97 1247 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 11.80/11.97 1248 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 11.80/11.97 1249 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Orderings_Olinorder(B). [resolve(37,a,17,b)].
% 11.80/11.97 1250 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(38,a,17,b)].
% 11.80/11.97 1251 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Orderings_Olinorder(B). [resolve(39,a,17,b)].
% 11.80/11.97 1252 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(40,a,17,b)].
% 11.80/11.97 1253 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 11.80/11.97 1254 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(42,a,17,b)].
% 11.80/11.97 1255 c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 11.80/11.97 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 11.80/11.97 1256 c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 11.80/11.97 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 11.80/11.97 1257 c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 11.80/11.97 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1257,b,1175,a)].
% 11.80/11.97 Derived: c_lessequals(A,A,tc_nat). [resolve(1257,b,1176,a)].
% 11.80/11.97 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 11.80/11.97 1258 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 11.80/11.97 Derived: class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 11.80/11.97 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 11.80/11.97 1259 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 11.85/11.99 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1259,b,1175,a)].
% 11.85/11.99 Derived: -c_less(A,A,tc_nat). [resolve(1259,b,1176,a)].
% 11.85/11.99 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 11.85/11.99 1260 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 11.85/11.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1260,c,1175,a)].
% 11.85/11.99 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1260,c,1176,a)].
% 11.85/11.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1260,c,1177,b)].
% 11.85/11.99 1261 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 11.85/11.99 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1261,b,1175,a)].
% 11.85/11.99 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1261,b,1176,a)].
% 11.85/11.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1261,b,1177,b)].
% 11.85/11.99 1262 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 11.85/11.99 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1262,c,1175,a)].
% 11.85/11.99 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1262,c,1176,a)].
% 11.85/11.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1262,c,1177,b)].
% 11.85/11.99 1263 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Orderings_Olinorder(B). [resolve(1167,c,1139,b)].
% 11.85/11.99 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1263,c,1175,a)].
% 11.85/11.99 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1263,c,1176,a)].
% 11.85/11.99 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(1263,c,1177,b)].
% 11.85/11.99 1264 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(1168,c,1139,b)].
% 11.85/11.99 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(1264,c,1175,a)].
% 11.85/11.99 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(1264,c,1176,a)].
% 11.85/11.99 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(1264,c,1177,b)].
% 11.85/11.99 1265 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Orderings_Olinorder(B). [resolve(1169,c,1139,b)].
% 11.85/11.99 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(1265,c,1175,a)].
% 11.85/11.99 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(1265,c,1176,a)].
% 11.85/11.99 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(1265,c,1177,b)].
% 11.85/11.99 1266 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Orderings_Olinorder(C). [resolve(1170,c,1139,b)].
% 12.02/12.20 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(1266,c,1175,a)].
% 12.02/12.20 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(1266,c,1176,a)].
% 12.02/12.20 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(1266,c,1177,b)].
% 12.02/12.20 1267 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 12.02/12.20 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1267,c,1175,a)].
% 12.02/12.20 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1267,c,1176,a)].
% 12.02/12.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1267,c,1177,b)].
% 12.02/12.20 1268 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1172,b,1139,b)].
% 12.02/12.20 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(1268,b,1175,a)].
% 12.02/12.20 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(1268,b,1176,a)].
% 12.02/12.20 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(1268,b,1177,b)].
% 12.02/12.20 1269 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 12.02/12.20 1270 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 12.02/12.20 1271 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 12.02/12.20 1272 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 12.02/12.20 1273 -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].
% 12.02/12.20 1274 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_7) # label(axiom). [assumption].
% 12.02/12.20 1275 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_7) # label(axiom). [assumption].
% 12.02/12.20 1276 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 12.02/12.20 1277 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_9) # label(axiom). [assumption].
% 12.02/12.20 1278 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 12.02/12.20 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 12.02/12.20 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1278,a,1277,b)].
% 12.02/12.20 1279 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 12.13/12.28 1280 -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].
% 12.13/12.28 1281 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 12.13/12.28 1282 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_9) # label(axiom). [assumption].
% 12.13/12.28 1283 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) # label(axiom). [assumption].
% 12.13/12.28 1284 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_57) # label(axiom). [assumption].
% 12.13/12.28 1285 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_43) # label(axiom). [assumption].
% 12.13/12.28 1286 -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].
% 12.13/12.28 1287 -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].
% 12.13/12.28 1288 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_16) # label(axiom). [assumption].
% 12.13/12.28 1289 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) # label(axiom). [assumption].
% 12.13/12.28 1290 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_7) # label(axiom). [assumption].
% 12.13/12.28 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 12.13/12.28 1291 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_22) # label(axiom). [assumption].
% 12.13/12.28 1292 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_12) # label(axiom). [assumption].
% 12.13/12.28 1293 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_16) # label(axiom). [assumption].
% 12.13/12.28 1294 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_9) # label(axiom). [assumption].
% 12.13/12.28 Derived: -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 12.13/12.28 1295 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 12.13/12.28 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1295,a,1277,b)].
% 12.13/12.28 1296 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 12.13/12.28 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 12.13/12.28 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 12.13/12.28 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 12.13/12.28 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 12.54/12.68 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 12.54/12.68 1297 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 12.54/12.68 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1297,b,1277,b)].
% 12.54/12.68 1298 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(34,a,14,b)].
% 12.54/12.68 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1298,c,1277,b)].
% 12.54/12.68 1299 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(35,a,14,b)].
% 12.54/12.68 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1299,b,1277,b)].
% 12.54/12.68 1300 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(36,a,14,b)].
% 12.54/12.68 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1300,c,1277,b)].
% 12.54/12.68 1301 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(37,a,14,b)].
% 12.54/12.68 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(1301,c,1277,b)].
% 12.54/12.68 1302 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(38,a,14,b)].
% 12.54/12.68 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(1302,c,1277,b)].
% 12.54/12.68 1303 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(39,a,14,b)].
% 12.54/12.68 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(1303,c,1277,b)].
% 12.54/12.68 1304 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(40,a,14,b)].
% 12.54/12.68 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(1304,c,1277,b)].
% 12.54/12.68 1305 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add(C). [resolve(41,a,14,b)].
% 12.54/12.68 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1305,c,1277,b)].
% 12.54/12.68 1306 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__semigroup__add(B). [resolve(42,a,14,b)].
% 12.54/12.68 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(1306,b,1277,b)].
% 12.54/12.68 1307 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 12.54/12.68 1308 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 12.54/12.68 1309 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 12.54/12.68 1310 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 12.61/12.76 1311 -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].
% 12.61/12.76 1312 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_6) # label(axiom). [assumption].
% 12.61/12.76 1313 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_6) # label(axiom). [assumption].
% 12.61/12.76 1314 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 12.61/12.76 1315 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_13) # label(axiom). [assumption].
% 12.61/12.76 1316 -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].
% 12.61/12.76 1317 -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].
% 12.61/12.76 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 12.61/12.76 1318 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) # label(axiom). [assumption].
% 12.61/12.76 1319 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_6) # label(axiom). [assumption].
% 12.61/12.76 1320 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) # label(axiom). [assumption].
% 12.61/12.76 1321 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_56) # label(axiom). [assumption].
% 12.61/12.76 1322 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_38) # label(axiom). [assumption].
% 12.61/12.76 1323 -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].
% 12.61/12.76 1324 -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].
% 12.61/12.76 1325 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_15) # label(axiom). [assumption].
% 12.61/12.76 1326 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_21) # label(axiom). [assumption].
% 12.61/12.76 1327 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 12.61/12.76 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 12.61/12.76 1328 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 12.61/12.76 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 12.61/12.76 1329 -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 12.70/12.84 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 12.70/12.84 1330 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(34,a,16,b)].
% 12.70/12.84 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1330,c,1316,b)].
% 12.70/12.84 1331 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(35,a,16,b)].
% 12.70/12.84 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1331,b,1316,b)].
% 12.70/12.84 1332 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(36,a,16,b)].
% 12.70/12.84 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1332,c,1316,b)].
% 12.70/12.84 1333 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(37,a,16,b)].
% 12.70/12.84 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__semigroup__add__imp__le(B). [resolve(1333,c,1316,b)].
% 12.70/12.84 1334 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(38,a,16,b)].
% 12.70/12.84 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__semigroup__add__imp__le(C). [resolve(1334,c,1316,b)].
% 12.70/12.84 1335 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(39,a,16,b)].
% 12.70/12.84 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__semigroup__add__imp__le(B). [resolve(1335,c,1316,b)].
% 12.70/12.84 1336 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(40,a,16,b)].
% 12.70/12.84 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__semigroup__add__imp__le(C). [resolve(1336,c,1316,b)].
% 12.70/12.84 1337 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(41,a,16,b)].
% 12.70/12.84 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1337,c,1316,b)].
% 12.70/12.84 1338 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__cancel__ab__semigroup__add(B). [resolve(42,a,16,b)].
% 12.70/12.84 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__semigroup__add__imp__le(B). [resolve(1338,b,1316,b)].
% 12.70/12.84 1339 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 12.70/12.84 1340 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(307,a,284,b)].
% 12.70/12.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 12.70/12.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1340,c,1311,b)].
% 12.70/12.84 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1340,c,1312,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1340,c,1313,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1340,c,1314,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1340,c,1315,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1340,c,1316,b)].
% 13.00/13.19 1341 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(C). [resolve(308,a,284,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1341,c,1311,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1341,c,1312,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1341,c,1313,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1341,c,1314,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1341,c,1315,b)].
% 13.00/13.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1341,c,1316,b)].
% 13.00/13.19 1342 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 13.00/13.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 13.00/13.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 13.00/13.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 13.00/13.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 13.00/13.19 1343 -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].
% 13.00/13.19 1344 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 13.00/13.19 1345 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 13.00/13.19 1346 -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].
% 13.00/13.19 1347 -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].
% 13.00/13.19 1348 -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].
% 13.00/13.19 1349 -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].
% 13.00/13.19 1350 -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].
% 13.00/13.19 1351 -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].
% 13.00/13.19 1352 -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].
% 13.08/13.23 1353 -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].
% 13.08/13.23 1354 -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].
% 13.08/13.23 1355 -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].
% 13.08/13.23 1356 -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].
% 13.08/13.23 1357 -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].
% 13.08/13.23 1358 -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].
% 13.08/13.23 1359 -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].
% 13.08/13.23 1360 -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].
% 13.08/13.23 1361 -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].
% 13.08/13.23 1362 -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].
% 13.08/13.23 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(1362,a,1344,a)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1362,a,1345,a)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1362,a,1346,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1362,a,1347,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1362,a,1348,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1362,a,1349,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1362,a,1350,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1362,a,1351,b)].
% 13.08/13.23 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(1362,a,1354,b)].
% 13.08/13.23 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(1362,a,1355,b)].
% 13.08/13.23 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(1362,a,1356,b)].
% 13.08/13.23 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(1362,a,1357,b)].
% 13.08/13.23 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1362,a,1358,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1362,a,1359,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1362,a,1360,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1362,a,1361,b)].
% 13.08/13.24 1363 -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].
% 13.08/13.24 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(1363,a,1344,a)].
% 13.08/13.24 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1363,a,1345,a)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1363,a,1346,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1363,a,1347,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1363,a,1348,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1363,a,1349,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1363,a,1350,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1363,a,1351,b)].
% 13.08/13.24 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(1363,a,1354,b)].
% 13.08/13.24 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(1363,a,1355,b)].
% 13.08/13.24 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(1363,a,1356,b)].
% 13.08/13.24 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(1363,a,1357,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1363,a,1358,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1363,a,1359,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1363,a,1360,b)].
% 13.08/13.24 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1363,a,1361,b)].
% 13.08/13.24 1364 -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].
% 13.08/13.24 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(1364,a,1344,a)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1364,a,1345,a)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1364,a,1346,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1364,a,1347,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1364,a,1348,b)].
% 13.08/13.24 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1364,a,1349,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1364,a,1350,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1364,a,1351,b)].
% 13.08/13.26 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(1364,a,1354,b)].
% 13.08/13.26 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(1364,a,1355,b)].
% 13.08/13.26 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(1364,a,1356,b)].
% 13.08/13.26 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(1364,a,1357,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1364,a,1358,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1364,a,1359,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1364,a,1360,b)].
% 13.08/13.26 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1364,a,1361,b)].
% 13.08/13.26 1365 -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].
% 13.08/13.26 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(1365,a,1344,a)].
% 13.08/13.26 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1365,a,1345,a)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1365,a,1346,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1365,a,1347,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1365,a,1348,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1365,a,1349,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1365,a,1350,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1365,a,1351,b)].
% 13.08/13.26 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(1365,a,1354,b)].
% 13.08/13.26 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(1365,a,1355,b)].
% 13.08/13.26 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(1365,a,1356,b)].
% 13.08/13.26 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(1365,a,1357,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1365,a,1358,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1365,a,1359,b)].
% 13.08/13.26 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1365,a,1360,b)].
% 13.08/13.27 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1365,a,1361,b)].
% 13.08/13.27 1366 -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].
% 13.08/13.27 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(1366,a,1344,a)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1366,a,1345,a)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1366,a,1346,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1366,a,1347,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1366,a,1348,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1366,a,1349,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1366,a,1350,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1366,a,1351,b)].
% 13.08/13.27 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(1366,a,1354,b)].
% 13.08/13.27 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(1366,a,1355,b)].
% 13.08/13.27 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(1366,a,1356,b)].
% 13.08/13.27 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(1366,a,1357,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1366,a,1358,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1366,a,1359,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1366,a,1360,b)].
% 13.08/13.27 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1366,a,1361,b)].
% 13.08/13.27 1367 -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].
% 13.08/13.27 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(1367,a,1344,a)].
% 13.08/13.27 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1367,a,1345,a)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1367,a,1346,b)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1367,a,1347,b)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1367,a,1348,b)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1367,a,1349,b)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1367,a,1350,b)].
% 13.08/13.27 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1367,a,1351,b)].
% 13.08/13.27 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(1367,a,1354,b)].
% 13.17/13.28 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(1367,a,1355,b)].
% 13.17/13.28 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(1367,a,1356,b)].
% 13.17/13.28 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(1367,a,1357,b)].
% 13.17/13.28 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1367,a,1358,b)].
% 13.17/13.28 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1367,a,1359,b)].
% 13.17/13.28 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1367,a,1360,b)].
% 13.17/13.28 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1367,a,1361,b)].
% 13.17/13.28 1368 -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].
% 13.17/13.28 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(1368,a,1344,a)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1368,a,1345,a)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1368,a,1346,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1368,a,1347,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1368,a,1348,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1368,a,1349,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1368,a,1350,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1368,a,1351,b)].
% 13.17/13.28 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(1368,a,1354,b)].
% 13.17/13.28 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(1368,a,1355,b)].
% 13.17/13.28 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(1368,a,1356,b)].
% 13.17/13.28 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(1368,a,1357,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1368,a,1358,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1368,a,1359,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1368,a,1360,b)].
% 13.17/13.28 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1368,a,1361,b)].
% 13.17/13.28 1369 -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].
% 13.17/13.28 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(1369,a,1344,a)].
% 13.17/13.28 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1369,a,1345,a)].
% 13.17/13.28 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1369,a,1346,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1369,a,1347,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1369,a,1348,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1369,a,1349,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1369,a,1350,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1369,a,1351,b)].
% 13.30/13.41 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(1369,a,1354,b)].
% 13.30/13.41 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(1369,a,1355,b)].
% 13.30/13.41 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(1369,a,1356,b)].
% 13.30/13.41 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(1369,a,1357,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1369,a,1358,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1369,a,1359,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1369,a,1360,b)].
% 13.30/13.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1369,a,1361,b)].
% 13.30/13.41 1370 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 13.30/13.41 1371 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 13.30/13.41 1372 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 13.30/13.41 1373 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(34,a,15,b)].
% 13.30/13.41 1374 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(35,a,15,b)].
% 13.30/13.41 1375 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(36,a,15,b)].
% 13.30/13.41 1376 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(37,a,15,b)].
% 13.30/13.41 1377 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(38,a,15,b)].
% 13.30/13.41 1378 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(39,a,15,b)].
% 13.30/13.41 1379 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(40,a,15,b)].
% 13.30/13.41 1380 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(41,a,15,b)].
% 13.30/13.41 1381 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__semigroup__add__imp__le(B). [resolve(42,a,15,b)].
% 13.30/13.41 1382 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(307,a,283,b)].
% 13.30/13.41 1383 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(308,a,283,b)].
% 13.51/13.65 1384 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1384,b,1351,b)].
% 13.51/13.65 1385 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1385,b,1344,a)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1385,b,1345,a)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1385,b,1351,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1385,b,1356,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 13.51/13.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 13.51/13.65 1386 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1386,b,1344,a)].
% 13.51/13.65 Derived: c_lessequals(A,A,tc_nat). [resolve(1386,b,1345,a)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1386,b,1351,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1386,b,1356,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 13.51/13.65 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 13.51/13.65 1387 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 13.51/13.65 Derived: class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 13.51/13.65 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 13.51/13.65 1388 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 13.51/13.65 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1388,b,1344,a)].
% 13.51/13.65 Derived: -c_less(A,A,tc_nat). [resolve(1388,b,1345,a)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1388,b,1351,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1388,b,1356,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 13.51/13.65 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 13.51/13.65 1389 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1330,c,1316,b)].
% 13.51/13.65 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1389,c,1344,a)].
% 13.51/13.65 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1389,c,1345,a)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1389,c,1346,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1389,c,1347,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1389,c,1348,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1389,c,1349,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1389,c,1350,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1389,c,1351,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1389,c,1354,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1389,c,1355,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1389,c,1356,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1389,c,1357,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1389,c,1358,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1389,c,1359,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1389,c,1360,b)].
% 13.51/13.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1389,c,1361,b)].
% 13.51/13.65 1390 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1331,b,1316,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1390,b,1344,a)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1390,b,1345,a)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1390,b,1347,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1390,b,1348,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1390,b,1349,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1390,b,1350,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1390,b,1351,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1390,b,1354,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1390,b,1355,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1390,b,1356,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1390,b,1357,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1390,b,1358,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1390,b,1359,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1390,b,1360,b)].
% 13.51/13.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1390,b,1361,b)].
% 13.51/13.65 1391 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1332,c,1316,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1391,c,1344,a)].
% 13.51/13.65 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1391,c,1345,a)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1391,c,1346,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1391,c,1347,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1391,c,1348,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1391,c,1349,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1391,c,1350,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1391,c,1351,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1391,c,1354,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1391,c,1355,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1391,c,1356,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1391,c,1357,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1391,c,1358,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1391,c,1359,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1391,c,1360,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1391,c,1361,b)].
% 13.51/13.65 1392 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1333,c,1316,b)].
% 13.51/13.65 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(1392,c,1344,a)].
% 13.51/13.65 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(1392,c,1345,a)].
% 13.51/13.65 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(B). [resolve(1392,c,1346,b)].
% 13.51/13.65 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__abs(B). [resolve(1392,c,1347,b)].
% 13.51/13.65 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(1392,c,1348,b)].
% 13.51/13.65 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(1392,c,1349,b)].
% 13.51/13.65 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(1392,c,1350,b)].
% 13.51/13.65 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(1392,c,1351,b)].
% 13.51/13.65 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(1392,c,1354,b)].
% 13.51/13.65 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(1392,c,1355,b)].
% 13.51/13.65 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(1392,c,1356,b)].
% 13.51/13.65 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(1392,c,1357,b)].
% 13.51/13.65 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__ring__strict(B). [resolve(1392,c,1358,b)].
% 13.51/13.65 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__semidom(B). [resolve(1392,c,1359,b)].
% 13.51/13.65 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(1392,c,1360,b)].
% 13.51/13.65 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(1392,c,1361,b)].
% 13.51/13.65 1393 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1334,c,1316,b)].
% 13.51/13.65 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(1393,c,1344,a)].
% 13.51/13.65 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(1393,c,1345,a)].
% 13.51/13.65 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(C). [resolve(1393,c,1346,b)].
% 13.51/13.65 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__abs(C). [resolve(1393,c,1347,b)].
% 13.51/13.65 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(1393,c,1348,b)].
% 13.51/13.65 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(1393,c,1349,b)].
% 13.51/13.65 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(1393,c,1350,b)].
% 13.51/13.65 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(1393,c,1351,b)].
% 13.51/13.65 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(1393,c,1354,b)].
% 13.51/13.65 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(1393,c,1355,b)].
% 13.51/13.65 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(1393,c,1356,b)].
% 13.51/13.65 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(1393,c,1357,b)].
% 13.51/13.65 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__ring__strict(C). [resolve(1393,c,1358,b)].
% 13.51/13.65 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__semidom(C). [resolve(1393,c,1359,b)].
% 13.51/13.65 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(1393,c,1360,b)].
% 13.51/13.65 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(1393,c,1361,b)].
% 13.51/13.65 1394 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1335,c,1316,b)].
% 13.51/13.65 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(1394,c,1344,a)].
% 13.51/13.65 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(1394,c,1345,a)].
% 13.51/13.65 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(B). [resolve(1394,c,1346,b)].
% 13.51/13.65 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__abs(B). [resolve(1394,c,1347,b)].
% 13.51/13.65 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(1394,c,1348,b)].
% 13.51/13.65 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(1394,c,1349,b)].
% 13.51/13.65 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(1394,c,1350,b)].
% 13.51/13.65 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(1394,c,1351,b)].
% 13.51/13.65 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(1394,c,1354,b)].
% 13.51/13.65 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(1394,c,1355,b)].
% 13.51/13.65 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(1394,c,1356,b)].
% 13.51/13.65 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(1394,c,1357,b)].
% 13.51/13.65 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__ring__strict(B). [resolve(1394,c,1358,b)].
% 13.51/13.65 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__semidom(B). [resolve(1394,c,1359,b)].
% 13.51/13.65 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(1394,c,1360,b)].
% 13.51/13.65 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(1394,c,1361,b)].
% 13.51/13.65 1395 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1336,c,1316,b)].
% 13.51/13.65 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(1395,c,1344,a)].
% 13.51/13.65 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(1395,c,1345,a)].
% 13.51/13.65 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(C). [resolve(1395,c,1346,b)].
% 13.51/13.65 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__abs(C). [resolve(1395,c,1347,b)].
% 13.51/13.65 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(1395,c,1348,b)].
% 13.51/13.65 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(1395,c,1349,b)].
% 13.51/13.65 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(1395,c,1350,b)].
% 13.51/13.65 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(1395,c,1351,b)].
% 13.51/13.65 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(1395,c,1354,b)].
% 13.51/13.65 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(1395,c,1355,b)].
% 13.51/13.65 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(1395,c,1356,b)].
% 13.51/13.65 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(1395,c,1357,b)].
% 13.51/13.65 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__ring__strict(C). [resolve(1395,c,1358,b)].
% 13.51/13.65 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__semidom(C). [resolve(1395,c,1359,b)].
% 13.51/13.65 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(1395,c,1360,b)].
% 13.51/13.65 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(1395,c,1361,b)].
% 13.51/13.65 1396 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1337,c,1316,b)].
% 13.51/13.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1396,c,1344,a)].
% 13.51/13.66 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1396,c,1345,a)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1396,c,1346,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1396,c,1347,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1396,c,1348,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1396,c,1349,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1396,c,1350,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1396,c,1351,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1396,c,1354,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1396,c,1355,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1396,c,1356,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1396,c,1357,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1396,c,1358,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1396,c,1359,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1396,c,1360,b)].
% 13.51/13.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1396,c,1361,b)].
% 13.51/13.66 1397 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__semigroup__add__imp__le(B). [resolve(1338,b,1316,b)].
% 13.51/13.66 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(1397,b,1344,a)].
% 13.51/13.66 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(1397,b,1345,a)].
% 13.51/13.66 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(B). [resolve(1397,b,1346,b)].
% 13.51/13.66 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__abs(B). [resolve(1397,b,1347,b)].
% 13.51/13.66 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(1397,b,1348,b)].
% 13.51/13.66 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(1397,b,1349,b)].
% 13.51/13.66 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(1397,b,1350,b)].
% 13.51/13.66 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(1397,b,1351,b)].
% 13.51/13.66 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(1397,b,1354,b)].
% 13.51/13.66 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(1397,b,1355,b)].
% 13.51/13.66 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(1397,b,1356,b)].
% 13.51/13.66 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(1397,b,1357,b)].
% 13.51/13.66 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__ring__strict(B). [resolve(1397,b,1358,b)].
% 13.51/13.66 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__semidom(B). [resolve(1397,b,1359,b)].
% 13.51/13.66 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(1397,b,1360,b)].
% 13.51/13.66 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(1397,b,1361,b)].
% 13.51/13.66 1398 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1340,c,1316,b)].
% 13.51/13.66 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1398,c,1344,a)].
% 13.51/13.66 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1398,c,1345,a)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1398,c,1347,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1398,c,1348,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1398,c,1349,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1398,c,1350,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1398,c,1351,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1398,c,1354,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1398,c,1355,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1398,c,1356,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1398,c,1357,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1398,c,1358,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1398,c,1359,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1398,c,1360,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1398,c,1361,b)].
% 13.51/13.66 1399 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(C). [resolve(1341,c,1316,b)].
% 13.51/13.66 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1399,c,1344,a)].
% 13.51/13.66 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1399,c,1345,a)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 13.51/13.66 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1399,c,1347,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1399,c,1348,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1399,c,1349,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1399,c,1350,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1399,c,1351,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1399,c,1354,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1399,c,1355,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1399,c,1356,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1399,c,1357,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1399,c,1358,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1399,c,1359,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1399,c,1360,b)].
% 13.69/13.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1399,c,1361,b)].
% 13.69/13.89 1400 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 13.69/13.89 1401 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 13.69/13.89 1402 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 13.69/13.89 1403 -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].
% 13.69/13.89 1404 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) # label(axiom). [assumption].
% 13.69/13.89 1405 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) # label(axiom). [assumption].
% 13.69/13.89 1406 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_40) # label(axiom). [assumption].
% 13.69/13.89 1407 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_32) # label(axiom). [assumption].
% 13.69/13.89 1408 -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].
% 13.69/13.89 1409 -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].
% 13.69/13.89 1410 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_9) # label(axiom). [assumption].
% 13.69/13.89 1411 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 13.69/13.89 1412 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 13.69/13.89 1413 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 13.69/13.89 1414 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(34,a,12,b)].
% 13.90/14.07 1415 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(35,a,12,b)].
% 13.90/14.07 1416 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(36,a,12,b)].
% 13.90/14.07 1417 -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(37,a,12,b)].
% 13.90/14.07 1418 -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(38,a,12,b)].
% 13.90/14.07 1419 -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(39,a,12,b)].
% 13.90/14.07 1420 -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(40,a,12,b)].
% 13.90/14.07 1421 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(41,a,12,b)].
% 13.90/14.07 1422 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(42,a,12,b)].
% 13.90/14.07 1423 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(307,a,281,b)].
% 13.90/14.07 1424 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(308,a,281,b)].
% 13.90/14.07 1425 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 13.90/14.07 1426 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 13.90/14.07 1427 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 13.90/14.07 1428 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 13.90/14.07 1429 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 13.90/14.07 1430 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 13.90/14.07 1431 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1164,c,1138,b)].
% 13.90/14.07 1432 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1165,b,1138,b)].
% 13.90/14.07 1433 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1166,c,1138,b)].
% 13.90/14.07 1434 -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(1167,c,1138,b)].
% 13.90/14.07 1435 -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(1168,c,1138,b)].
% 13.90/14.07 1436 -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(1169,c,1138,b)].
% 13.90/14.07 1437 -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(1170,c,1138,b)].
% 13.90/14.07 1438 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1171,c,1138,b)].
% 13.90/14.07 1439 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(1172,b,1138,b)].
% 13.90/14.09 1440 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1185,a,1177,b)].
% 13.90/14.09 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(1440,e,1401,a)].
% 13.90/14.09 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(1440,e,1402,a)].
% 13.90/14.09 1441 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1186,a,1177,b)].
% 13.90/14.09 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(1441,d,1401,a)].
% 13.90/14.09 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(1441,d,1402,a)].
% 13.90/14.09 1442 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1187,a,1177,b)].
% 13.90/14.09 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(1442,d,1401,a)].
% 13.90/14.09 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(1442,d,1402,a)].
% 13.90/14.09 1443 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1188,a,1177,b)].
% 13.90/14.09 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(1443,f,1401,a)].
% 13.90/14.09 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(1443,f,1402,a)].
% 13.90/14.09 1444 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1189,a,1177,b)].
% 13.90/14.09 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(1444,e,1401,a)].
% 13.90/14.09 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(1444,e,1402,a)].
% 13.90/14.09 1445 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1190,a,1177,b)].
% 13.90/14.09 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(1445,e,1401,a)].
% 13.90/14.09 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(1445,e,1402,a)].
% 13.90/14.09 1446 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1191,a,1177,b)].
% 13.99/14.10 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1446,f,1401,a)].
% 13.99/14.10 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(1446,f,1402,a)].
% 13.99/14.10 1447 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1192,a,1177,b)].
% 13.99/14.10 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1447,e,1401,a)].
% 13.99/14.10 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(1447,e,1402,a)].
% 13.99/14.10 1448 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1193,a,1177,b)].
% 13.99/14.10 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1448,e,1401,a)].
% 13.99/14.10 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(1448,e,1402,a)].
% 13.99/14.10 1449 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1194,a,1177,b)].
% 13.99/14.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1449,b,1401,a)].
% 13.99/14.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1449,b,1402,a)].
% 13.99/14.10 1450 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1195,a,1177,b)].
% 13.99/14.10 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1450,f,1401,a)].
% 13.99/14.10 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(1450,f,1402,a)].
% 13.99/14.10 1451 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1196,a,1177,b)].
% 13.99/14.10 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1451,e,1401,a)].
% 13.99/14.10 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(1451,e,1402,a)].
% 13.99/14.10 1452 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1197,a,1177,b)].
% 13.99/14.10 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(1452,e,1401,a)].
% 13.99/14.12 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1452,e,1402,a)].
% 13.99/14.12 1453 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1198,a,1177,b)].
% 13.99/14.12 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(1453,f,1401,a)].
% 13.99/14.12 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(1453,f,1402,a)].
% 13.99/14.12 1454 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1199,a,1177,b)].
% 13.99/14.12 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(1454,e,1401,a)].
% 13.99/14.12 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1454,e,1402,a)].
% 13.99/14.12 1455 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1200,a,1177,b)].
% 13.99/14.12 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(1455,e,1401,a)].
% 13.99/14.12 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1455,e,1402,a)].
% 13.99/14.12 1456 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1201,a,1177,b)].
% 13.99/14.12 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(1456,d,1401,a)].
% 13.99/14.12 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(1456,d,1402,a)].
% 13.99/14.12 1457 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1202,a,1177,b)].
% 13.99/14.12 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(1457,d,1401,a)].
% 13.99/14.12 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(1457,d,1402,a)].
% 13.99/14.12 1458 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1203,a,1177,b)].
% 13.99/14.12 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(1458,e,1401,a)].
% 13.99/14.12 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(1458,e,1402,a)].
% 13.99/14.13 1459 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1204,a,1177,b)].
% 13.99/14.13 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1459,b,1401,a)].
% 13.99/14.13 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1459,b,1402,a)].
% 13.99/14.13 1460 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1205,a,1177,b)].
% 13.99/14.13 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(1460,d,1401,a)].
% 13.99/14.13 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(1460,d,1402,a)].
% 13.99/14.13 1461 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1206,a,1177,b)].
% 13.99/14.13 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(1461,e,1401,a)].
% 13.99/14.13 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(1461,e,1402,a)].
% 13.99/14.13 1462 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1207,a,1177,b)].
% 13.99/14.13 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(1462,e,1401,a)].
% 13.99/14.13 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(1462,e,1402,a)].
% 13.99/14.13 1463 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1208,b,1177,b)].
% 13.99/14.13 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(1463,d,1401,a)].
% 13.99/14.13 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(1463,d,1402,a)].
% 13.99/14.13 1464 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1209,b,1177,b)].
% 13.99/14.13 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(1464,d,1401,a)].
% 13.99/14.13 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(1464,d,1402,a)].
% 13.99/14.13 1465 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1210,a,1177,b)].
% 13.99/14.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1465,c,1401,a)].
% 13.99/14.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1465,c,1402,a)].
% 13.99/14.13 1466 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1211,a,1177,b)].
% 13.99/14.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1466,c,1401,a)].
% 13.99/14.13 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1466,c,1402,a)].
% 13.99/14.13 1467 -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1212,a,1177,b)].
% 13.99/14.15 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(1467,d,1401,a)].
% 13.99/14.15 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(1467,d,1402,a)].
% 13.99/14.15 1468 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1213,a,1177,b)].
% 13.99/14.15 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1468,c,1401,a)].
% 13.99/14.15 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1468,c,1402,a)].
% 13.99/14.15 1469 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1214,a,1177,b)].
% 13.99/14.15 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1469,c,1401,a)].
% 13.99/14.15 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1469,c,1402,a)].
% 13.99/14.15 1470 -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1215,a,1177,b)].
% 13.99/14.15 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(1470,d,1401,a)].
% 13.99/14.15 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(1470,d,1402,a)].
% 13.99/14.15 1471 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1216,a,1177,b)].
% 13.99/14.15 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1471,c,1401,a)].
% 13.99/14.15 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1471,c,1402,a)].
% 13.99/14.15 1472 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1217,a,1177,b)].
% 13.99/14.15 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1472,c,1401,a)].
% 13.99/14.15 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1472,c,1402,a)].
% 13.99/14.15 1473 -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1218,a,1177,b)].
% 13.99/14.15 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(1473,d,1401,a)].
% 13.99/14.15 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(1473,d,1402,a)].
% 13.99/14.15 1474 c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 13.99/14.15 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1474,b,1401,a)].
% 13.99/14.15 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1474,b,1402,a)].
% 13.99/14.15 1475 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1220,a,1177,b)].
% 13.99/14.15 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(1475,b,1401,a)].
% 13.99/14.15 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(1475,b,1402,a)].
% 13.99/14.15 1476 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1221,a,1177,b)].
% 13.99/14.15 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1476,c,1401,a)].
% 13.99/14.15 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1476,c,1402,a)].
% 13.99/14.15 1477 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1222,a,1177,b)].
% 13.99/14.17 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1477,c,1401,a)].
% 13.99/14.17 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1477,c,1402,a)].
% 13.99/14.17 1478 -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1223,a,1177,b)].
% 13.99/14.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(1478,d,1401,a)].
% 13.99/14.17 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(1478,d,1402,a)].
% 13.99/14.17 1479 c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 13.99/14.17 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1479,b,1401,a)].
% 13.99/14.17 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1479,b,1402,a)].
% 13.99/14.17 1480 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1225,a,1177,b)].
% 13.99/14.17 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(1480,b,1401,a)].
% 13.99/14.17 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(1480,b,1402,a)].
% 13.99/14.17 1481 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1226,a,1177,b)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1481,b,1401,a)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1481,b,1402,a)].
% 13.99/14.17 1482 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1227,a,1177,b)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1482,b,1401,a)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1482,b,1402,a)].
% 13.99/14.17 1483 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1228,a,1177,b)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1483,b,1401,a)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1483,b,1402,a)].
% 13.99/14.17 1484 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1229,a,1177,b)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1484,b,1401,a)].
% 13.99/14.17 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1484,b,1402,a)].
% 13.99/14.17 1485 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1230,a,1177,b)].
% 13.99/14.17 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1485,c,1401,a)].
% 13.99/14.17 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1485,c,1402,a)].
% 13.99/14.17 1486 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1231,a,1177,b)].
% 13.99/14.17 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1486,c,1401,a)].
% 13.99/14.18 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1486,c,1402,a)].
% 13.99/14.18 1487 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1232,a,1177,b)].
% 13.99/14.18 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1487,c,1401,a)].
% 13.99/14.18 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1487,c,1402,a)].
% 13.99/14.18 1488 -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1233,a,1177,b)].
% 13.99/14.18 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(1488,c,1401,a)].
% 13.99/14.18 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(1488,c,1402,a)].
% 13.99/14.18 1489 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1234,a,1177,b)].
% 13.99/14.18 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(1489,c,1401,a)].
% 13.99/14.18 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(1489,c,1402,a)].
% 13.99/14.18 1490 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1235,a,1177,b)].
% 13.99/14.18 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(1490,c,1401,a)].
% 13.99/14.18 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(1490,c,1402,a)].
% 13.99/14.18 1491 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1236,a,1177,b)].
% 13.99/14.18 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(1491,d,1401,a)].
% 13.99/14.18 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(1491,d,1402,a)].
% 13.99/14.18 1492 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1237,a,1177,b)].
% 13.99/14.18 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(1492,d,1401,a)].
% 13.99/14.18 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(1492,d,1402,a)].
% 13.99/14.18 1493 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1238,a,1177,b)].
% 13.99/14.19 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(1493,c,1401,a)].
% 13.99/14.19 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(1493,c,1402,a)].
% 13.99/14.19 1494 -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_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1239,a,1177,b)].
% 13.99/14.19 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(1494,d,1401,a)].
% 13.99/14.19 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(1494,d,1402,a)].
% 13.99/14.19 1495 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1240,a,1177,b)].
% 13.99/14.19 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1495,c,1401,a)].
% 13.99/14.19 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1495,c,1402,a)].
% 13.99/14.19 1496 -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1241,a,1177,b)].
% 13.99/14.19 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(1496,c,1401,a)].
% 13.99/14.19 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1496,c,1402,a)].
% 13.99/14.19 1497 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1242,a,1177,b)].
% 13.99/14.19 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(1497,c,1401,a)].
% 13.99/14.19 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)). [resolve(1497,c,1402,a)].
% 13.99/14.19 1498 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1498,b,1401,a)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1498,b,1402,a)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1498,b,1406,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 13.99/14.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 13.99/14.19 1499 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 13.99/14.19 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1499,b,1401,a)].
% 13.99/14.19 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1499,b,1402,a)].
% 13.99/14.19 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 13.99/14.19 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1499,b,1406,b)].
% 13.99/14.19 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 14.10/14.21 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 14.10/14.21 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 14.10/14.21 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 14.10/14.21 1500 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 14.10/14.21 1501 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 14.10/14.21 1502 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 14.10/14.21 1503 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1260,c,1177,b)].
% 14.10/14.21 1504 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1261,b,1177,b)].
% 14.10/14.21 1505 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1262,c,1177,b)].
% 14.10/14.21 1506 -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(1263,c,1177,b)].
% 14.10/14.21 1507 -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(1264,c,1177,b)].
% 14.10/14.21 1508 -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(1265,c,1177,b)].
% 14.10/14.21 1509 -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(1266,c,1177,b)].
% 14.10/14.21 1510 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1267,c,1177,b)].
% 14.10/14.21 1511 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(1268,b,1177,b)].
% 14.10/14.21 1512 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 14.10/14.21 1513 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1340,c,1314,b)].
% 14.10/14.21 1514 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1341,c,1314,b)].
% 14.10/14.21 1515 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1362,a,1350,b)].
% 14.10/14.21 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(1515,c,1401,a)].
% 14.10/14.21 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1515,c,1402,a)].
% 14.10/14.21 1516 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1363,a,1350,b)].
% 14.10/14.21 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(1516,c,1401,a)].
% 14.10/14.21 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1516,c,1402,a)].
% 14.10/14.21 1517 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1364,a,1350,b)].
% 14.10/14.21 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(1517,c,1401,a)].
% 14.10/14.21 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1517,c,1402,a)].
% 14.10/14.24 1518 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1365,a,1350,b)].
% 14.10/14.24 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(1518,c,1401,a)].
% 14.10/14.24 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1518,c,1402,a)].
% 14.10/14.24 1519 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1366,a,1350,b)].
% 14.10/14.24 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(1519,c,1401,a)].
% 14.10/14.24 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1519,c,1402,a)].
% 14.10/14.24 1520 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1367,a,1350,b)].
% 14.10/14.24 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(1520,c,1401,a)].
% 14.10/14.24 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1520,c,1402,a)].
% 14.10/14.24 1521 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1368,a,1350,b)].
% 14.10/14.24 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(1521,c,1401,a)].
% 14.10/14.24 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1521,c,1402,a)].
% 14.10/14.24 1522 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1369,a,1350,b)].
% 14.10/14.24 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(1522,c,1401,a)].
% 14.10/14.24 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1522,c,1402,a)].
% 14.10/14.24 1523 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1523,b,1401,a)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1523,b,1402,a)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1523,b,1406,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 14.10/14.24 1524 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 14.10/14.24 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1524,b,1401,a)].
% 14.10/14.24 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1524,b,1402,a)].
% 14.10/14.24 1525 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 14.10/14.24 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1525,b,1401,a)].
% 14.10/14.24 Derived: c_lessequals(A,A,tc_nat). [resolve(1525,b,1402,a)].
% 14.10/14.24 1526 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 14.10/14.24 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 14.10/14.24 Derived: class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 14.10/14.24 1527 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 14.10/14.26 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1527,b,1401,a)].
% 14.10/14.26 Derived: -c_less(A,A,tc_nat). [resolve(1527,b,1402,a)].
% 14.10/14.26 1528 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1389,c,1350,b)].
% 14.10/14.26 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1528,c,1401,a)].
% 14.10/14.26 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1528,c,1402,a)].
% 14.10/14.26 1529 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1390,b,1350,b)].
% 14.10/14.26 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1529,b,1401,a)].
% 14.10/14.26 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1529,b,1402,a)].
% 14.10/14.26 1530 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1391,c,1350,b)].
% 14.10/14.26 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1530,c,1401,a)].
% 14.10/14.26 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1530,c,1402,a)].
% 14.10/14.26 1531 -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(1392,c,1350,b)].
% 14.10/14.26 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(1531,c,1401,a)].
% 14.10/14.26 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(1531,c,1402,a)].
% 14.10/14.26 1532 -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(1393,c,1350,b)].
% 14.10/14.26 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(1532,c,1401,a)].
% 14.10/14.26 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(1532,c,1402,a)].
% 14.10/14.26 1533 -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(1394,c,1350,b)].
% 14.10/14.26 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(1533,c,1401,a)].
% 14.10/14.26 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(1533,c,1402,a)].
% 14.10/14.26 1534 -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(1395,c,1350,b)].
% 14.10/14.26 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(1534,c,1401,a)].
% 14.10/14.26 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(1534,c,1402,a)].
% 14.10/14.26 1535 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1396,c,1350,b)].
% 14.10/14.26 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1535,c,1401,a)].
% 14.10/14.26 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1535,c,1402,a)].
% 14.10/14.26 1536 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(1397,b,1350,b)].
% 14.79/14.91 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(1536,b,1401,a)].
% 14.79/14.91 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(1536,b,1402,a)].
% 14.79/14.91 1537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1398,c,1350,b)].
% 14.79/14.91 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1537,c,1401,a)].
% 14.79/14.91 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1537,c,1402,a)].
% 14.79/14.91 1538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1399,c,1350,b)].
% 14.79/14.91 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1538,c,1401,a)].
% 14.79/14.91 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1538,c,1402,a)].
% 14.79/14.91 1539 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 14.79/14.91 1540 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 14.79/14.91 1541 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 14.79/14.91 1542 -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].
% 14.79/14.91 1543 -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].
% 14.79/14.91 1544 -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].
% 14.79/14.91 1545 -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].
% 14.79/14.91 1546 -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].
% 14.79/14.91 1547 -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].
% 14.79/14.91 1548 -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].
% 14.79/14.91 1549 -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].
% 14.79/14.91 1550 -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].
% 14.79/14.91 1551 -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].
% 14.79/14.91 1552 -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].
% 14.79/14.91 1553 -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].
% 14.79/14.91 1554 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 14.79/14.91 1555 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 14.85/15.01 1556 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 14.85/15.01 1557 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 14.85/15.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 14.85/15.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 14.85/15.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1557,a,1551,b)].
% 14.85/15.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 14.85/15.01 1558 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 14.85/15.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 14.85/15.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 14.85/15.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1558,b,1551,b)].
% 14.85/15.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 14.85/15.01 1559 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(34,a,31,b)].
% 14.85/15.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1559,c,1549,b)].
% 14.85/15.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1559,c,1550,b)].
% 14.85/15.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1559,c,1551,b)].
% 14.85/15.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1559,c,1552,b)].
% 14.85/15.01 1560 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(35,a,31,b)].
% 14.85/15.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1560,b,1549,b)].
% 14.85/15.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1560,b,1550,b)].
% 14.85/15.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1560,b,1551,b)].
% 14.85/15.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1560,b,1552,b)].
% 14.85/15.01 1561 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(36,a,31,b)].
% 14.85/15.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1561,c,1549,b)].
% 14.85/15.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1561,c,1550,b)].
% 14.85/15.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1561,c,1551,b)].
% 14.85/15.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1561,c,1552,b)].
% 14.85/15.01 1562 -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__semiring(B). [resolve(37,a,31,b)].
% 14.85/15.01 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(1562,c,1549,b)].
% 14.85/15.01 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(1562,c,1550,b)].
% 14.93/15.03 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(1562,c,1551,b)].
% 14.93/15.03 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(1562,c,1552,b)].
% 14.93/15.03 1563 -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__semiring(C). [resolve(38,a,31,b)].
% 14.93/15.03 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(1563,c,1549,b)].
% 14.93/15.03 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(1563,c,1550,b)].
% 14.93/15.03 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(1563,c,1551,b)].
% 14.93/15.03 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(1563,c,1552,b)].
% 14.93/15.03 1564 -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__semiring(B). [resolve(39,a,31,b)].
% 14.93/15.03 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(1564,c,1549,b)].
% 14.93/15.03 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(1564,c,1550,b)].
% 14.93/15.03 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(1564,c,1551,b)].
% 14.93/15.03 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(1564,c,1552,b)].
% 14.93/15.03 1565 -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__semiring(C). [resolve(40,a,31,b)].
% 14.93/15.03 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(1565,c,1549,b)].
% 14.93/15.03 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(1565,c,1550,b)].
% 14.93/15.03 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(1565,c,1551,b)].
% 14.93/15.03 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(1565,c,1552,b)].
% 14.93/15.03 1566 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__semiring(C). [resolve(41,a,31,b)].
% 14.93/15.03 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1566,c,1549,b)].
% 14.93/15.03 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1566,c,1550,b)].
% 14.93/15.03 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1566,c,1551,b)].
% 14.93/15.03 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1566,c,1552,b)].
% 14.93/15.07 1567 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__semiring(B). [resolve(42,a,31,b)].
% 14.93/15.07 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(1567,b,1549,b)].
% 14.93/15.07 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(1567,b,1550,b)].
% 14.93/15.07 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(1567,b,1551,b)].
% 14.93/15.07 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(1567,b,1552,b)].
% 14.93/15.07 1568 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 14.93/15.07 1569 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 14.93/15.07 1570 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 14.93/15.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 14.93/15.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 14.93/15.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 14.93/15.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 14.93/15.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 14.93/15.07 1571 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(108,b,97,b)].
% 14.93/15.07 1572 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(109,b,97,b)].
% 14.93/15.07 1573 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 14.93/15.07 1574 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 14.93/15.07 1575 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(221,c,210,b)].
% 14.93/15.07 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1575,c,1543,b)].
% 14.93/15.07 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1575,c,1547,b)].
% 14.93/15.07 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1575,c,1548,b)].
% 14.93/15.07 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1575,c,1549,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1575,c,1550,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1575,c,1552,b)].
% 14.99/15.08 1576 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(222,c,210,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1576,c,1543,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1576,c,1547,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1576,c,1548,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1576,c,1549,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1576,c,1550,b)].
% 14.99/15.08 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1576,c,1552,b)].
% 14.99/15.08 1577 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 14.99/15.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 14.99/15.08 1578 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 14.99/15.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 14.99/15.08 1579 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 14.99/15.08 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 14.99/15.08 1580 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 14.99/15.08 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 14.99/15.08 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 14.99/15.08 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 15.46/15.57 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 15.46/15.57 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 15.46/15.57 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 15.46/15.57 1581 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 15.46/15.57 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 15.46/15.57 1582 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 15.46/15.57 1583 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 15.46/15.57 1584 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 15.46/15.57 1585 -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].
% 15.46/15.57 1586 -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].
% 15.46/15.57 1587 -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].
% 15.46/15.57 1588 -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].
% 15.46/15.57 1589 -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].
% 15.46/15.57 1590 -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].
% 15.46/15.57 1591 -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].
% 15.46/15.57 1592 -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].
% 15.46/15.57 1593 -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].
% 15.46/15.57 1594 -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].
% 15.46/15.57 1595 -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].
% 15.46/15.57 1596 -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].
% 15.46/15.57 1597 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 15.46/15.57 1598 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 15.46/15.57 1599 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(34,a,27,b)].
% 15.46/15.57 1600 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(35,a,27,b)].
% 15.46/15.57 1601 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(36,a,27,b)].
% 15.52/15.65 1602 -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(37,a,27,b)].
% 15.52/15.65 1603 -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(38,a,27,b)].
% 15.52/15.65 1604 -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(39,a,27,b)].
% 15.52/15.65 1605 -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(40,a,27,b)].
% 15.52/15.65 1606 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(41,a,27,b)].
% 15.52/15.65 1607 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(42,a,27,b)].
% 15.52/15.65 1608 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 15.52/15.65 1609 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 15.52/15.65 1610 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 15.52/15.65 1611 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(108,b,93,b)].
% 15.52/15.65 1612 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(109,b,93,b)].
% 15.52/15.65 1613 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 15.52/15.65 1614 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 15.52/15.65 1615 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(221,c,206,b)].
% 15.52/15.65 1616 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(222,c,206,b)].
% 15.52/15.65 1617 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 15.52/15.65 1618 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 15.52/15.65 1619 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 15.52/15.65 1620 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 15.52/15.65 1621 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(307,a,300,b)].
% 15.52/15.65 1622 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(308,a,300,b)].
% 15.52/15.65 1623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 15.52/15.65 1624 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 15.52/15.65 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 15.52/15.65 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 15.52/15.65 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 15.52/15.65 1625 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 15.82/15.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 15.82/15.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 15.82/15.93 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 15.82/15.93 1626 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 15.82/15.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 15.82/15.93 1627 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(389,c,369,b)].
% 15.82/15.93 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1627,c,1592,b)].
% 15.82/15.93 1628 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(390,c,369,b)].
% 15.82/15.93 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1628,c,1592,b)].
% 15.82/15.93 1629 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 15.82/15.93 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 15.82/15.93 1630 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 15.82/15.93 1631 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1631,b,1583,a)].
% 15.82/15.93 Derived: c_lessequals(A,A,tc_nat). [resolve(1631,b,1584,a)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1631,b,1587,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 15.82/15.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 15.82/15.93 1632 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 15.82/15.93 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1632,b,1583,a)].
% 15.82/15.93 Derived: -c_less(A,A,tc_nat). [resolve(1632,b,1584,a)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1632,b,1587,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 15.82/15.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 15.82/15.93 1633 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1559,c,1550,b)].
% 15.82/15.94 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1633,c,1583,a)].
% 15.82/15.94 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1633,c,1584,a)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1633,c,1585,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1633,c,1586,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1633,c,1587,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1633,c,1588,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1633,c,1589,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1633,c,1590,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1633,c,1591,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1633,c,1592,b)].
% 15.82/15.94 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1633,c,1596,b)].
% 15.82/15.94 1634 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1560,b,1550,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1634,b,1583,a)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1634,b,1584,a)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1634,b,1585,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1634,b,1586,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1634,b,1587,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1634,b,1588,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1634,b,1589,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1634,b,1590,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1634,b,1591,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1634,b,1592,b)].
% 15.82/15.94 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1634,b,1596,b)].
% 15.82/15.94 1635 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1561,c,1550,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1635,c,1583,a)].
% 15.82/15.94 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1635,c,1584,a)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1635,c,1585,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1635,c,1586,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1635,c,1587,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1635,c,1588,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1635,c,1589,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1635,c,1590,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1635,c,1591,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1635,c,1592,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1635,c,1596,b)].
% 15.82/15.94 1636 -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(1562,c,1550,b)].
% 15.82/15.94 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(1636,c,1583,a)].
% 15.82/15.94 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(1636,c,1584,a)].
% 15.82/15.94 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_Olordered__ring(B). [resolve(1636,c,1585,b)].
% 15.82/15.94 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(1636,c,1586,b)].
% 15.82/15.94 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(1636,c,1587,b)].
% 15.82/15.94 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(1636,c,1588,b)].
% 15.82/15.94 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__ring__strict(B). [resolve(1636,c,1589,b)].
% 15.82/15.94 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__semidom(B). [resolve(1636,c,1590,b)].
% 15.82/15.94 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__semiring__strict(B). [resolve(1636,c,1591,b)].
% 15.82/15.94 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_Opordered__cancel__comm__semiring(B). [resolve(1636,c,1592,b)].
% 15.82/15.94 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_Opordered__ring(B). [resolve(1636,c,1596,b)].
% 15.82/15.94 1637 -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(1563,c,1550,b)].
% 15.82/15.94 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(1637,c,1583,a)].
% 15.82/15.94 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(1637,c,1584,a)].
% 15.82/15.94 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_Olordered__ring(C). [resolve(1637,c,1585,b)].
% 15.82/15.94 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(1637,c,1586,b)].
% 15.82/15.94 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(1637,c,1587,b)].
% 15.82/15.94 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(1637,c,1588,b)].
% 15.82/15.94 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__ring__strict(C). [resolve(1637,c,1589,b)].
% 15.82/15.94 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__semidom(C). [resolve(1637,c,1590,b)].
% 15.82/15.94 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__semiring__strict(C). [resolve(1637,c,1591,b)].
% 15.82/15.94 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_Opordered__cancel__comm__semiring(C). [resolve(1637,c,1592,b)].
% 15.82/15.94 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_Opordered__ring(C). [resolve(1637,c,1596,b)].
% 15.82/15.94 1638 -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(1564,c,1550,b)].
% 15.82/15.94 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(1638,c,1583,a)].
% 15.82/15.94 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(1638,c,1584,a)].
% 15.82/15.94 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_Olordered__ring(B). [resolve(1638,c,1585,b)].
% 15.82/15.94 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(1638,c,1586,b)].
% 15.82/15.94 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(1638,c,1587,b)].
% 15.82/15.94 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(1638,c,1588,b)].
% 15.82/15.94 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__ring__strict(B). [resolve(1638,c,1589,b)].
% 15.82/15.94 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__semidom(B). [resolve(1638,c,1590,b)].
% 15.82/15.94 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__semiring__strict(B). [resolve(1638,c,1591,b)].
% 15.82/15.94 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_Opordered__cancel__comm__semiring(B). [resolve(1638,c,1592,b)].
% 15.82/15.94 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_Opordered__ring(B). [resolve(1638,c,1596,b)].
% 15.82/15.94 1639 -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(1565,c,1550,b)].
% 15.82/15.94 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(1639,c,1583,a)].
% 15.82/15.94 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(1639,c,1584,a)].
% 15.82/15.94 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_Olordered__ring(C). [resolve(1639,c,1585,b)].
% 15.82/15.94 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(1639,c,1586,b)].
% 15.82/15.94 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__field(C). [resolve(1639,c,1587,b)].
% 15.82/15.94 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__idom(C). [resolve(1639,c,1588,b)].
% 15.82/15.94 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__ring__strict(C). [resolve(1639,c,1589,b)].
% 15.82/15.94 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__semidom(C). [resolve(1639,c,1590,b)].
% 15.82/15.94 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__semiring__strict(C). [resolve(1639,c,1591,b)].
% 15.82/15.94 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_Opordered__cancel__comm__semiring(C). [resolve(1639,c,1592,b)].
% 15.82/15.94 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_Opordered__ring(C). [resolve(1639,c,1596,b)].
% 15.82/15.94 1640 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1566,c,1550,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1640,c,1583,a)].
% 15.82/15.94 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1640,c,1584,a)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1640,c,1585,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1640,c,1586,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1640,c,1587,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1640,c,1588,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1640,c,1589,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1640,c,1590,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1640,c,1591,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1640,c,1592,b)].
% 15.82/15.94 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1640,c,1596,b)].
% 15.82/15.94 1641 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(1567,b,1550,b)].
% 15.82/15.95 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(1641,b,1583,a)].
% 15.82/15.95 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(1641,b,1584,a)].
% 15.82/15.95 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_Olordered__ring(B). [resolve(1641,b,1585,b)].
% 15.82/15.95 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(1641,b,1586,b)].
% 15.82/15.95 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(1641,b,1587,b)].
% 15.82/15.95 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(1641,b,1588,b)].
% 15.82/15.95 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__ring__strict(B). [resolve(1641,b,1589,b)].
% 15.82/15.95 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__semidom(B). [resolve(1641,b,1590,b)].
% 15.82/15.95 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__semiring__strict(B). [resolve(1641,b,1591,b)].
% 15.82/15.95 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_Opordered__cancel__comm__semiring(B). [resolve(1641,b,1592,b)].
% 15.82/15.95 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_Opordered__ring(B). [resolve(1641,b,1596,b)].
% 15.82/15.95 1642 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1642,b,1583,a)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1642,b,1584,a)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1642,b,1587,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 15.82/15.95 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 15.82/15.95 1643 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1575,c,1550,b)].
% 15.82/15.95 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(1643,c,1583,a)].
% 15.82/15.95 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(1643,c,1584,a)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1643,c,1585,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1643,c,1586,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1643,c,1587,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1643,c,1588,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1643,c,1589,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1643,c,1590,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1643,c,1591,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1643,c,1592,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1643,c,1596,b)].
% 15.82/15.95 1644 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1576,c,1550,b)].
% 15.82/15.95 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(1644,c,1583,a)].
% 15.82/15.95 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(1644,c,1584,a)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1644,c,1585,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1644,c,1586,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1644,c,1587,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1644,c,1588,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1644,c,1589,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1644,c,1590,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1644,c,1591,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1644,c,1592,b)].
% 15.82/15.95 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1644,c,1596,b)].
% 15.82/15.95 1645 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1645,b,1583,a)].
% 15.82/15.95 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1645,b,1584,a)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1645,b,1587,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 15.82/15.95 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 15.82/15.95 1646 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1646,b,1583,a)].
% 15.82/15.95 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1646,b,1584,a)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1646,b,1587,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 15.82/15.95 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 16.05/16.17 1647 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 16.05/16.17 Derived: class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 16.05/16.17 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 16.05/16.17 1648 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 16.05/16.17 1649 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 16.05/16.17 1650 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 16.05/16.17 1651 -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].
% 16.05/16.17 1652 -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].
% 16.05/16.17 1653 -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].
% 16.05/16.17 1654 -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].
% 16.05/16.17 1655 -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].
% 16.05/16.17 1656 -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].
% 16.05/16.17 1657 -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].
% 16.05/16.17 1658 -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].
% 16.05/16.17 1659 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 16.05/16.17 1660 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 16.05/16.17 1661 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(34,a,25,b)].
% 16.05/16.17 1662 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(35,a,25,b)].
% 16.05/16.17 1663 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(36,a,25,b)].
% 16.05/16.17 1664 -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(37,a,25,b)].
% 16.14/16.23 1665 -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(38,a,25,b)].
% 16.14/16.23 1666 -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(39,a,25,b)].
% 16.14/16.23 1667 -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(40,a,25,b)].
% 16.14/16.23 1668 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(41,a,25,b)].
% 16.14/16.23 1669 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(42,a,25,b)].
% 16.14/16.23 1670 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 16.14/16.23 1671 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 16.14/16.23 1672 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 16.14/16.23 1673 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(108,b,91,b)].
% 16.14/16.23 1674 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(109,b,91,b)].
% 16.14/16.23 1675 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 16.14/16.23 1676 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 16.14/16.23 1677 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(221,c,204,b)].
% 16.14/16.23 1678 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(222,c,204,b)].
% 16.14/16.23 1679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 16.14/16.23 1680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 16.14/16.23 1681 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 16.14/16.23 1682 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 16.14/16.23 1683 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(307,a,298,b)].
% 16.14/16.23 1684 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(308,a,298,b)].
% 16.14/16.23 1685 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 16.14/16.23 1686 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 16.14/16.23 1687 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 16.14/16.23 1688 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 16.14/16.23 1689 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(389,c,367,b)].
% 16.14/16.23 1690 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(390,c,367,b)].
% 16.14/16.23 1691 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 16.27/16.36 1692 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 16.27/16.36 1693 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 16.27/16.36 1694 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 16.27/16.36 1695 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 16.27/16.36 1696 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 16.27/16.36 1697 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1164,c,1146,b)].
% 16.27/16.36 1698 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1165,b,1146,b)].
% 16.27/16.36 1699 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1166,c,1146,b)].
% 16.27/16.36 1700 -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(1167,c,1146,b)].
% 16.27/16.36 1701 -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(1168,c,1146,b)].
% 16.27/16.36 1702 -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(1169,c,1146,b)].
% 16.27/16.36 1703 -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(1170,c,1146,b)].
% 16.27/16.36 1704 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1171,c,1146,b)].
% 16.27/16.36 1705 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(1172,b,1146,b)].
% 16.27/16.36 1706 -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__semiring__strict(C). [resolve(1185,a,1183,b)].
% 16.27/16.36 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(1706,e,1651,b)].
% 16.27/16.36 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(1706,e,1652,b)].
% 16.27/16.36 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(1706,e,1653,b)].
% 16.27/16.36 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__ring__strict(C). [resolve(1706,e,1654,b)].
% 16.27/16.36 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__semidom(C). [resolve(1706,e,1655,b)].
% 16.27/16.36 1707 -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__semiring__strict(B). [resolve(1186,a,1183,b)].
% 16.27/16.36 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(1707,d,1651,b)].
% 16.27/16.36 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(1707,d,1652,b)].
% 16.27/16.36 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(1707,d,1653,b)].
% 16.28/16.37 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__ring__strict(B). [resolve(1707,d,1654,b)].
% 16.28/16.37 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__semidom(B). [resolve(1707,d,1655,b)].
% 16.28/16.37 1708 -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__semiring__strict(B). [resolve(1187,a,1183,b)].
% 16.28/16.37 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(1708,d,1651,b)].
% 16.28/16.37 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(1708,d,1652,b)].
% 16.28/16.37 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(1708,d,1653,b)].
% 16.28/16.37 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__ring__strict(B). [resolve(1708,d,1654,b)].
% 16.28/16.37 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__semidom(B). [resolve(1708,d,1655,b)].
% 16.28/16.37 1709 -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__semiring__strict(C). [resolve(1188,a,1183,b)].
% 16.28/16.37 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(1709,f,1651,b)].
% 16.28/16.37 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(1709,f,1652,b)].
% 16.28/16.37 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(1709,f,1653,b)].
% 16.28/16.37 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__ring__strict(C). [resolve(1709,f,1654,b)].
% 16.28/16.37 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__semidom(C). [resolve(1709,f,1655,b)].
% 16.28/16.37 1710 -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__semiring__strict(B). [resolve(1189,a,1183,b)].
% 16.28/16.37 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(1710,e,1651,b)].
% 16.28/16.37 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(1710,e,1652,b)].
% 16.28/16.37 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(1710,e,1653,b)].
% 16.28/16.38 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__ring__strict(B). [resolve(1710,e,1654,b)].
% 16.28/16.38 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__semidom(B). [resolve(1710,e,1655,b)].
% 16.28/16.38 1711 -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__semiring__strict(B). [resolve(1190,a,1183,b)].
% 16.28/16.38 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(1711,e,1651,b)].
% 16.28/16.38 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(1711,e,1652,b)].
% 16.28/16.38 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(1711,e,1653,b)].
% 16.28/16.38 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__ring__strict(B). [resolve(1711,e,1654,b)].
% 16.28/16.38 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__semidom(B). [resolve(1711,e,1655,b)].
% 16.28/16.38 1712 -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__semiring__strict(C). [resolve(1191,a,1183,b)].
% 16.28/16.38 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(1712,f,1651,b)].
% 16.28/16.38 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(1712,f,1652,b)].
% 16.28/16.38 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(1712,f,1653,b)].
% 16.28/16.38 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__ring__strict(C). [resolve(1712,f,1654,b)].
% 16.28/16.38 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__semidom(C). [resolve(1712,f,1655,b)].
% 16.28/16.38 1713 -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__semiring__strict(B). [resolve(1192,a,1183,b)].
% 16.28/16.38 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(1713,e,1651,b)].
% 16.28/16.38 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(1713,e,1652,b)].
% 16.28/16.38 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(1713,e,1653,b)].
% 16.28/16.39 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__ring__strict(B). [resolve(1713,e,1654,b)].
% 16.28/16.39 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__semidom(B). [resolve(1713,e,1655,b)].
% 16.28/16.39 1714 -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__semiring__strict(B). [resolve(1193,a,1183,b)].
% 16.28/16.39 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(1714,e,1651,b)].
% 16.28/16.39 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(1714,e,1652,b)].
% 16.28/16.39 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(1714,e,1653,b)].
% 16.28/16.39 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__ring__strict(B). [resolve(1714,e,1654,b)].
% 16.28/16.39 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__semidom(B). [resolve(1714,e,1655,b)].
% 16.28/16.39 1715 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1194,a,1183,b)].
% 16.28/16.39 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1715,b,1651,b)].
% 16.28/16.39 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1715,b,1652,b)].
% 16.28/16.39 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1715,b,1653,b)].
% 16.28/16.39 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1715,b,1654,b)].
% 16.28/16.39 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1715,b,1655,b)].
% 16.28/16.39 1716 -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__semiring__strict(C). [resolve(1195,a,1183,b)].
% 16.28/16.39 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(1716,f,1651,b)].
% 16.28/16.39 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(1716,f,1652,b)].
% 16.28/16.39 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(1716,f,1653,b)].
% 16.28/16.39 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__ring__strict(C). [resolve(1716,f,1654,b)].
% 16.28/16.39 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__semidom(C). [resolve(1716,f,1655,b)].
% 16.28/16.40 1717 -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__semiring__strict(B). [resolve(1196,a,1183,b)].
% 16.28/16.40 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(1717,e,1651,b)].
% 16.28/16.40 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(1717,e,1652,b)].
% 16.28/16.40 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(1717,e,1653,b)].
% 16.28/16.40 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__ring__strict(B). [resolve(1717,e,1654,b)].
% 16.28/16.40 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__semidom(B). [resolve(1717,e,1655,b)].
% 16.28/16.40 1718 -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__semiring__strict(B). [resolve(1197,a,1183,b)].
% 16.28/16.40 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(1718,e,1651,b)].
% 16.28/16.40 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(1718,e,1652,b)].
% 16.28/16.40 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(1718,e,1653,b)].
% 16.28/16.40 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__ring__strict(B). [resolve(1718,e,1654,b)].
% 16.28/16.40 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__semidom(B). [resolve(1718,e,1655,b)].
% 16.28/16.40 1719 -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__semiring__strict(C). [resolve(1198,a,1183,b)].
% 16.28/16.40 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(1719,f,1651,b)].
% 16.28/16.40 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(1719,f,1652,b)].
% 16.28/16.40 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(1719,f,1653,b)].
% 16.28/16.40 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__ring__strict(C). [resolve(1719,f,1654,b)].
% 16.28/16.40 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__semidom(C). [resolve(1719,f,1655,b)].
% 16.32/16.41 1720 -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__semiring__strict(B). [resolve(1199,a,1183,b)].
% 16.32/16.41 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(1720,e,1651,b)].
% 16.32/16.41 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(1720,e,1652,b)].
% 16.32/16.41 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(1720,e,1653,b)].
% 16.32/16.41 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__ring__strict(B). [resolve(1720,e,1654,b)].
% 16.32/16.41 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__semidom(B). [resolve(1720,e,1655,b)].
% 16.32/16.41 1721 -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__semiring__strict(B). [resolve(1200,a,1183,b)].
% 16.32/16.41 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(1721,e,1651,b)].
% 16.32/16.41 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(1721,e,1652,b)].
% 16.32/16.41 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(1721,e,1653,b)].
% 16.32/16.41 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__ring__strict(B). [resolve(1721,e,1654,b)].
% 16.32/16.41 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__semidom(B). [resolve(1721,e,1655,b)].
% 16.32/16.41 1722 -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__semiring__strict(B). [resolve(1201,a,1183,b)].
% 16.32/16.41 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(1722,d,1651,b)].
% 16.32/16.41 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(1722,d,1652,b)].
% 16.32/16.41 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(1722,d,1653,b)].
% 16.32/16.41 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__ring__strict(B). [resolve(1722,d,1654,b)].
% 16.32/16.41 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__semidom(B). [resolve(1722,d,1655,b)].
% 16.32/16.41 1723 -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__semiring__strict(B). [resolve(1202,a,1183,b)].
% 16.32/16.42 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(1723,d,1651,b)].
% 16.32/16.42 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(1723,d,1652,b)].
% 16.32/16.42 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(1723,d,1653,b)].
% 16.32/16.42 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__ring__strict(B). [resolve(1723,d,1654,b)].
% 16.32/16.42 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__semidom(B). [resolve(1723,d,1655,b)].
% 16.32/16.42 1724 -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__semiring__strict(C). [resolve(1203,a,1183,b)].
% 16.32/16.42 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(1724,e,1651,b)].
% 16.32/16.42 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(1724,e,1652,b)].
% 16.32/16.42 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(1724,e,1653,b)].
% 16.32/16.42 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__ring__strict(C). [resolve(1724,e,1654,b)].
% 16.32/16.42 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__semidom(C). [resolve(1724,e,1655,b)].
% 16.32/16.42 1725 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1204,a,1183,b)].
% 16.32/16.42 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1725,b,1651,b)].
% 16.32/16.42 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1725,b,1652,b)].
% 16.32/16.42 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1725,b,1653,b)].
% 16.32/16.42 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1725,b,1654,b)].
% 16.32/16.42 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1725,b,1655,b)].
% 16.32/16.42 1726 -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__semiring__strict(B). [resolve(1205,a,1183,b)].
% 16.32/16.42 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(1726,d,1651,b)].
% 16.32/16.42 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(1726,d,1652,b)].
% 16.32/16.42 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(1726,d,1653,b)].
% 16.32/16.43 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__ring__strict(B). [resolve(1726,d,1654,b)].
% 16.32/16.43 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__semidom(B). [resolve(1726,d,1655,b)].
% 16.32/16.43 1727 -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__semiring__strict(C). [resolve(1206,a,1183,b)].
% 16.32/16.43 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(1727,e,1651,b)].
% 16.32/16.43 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(1727,e,1652,b)].
% 16.32/16.43 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(1727,e,1653,b)].
% 16.32/16.43 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__ring__strict(C). [resolve(1727,e,1654,b)].
% 16.32/16.43 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__semidom(C). [resolve(1727,e,1655,b)].
% 16.32/16.43 1728 -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__semiring__strict(C). [resolve(1207,a,1183,b)].
% 16.32/16.43 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(1728,e,1651,b)].
% 16.32/16.43 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(1728,e,1652,b)].
% 16.32/16.43 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(1728,e,1653,b)].
% 16.32/16.43 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__ring__strict(C). [resolve(1728,e,1654,b)].
% 16.32/16.43 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__semidom(C). [resolve(1728,e,1655,b)].
% 16.32/16.43 1729 -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__semiring__strict(A). [resolve(1208,b,1183,b)].
% 16.32/16.43 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(1729,d,1651,b)].
% 16.32/16.43 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(1729,d,1652,b)].
% 16.32/16.43 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(1729,d,1653,b)].
% 16.32/16.43 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__ring__strict(A). [resolve(1729,d,1654,b)].
% 16.32/16.43 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__semidom(A). [resolve(1729,d,1655,b)].
% 16.35/16.44 1730 -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__semiring__strict(A). [resolve(1209,b,1183,b)].
% 16.35/16.44 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(1730,d,1651,b)].
% 16.35/16.44 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(1730,d,1652,b)].
% 16.35/16.44 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(1730,d,1653,b)].
% 16.35/16.44 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__ring__strict(A). [resolve(1730,d,1654,b)].
% 16.35/16.44 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__semidom(A). [resolve(1730,d,1655,b)].
% 16.35/16.44 1731 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1210,a,1183,b)].
% 16.35/16.44 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(1731,c,1651,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1731,c,1652,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1731,c,1653,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1731,c,1654,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1731,c,1655,b)].
% 16.35/16.44 1732 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1211,a,1183,b)].
% 16.35/16.44 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(1732,c,1651,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1732,c,1652,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1732,c,1653,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1732,c,1654,b)].
% 16.35/16.44 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1732,c,1655,b)].
% 16.35/16.44 1733 -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__semiring__strict(C). [resolve(1212,a,1183,b)].
% 16.35/16.44 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(1733,d,1651,b)].
% 16.35/16.44 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(1733,d,1652,b)].
% 16.35/16.44 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(1733,d,1653,b)].
% 16.35/16.44 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__ring__strict(C). [resolve(1733,d,1654,b)].
% 16.35/16.44 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__semidom(C). [resolve(1733,d,1655,b)].
% 16.35/16.44 1734 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1213,a,1183,b)].
% 16.35/16.44 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(1734,c,1651,b)].
% 16.35/16.44 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1734,c,1652,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1734,c,1653,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1734,c,1654,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1734,c,1655,b)].
% 16.35/16.45 1735 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1214,a,1183,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1735,c,1651,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1735,c,1652,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1735,c,1653,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1735,c,1654,b)].
% 16.35/16.45 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1735,c,1655,b)].
% 16.35/16.45 1736 -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__semiring__strict(C). [resolve(1215,a,1183,b)].
% 16.35/16.45 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1736,d,1651,b)].
% 16.35/16.45 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1736,d,1652,b)].
% 16.35/16.45 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1736,d,1653,b)].
% 16.35/16.45 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1736,d,1654,b)].
% 16.35/16.45 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1736,d,1655,b)].
% 16.35/16.45 1737 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1216,a,1183,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1737,c,1651,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1737,c,1652,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1737,c,1653,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1737,c,1654,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1737,c,1655,b)].
% 16.35/16.45 1738 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1217,a,1183,b)].
% 16.35/16.45 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(1738,c,1651,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1738,c,1652,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1738,c,1653,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1738,c,1654,b)].
% 16.35/16.45 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1738,c,1655,b)].
% 16.35/16.46 1739 -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__semiring__strict(C). [resolve(1218,a,1183,b)].
% 16.35/16.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1739,d,1651,b)].
% 16.35/16.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1739,d,1652,b)].
% 16.35/16.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1739,d,1653,b)].
% 16.35/16.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1739,d,1654,b)].
% 16.35/16.46 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1739,d,1655,b)].
% 16.35/16.46 1740 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1740,b,1652,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 16.35/16.46 1741 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1220,a,1183,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1741,b,1651,b)].
% 16.35/16.46 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(1741,b,1652,b)].
% 16.35/16.46 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(1741,b,1653,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1741,b,1654,b)].
% 16.35/16.46 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1741,b,1655,b)].
% 16.35/16.46 1742 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1221,a,1183,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1742,c,1651,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1742,c,1652,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1742,c,1653,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1742,c,1654,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1742,c,1655,b)].
% 16.35/16.46 1743 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1222,a,1183,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1743,c,1651,b)].
% 16.35/16.46 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1743,c,1652,b)].
% 16.35/16.47 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1743,c,1653,b)].
% 16.35/16.47 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1743,c,1654,b)].
% 16.35/16.47 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1743,c,1655,b)].
% 16.35/16.47 1744 -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__semiring__strict(C). [resolve(1223,a,1183,b)].
% 16.35/16.47 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(1744,d,1651,b)].
% 16.35/16.47 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(1744,d,1652,b)].
% 16.35/16.47 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(1744,d,1653,b)].
% 16.35/16.47 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__ring__strict(C). [resolve(1744,d,1654,b)].
% 16.35/16.47 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__semidom(C). [resolve(1744,d,1655,b)].
% 16.35/16.47 1745 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1745,b,1652,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 16.35/16.47 1746 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1225,a,1183,b)].
% 16.35/16.47 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(1746,b,1651,b)].
% 16.35/16.47 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(1746,b,1652,b)].
% 16.35/16.47 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(1746,b,1653,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1746,b,1654,b)].
% 16.35/16.47 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1746,b,1655,b)].
% 16.35/16.47 1747 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1226,a,1183,b)].
% 16.35/16.47 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(1747,b,1651,b)].
% 16.35/16.47 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1747,b,1652,b)].
% 16.35/16.47 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1747,b,1653,b)].
% 16.35/16.47 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1747,b,1654,b)].
% 16.35/16.47 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1747,b,1655,b)].
% 16.35/16.48 1748 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1227,a,1183,b)].
% 16.35/16.48 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(1748,b,1651,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1748,b,1652,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1748,b,1653,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1748,b,1654,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1748,b,1655,b)].
% 16.35/16.48 1749 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1228,a,1183,b)].
% 16.35/16.48 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(1749,b,1651,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1749,b,1652,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1749,b,1653,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1749,b,1654,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1749,b,1655,b)].
% 16.35/16.48 1750 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1229,a,1183,b)].
% 16.35/16.48 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(1750,b,1651,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1750,b,1652,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1750,b,1653,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1750,b,1654,b)].
% 16.35/16.48 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1750,b,1655,b)].
% 16.35/16.48 1751 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1230,a,1183,b)].
% 16.35/16.48 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1751,c,1651,b)].
% 16.35/16.48 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1751,c,1652,b)].
% 16.35/16.48 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1751,c,1653,b)].
% 16.35/16.48 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1751,c,1654,b)].
% 16.35/16.48 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1751,c,1655,b)].
% 16.35/16.48 1752 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1231,a,1183,b)].
% 16.35/16.49 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1752,c,1651,b)].
% 16.35/16.49 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1752,c,1652,b)].
% 16.35/16.49 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1752,c,1653,b)].
% 16.35/16.49 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1752,c,1654,b)].
% 16.35/16.49 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1752,c,1655,b)].
% 16.35/16.49 1753 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1232,a,1183,b)].
% 16.35/16.49 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1753,c,1651,b)].
% 16.35/16.49 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1753,c,1652,b)].
% 16.35/16.49 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1753,c,1653,b)].
% 16.35/16.49 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1753,c,1654,b)].
% 16.35/16.49 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1753,c,1655,b)].
% 16.35/16.49 1754 -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__semiring__strict(B). [resolve(1233,a,1183,b)].
% 16.35/16.49 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(1754,c,1651,b)].
% 16.35/16.49 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(1754,c,1652,b)].
% 16.35/16.49 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(1754,c,1653,b)].
% 16.35/16.49 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__ring__strict(B). [resolve(1754,c,1654,b)].
% 16.35/16.49 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__semidom(B). [resolve(1754,c,1655,b)].
% 16.35/16.49 1755 -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__semiring__strict(C). [resolve(1234,a,1183,b)].
% 16.35/16.49 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(1755,c,1651,b)].
% 16.35/16.49 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(1755,c,1652,b)].
% 16.35/16.49 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(1755,c,1653,b)].
% 16.35/16.49 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__ring__strict(C). [resolve(1755,c,1654,b)].
% 16.35/16.49 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__semidom(C). [resolve(1755,c,1655,b)].
% 16.35/16.50 1756 -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__semiring__strict(C). [resolve(1235,a,1183,b)].
% 16.35/16.50 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(1756,c,1651,b)].
% 16.35/16.50 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(1756,c,1652,b)].
% 16.35/16.50 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(1756,c,1653,b)].
% 16.35/16.50 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__ring__strict(C). [resolve(1756,c,1654,b)].
% 16.35/16.50 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__semidom(C). [resolve(1756,c,1655,b)].
% 16.35/16.50 1757 -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__semiring__strict(C). [resolve(1236,a,1183,b)].
% 16.35/16.50 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(1757,d,1651,b)].
% 16.35/16.50 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(1757,d,1652,b)].
% 16.35/16.50 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(1757,d,1653,b)].
% 16.35/16.50 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__ring__strict(C). [resolve(1757,d,1654,b)].
% 16.35/16.50 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__semidom(C). [resolve(1757,d,1655,b)].
% 16.35/16.50 1758 -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__semiring__strict(C). [resolve(1237,a,1183,b)].
% 16.35/16.50 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(1758,d,1651,b)].
% 16.35/16.50 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(1758,d,1652,b)].
% 16.35/16.50 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(1758,d,1653,b)].
% 16.35/16.50 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__ring__strict(C). [resolve(1758,d,1654,b)].
% 16.35/16.51 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__semidom(C). [resolve(1758,d,1655,b)].
% 16.35/16.51 1759 -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__semiring__strict(C). [resolve(1238,a,1183,b)].
% 16.35/16.51 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(1759,c,1651,b)].
% 16.35/16.51 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(1759,c,1652,b)].
% 16.35/16.51 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(1759,c,1653,b)].
% 16.35/16.51 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__ring__strict(C). [resolve(1759,c,1654,b)].
% 16.35/16.51 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__semidom(C). [resolve(1759,c,1655,b)].
% 16.35/16.51 1760 -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__semiring__strict(C). [resolve(1239,a,1183,b)].
% 16.35/16.51 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(1760,d,1651,b)].
% 16.35/16.51 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(1760,d,1652,b)].
% 16.35/16.51 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(1760,d,1653,b)].
% 16.35/16.51 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__ring__strict(C). [resolve(1760,d,1654,b)].
% 16.35/16.51 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__semidom(C). [resolve(1760,d,1655,b)].
% 16.35/16.51 1761 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1240,a,1183,b)].
% 16.35/16.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1761,c,1651,b)].
% 16.35/16.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1761,c,1652,b)].
% 16.35/16.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1761,c,1653,b)].
% 16.35/16.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1761,c,1654,b)].
% 16.35/16.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1761,c,1655,b)].
% 16.35/16.51 1762 -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__semiring__strict(B). [resolve(1241,a,1183,b)].
% 16.35/16.51 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(1762,c,1651,b)].
% 16.44/16.53 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(1762,c,1652,b)].
% 16.44/16.53 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(1762,c,1653,b)].
% 16.44/16.53 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__ring__strict(B). [resolve(1762,c,1654,b)].
% 16.44/16.53 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__semidom(B). [resolve(1762,c,1655,b)].
% 16.44/16.53 1763 -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__semiring__strict(C). [resolve(1242,a,1183,b)].
% 16.44/16.53 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(1763,c,1651,b)].
% 16.44/16.53 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(1763,c,1652,b)].
% 16.44/16.53 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(1763,c,1653,b)].
% 16.44/16.53 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__ring__strict(C). [resolve(1763,c,1654,b)].
% 16.44/16.53 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__semidom(C). [resolve(1763,c,1655,b)].
% 16.44/16.53 1764 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 16.44/16.53 1765 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1362,a,1360,b)].
% 16.44/16.53 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(1765,c,1651,b)].
% 16.44/16.53 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(1765,c,1652,b)].
% 16.44/16.53 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(1765,c,1653,b)].
% 16.44/16.53 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1765,c,1654,b)].
% 16.44/16.53 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1765,c,1655,b)].
% 16.44/16.53 1766 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1363,a,1360,b)].
% 16.44/16.53 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(1766,c,1651,b)].
% 16.44/16.53 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(1766,c,1652,b)].
% 16.44/16.53 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(1766,c,1653,b)].
% 16.44/16.53 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1766,c,1654,b)].
% 16.44/16.53 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1766,c,1655,b)].
% 16.44/16.53 1767 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1364,a,1360,b)].
% 16.44/16.54 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(1767,c,1651,b)].
% 16.44/16.54 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(1767,c,1652,b)].
% 16.44/16.54 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(1767,c,1653,b)].
% 16.44/16.54 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1767,c,1654,b)].
% 16.44/16.54 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1767,c,1655,b)].
% 16.44/16.54 1768 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1365,a,1360,b)].
% 16.44/16.54 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(1768,c,1651,b)].
% 16.44/16.54 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(1768,c,1652,b)].
% 16.44/16.54 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(1768,c,1653,b)].
% 16.44/16.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1768,c,1654,b)].
% 16.44/16.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1768,c,1655,b)].
% 16.44/16.54 1769 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1366,a,1360,b)].
% 16.44/16.54 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(1769,c,1651,b)].
% 16.44/16.54 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(1769,c,1652,b)].
% 16.44/16.54 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(1769,c,1653,b)].
% 16.44/16.54 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1769,c,1654,b)].
% 16.44/16.54 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1769,c,1655,b)].
% 16.44/16.54 1770 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1367,a,1360,b)].
% 16.44/16.54 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(1770,c,1651,b)].
% 16.44/16.54 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(1770,c,1652,b)].
% 16.44/16.54 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(1770,c,1653,b)].
% 16.44/16.54 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1770,c,1654,b)].
% 16.44/16.54 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1770,c,1655,b)].
% 16.44/16.54 1771 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1368,a,1360,b)].
% 16.44/16.54 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(1771,c,1651,b)].
% 16.44/16.54 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(1771,c,1652,b)].
% 16.44/16.54 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(1771,c,1653,b)].
% 16.44/16.54 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1771,c,1654,b)].
% 16.44/16.58 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1771,c,1655,b)].
% 16.44/16.58 1772 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1369,a,1360,b)].
% 16.44/16.58 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(1772,c,1651,b)].
% 16.44/16.58 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(1772,c,1652,b)].
% 16.44/16.58 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(1772,c,1653,b)].
% 16.44/16.58 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1772,c,1654,b)].
% 16.44/16.58 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1772,c,1655,b)].
% 16.44/16.58 1773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 16.44/16.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 16.44/16.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1773,b,1652,b)].
% 16.44/16.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 16.44/16.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 16.44/16.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 16.44/16.58 1774 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 16.44/16.58 1775 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 16.44/16.59 1776 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 16.44/16.59 1777 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1389,c,1360,b)].
% 16.44/16.59 1778 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1390,b,1360,b)].
% 16.44/16.59 1779 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1391,c,1360,b)].
% 16.44/16.59 1780 -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(1392,c,1360,b)].
% 16.44/16.59 1781 -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(1393,c,1360,b)].
% 16.44/16.59 1782 -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(1394,c,1360,b)].
% 16.44/16.59 1783 -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(1395,c,1360,b)].
% 16.44/16.59 1784 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1396,c,1360,b)].
% 16.44/16.59 1785 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(1397,b,1360,b)].
% 16.44/16.59 1786 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1398,c,1360,b)].
% 16.44/16.59 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1786,c,1651,b)].
% 16.44/16.59 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1786,c,1652,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1786,c,1653,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1786,c,1654,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1786,c,1655,b)].
% 16.52/16.63 1787 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1399,c,1360,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1787,c,1651,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1787,c,1652,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1787,c,1653,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1787,c,1654,b)].
% 16.52/16.63 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1787,c,1655,b)].
% 16.52/16.63 1788 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1788,b,1649,a)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1788,b,1650,a)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1788,b,1652,b)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 16.52/16.63 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 16.52/16.63 1789 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1789,b,1649,a)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1789,b,1650,a)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1789,b,1652,b)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 16.52/16.63 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 16.52/16.63 1790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1790,b,1649,a)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1790,b,1650,a)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1790,b,1652,b)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 16.52/16.63 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 16.52/16.63 1791 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 16.52/16.63 1792 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1575,c,1548,b)].
% 16.52/16.64 1793 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1576,c,1548,b)].
% 16.52/16.64 1794 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 16.52/16.64 1795 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 16.52/16.64 1796 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 16.52/16.64 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1796,b,1649,a)].
% 16.52/16.64 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(1796,b,1650,a)].
% 16.52/16.64 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 16.52/16.64 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1796,b,1652,b)].
% 16.52/16.64 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 16.52/16.64 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 16.52/16.64 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 16.52/16.64 1797 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 16.52/16.64 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1797,b,1649,a)].
% 16.52/16.64 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(1797,b,1650,a)].
% 16.52/16.64 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 16.52/16.64 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1797,b,1652,b)].
% 16.52/16.64 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 16.52/16.64 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 16.52/16.64 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 16.52/16.64 1798 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 16.52/16.64 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1798,b,1649,a)].
% 16.52/16.64 Derived: c_lessequals(A,A,tc_nat). [resolve(1798,b,1650,a)].
% 16.52/16.64 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 16.52/16.64 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1798,b,1652,b)].
% 16.52/16.64 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 16.52/16.64 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 16.52/16.64 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 16.52/16.64 1799 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 16.52/16.64 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1799,b,1649,a)].
% 16.52/16.64 Derived: -c_less(A,A,tc_nat). [resolve(1799,b,1650,a)].
% 16.52/16.64 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 16.52/16.64 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1799,b,1652,b)].
% 16.52/16.64 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 16.52/16.64 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 16.52/16.64 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 16.52/16.64 1800 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1633,c,1591,b)].
% 16.52/16.64 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1800,c,1649,a)].
% 16.52/16.64 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1800,c,1650,a)].
% 16.52/16.64 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1800,c,1651,b)].
% 16.52/16.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1800,c,1652,b)].
% 16.52/16.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1800,c,1653,b)].
% 16.52/16.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1800,c,1654,b)].
% 16.52/16.65 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1800,c,1655,b)].
% 16.52/16.65 1801 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1634,b,1591,b)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1801,b,1649,a)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1801,b,1650,a)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1801,b,1651,b)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1801,b,1652,b)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1801,b,1653,b)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1801,b,1654,b)].
% 16.52/16.65 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1801,b,1655,b)].
% 16.52/16.65 1802 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1635,c,1591,b)].
% 16.52/16.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1802,c,1649,a)].
% 16.52/16.65 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1802,c,1650,a)].
% 16.52/16.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1802,c,1651,b)].
% 16.52/16.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1802,c,1652,b)].
% 16.52/16.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1802,c,1653,b)].
% 16.52/16.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1802,c,1654,b)].
% 16.52/16.65 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1802,c,1655,b)].
% 16.52/16.65 1803 -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(1636,c,1591,b)].
% 16.52/16.65 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(1803,c,1649,a)].
% 16.52/16.65 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(1803,c,1650,a)].
% 16.52/16.65 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(1803,c,1651,b)].
% 16.52/16.65 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(1803,c,1652,b)].
% 16.52/16.65 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(1803,c,1653,b)].
% 16.52/16.66 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__ring__strict(B). [resolve(1803,c,1654,b)].
% 16.52/16.66 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__semidom(B). [resolve(1803,c,1655,b)].
% 16.52/16.66 1804 -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(1637,c,1591,b)].
% 16.52/16.66 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(1804,c,1649,a)].
% 16.52/16.66 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(1804,c,1650,a)].
% 16.52/16.66 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(1804,c,1651,b)].
% 16.52/16.66 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(1804,c,1652,b)].
% 16.52/16.66 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(1804,c,1653,b)].
% 16.52/16.66 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__ring__strict(C). [resolve(1804,c,1654,b)].
% 16.52/16.66 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__semidom(C). [resolve(1804,c,1655,b)].
% 16.52/16.66 1805 -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(1638,c,1591,b)].
% 16.52/16.66 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(1805,c,1649,a)].
% 16.52/16.66 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(1805,c,1650,a)].
% 16.52/16.66 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(1805,c,1651,b)].
% 16.52/16.66 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(1805,c,1652,b)].
% 16.52/16.66 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(1805,c,1653,b)].
% 16.52/16.66 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__ring__strict(B). [resolve(1805,c,1654,b)].
% 16.52/16.66 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__semidom(B). [resolve(1805,c,1655,b)].
% 16.52/16.66 1806 -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(1639,c,1591,b)].
% 16.52/16.66 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(1806,c,1649,a)].
% 16.52/16.66 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(1806,c,1650,a)].
% 16.52/16.66 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(1806,c,1651,b)].
% 16.52/16.66 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(1806,c,1652,b)].
% 16.52/16.66 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(1806,c,1653,b)].
% 16.52/16.66 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__ring__strict(C). [resolve(1806,c,1654,b)].
% 16.52/16.66 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__semidom(C). [resolve(1806,c,1655,b)].
% 16.52/16.66 1807 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1640,c,1591,b)].
% 16.52/16.66 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1807,c,1649,a)].
% 16.52/16.66 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1807,c,1650,a)].
% 16.52/16.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1807,c,1651,b)].
% 16.52/16.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1807,c,1652,b)].
% 16.52/16.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1807,c,1653,b)].
% 16.52/16.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1807,c,1654,b)].
% 16.52/16.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1807,c,1655,b)].
% 16.52/16.66 1808 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(1641,b,1591,b)].
% 16.52/16.66 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(1808,b,1649,a)].
% 16.52/16.66 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(1808,b,1650,a)].
% 16.52/16.66 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(1808,b,1651,b)].
% 16.52/16.66 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(1808,b,1652,b)].
% 16.52/16.66 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(1808,b,1653,b)].
% 16.52/16.66 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__ring__strict(B). [resolve(1808,b,1654,b)].
% 16.52/16.66 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__semidom(B). [resolve(1808,b,1655,b)].
% 16.52/16.66 1809 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 16.52/16.66 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1809,b,1649,a)].
% 16.52/16.66 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1809,b,1650,a)].
% 16.52/16.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 16.52/16.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1809,b,1652,b)].
% 16.52/16.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 16.52/16.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 16.52/16.67 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 16.52/16.67 1810 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1643,c,1591,b)].
% 16.52/16.67 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(1810,c,1649,a)].
% 16.52/16.67 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(1810,c,1650,a)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1810,c,1651,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1810,c,1652,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1810,c,1653,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1810,c,1654,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1810,c,1655,b)].
% 16.52/16.67 1811 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1644,c,1591,b)].
% 16.52/16.67 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(1811,c,1649,a)].
% 16.52/16.67 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(1811,c,1650,a)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1811,c,1651,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1811,c,1652,b)].
% 16.52/16.67 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1811,c,1653,b)].
% 16.73/16.88 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1811,c,1654,b)].
% 16.73/16.88 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1811,c,1655,b)].
% 16.73/16.88 1812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 16.73/16.88 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1812,b,1649,a)].
% 16.73/16.88 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1812,b,1650,a)].
% 16.73/16.88 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 16.73/16.88 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1812,b,1652,b)].
% 16.73/16.88 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 16.73/16.88 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 16.73/16.88 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 16.73/16.88 1813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 16.73/16.88 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1813,b,1649,a)].
% 16.73/16.88 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1813,b,1650,a)].
% 16.73/16.88 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 16.73/16.88 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1813,b,1652,b)].
% 16.73/16.88 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 16.73/16.88 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 16.73/16.88 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 16.73/16.88 1814 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 16.73/16.88 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 16.73/16.88 Derived: class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 16.73/16.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 16.73/16.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 16.73/16.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 16.73/16.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 16.73/16.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 16.73/16.88 1815 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 16.73/16.88 1816 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 16.73/16.88 1817 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 16.73/16.88 1818 -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].
% 16.73/16.88 1819 -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].
% 16.73/16.88 1820 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_41) # label(axiom). [assumption].
% 16.73/16.88 1821 -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].
% 16.90/17.00 1822 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) # label(axiom). [assumption].
% 16.90/17.00 1823 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_20) # label(axiom). [assumption].
% 16.90/17.00 1824 -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].
% 16.90/17.00 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 16.90/17.00 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 16.90/17.00 1825 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_5) # label(axiom). [assumption].
% 16.90/17.00 1826 -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].
% 16.90/17.00 1827 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_9) # label(axiom). [assumption].
% 16.90/17.00 1828 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 16.90/17.00 1829 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 16.90/17.00 1830 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(34,a,29,b)].
% 16.90/17.00 1831 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(35,a,29,b)].
% 16.90/17.00 1832 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(36,a,29,b)].
% 16.90/17.01 1833 -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(37,a,29,b)].
% 16.90/17.01 1834 -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(38,a,29,b)].
% 16.90/17.01 1835 -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(39,a,29,b)].
% 16.90/17.01 1836 -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(40,a,29,b)].
% 16.90/17.01 1837 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(41,a,29,b)].
% 16.90/17.01 1838 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(42,a,29,b)].
% 16.90/17.01 1839 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 16.90/17.01 1840 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 16.90/17.01 1841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 16.90/17.01 1842 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(108,b,95,b)].
% 16.90/17.01 1843 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(109,b,95,b)].
% 17.21/17.29 1844 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 17.21/17.29 1845 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 17.21/17.29 1846 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(221,c,208,b)].
% 17.21/17.29 1847 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(222,c,208,b)].
% 17.21/17.29 1848 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 17.21/17.29 1849 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 17.21/17.29 1850 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 17.21/17.29 1851 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 17.21/17.29 1852 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 17.21/17.29 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 17.21/17.29 1853 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 17.21/17.29 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1853,b,1823,b)].
% 17.21/17.29 1854 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 17.21/17.29 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1854,b,1823,b)].
% 17.21/17.29 1855 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1559,c,1552,b)].
% 17.21/17.29 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1855,c,1823,b)].
% 17.21/17.29 1856 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1560,b,1552,b)].
% 17.21/17.29 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1856,b,1823,b)].
% 17.21/17.29 1857 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1561,c,1552,b)].
% 17.21/17.29 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1857,c,1823,b)].
% 17.21/17.29 1858 -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(1562,c,1552,b)].
% 17.21/17.29 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(1858,c,1823,b)].
% 17.21/17.29 1859 -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(1563,c,1552,b)].
% 17.21/17.29 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(1859,c,1823,b)].
% 17.21/17.29 1860 -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(1564,c,1552,b)].
% 17.21/17.29 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(1860,c,1823,b)].
% 17.21/17.29 1861 -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(1565,c,1552,b)].
% 17.42/17.54 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(1861,c,1823,b)].
% 17.42/17.54 1862 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1566,c,1552,b)].
% 17.42/17.54 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1862,c,1823,b)].
% 17.42/17.54 1863 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(1567,b,1552,b)].
% 17.42/17.54 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(1863,b,1823,b)].
% 17.42/17.54 1864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 17.42/17.54 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1864,b,1823,b)].
% 17.42/17.54 1865 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1575,c,1552,b)].
% 17.42/17.54 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1865,c,1823,b)].
% 17.42/17.54 1866 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1576,c,1552,b)].
% 17.42/17.54 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1866,c,1823,b)].
% 17.42/17.54 1867 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 17.42/17.54 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1867,b,1816,a)].
% 17.42/17.54 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1867,b,1817,a)].
% 17.42/17.54 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1867,b,1823,b)].
% 17.42/17.54 1868 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 17.42/17.54 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1868,b,1823,b)].
% 17.42/17.54 1869 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 17.42/17.54 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1869,b,1823,b)].
% 17.42/17.54 1870 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 17.42/17.54 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1870,b,1823,b)].
% 17.42/17.54 1871 -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].
% 17.42/17.54 1872 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 17.42/17.54 1873 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 17.42/17.54 1874 -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].
% 17.42/17.54 1875 -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].
% 17.51/17.65 1876 -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].
% 17.51/17.65 1877 -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].
% 17.51/17.65 1878 -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].
% 17.51/17.65 1879 -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].
% 17.51/17.65 1880 -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].
% 17.51/17.65 1881 -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].
% 17.51/17.65 1882 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 17.51/17.65 1883 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 17.51/17.65 1884 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(34,a,26,b)].
% 17.51/17.65 1885 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(35,a,26,b)].
% 17.51/17.65 1886 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(36,a,26,b)].
% 17.51/17.65 1887 -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(37,a,26,b)].
% 17.51/17.65 1888 -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(38,a,26,b)].
% 17.51/17.65 1889 -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(39,a,26,b)].
% 17.51/17.65 1890 -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(40,a,26,b)].
% 17.51/17.65 1891 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(41,a,26,b)].
% 17.51/17.65 1892 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(42,a,26,b)].
% 17.51/17.65 1893 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 17.51/17.65 1894 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 17.51/17.65 1895 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 17.51/17.65 1896 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(108,b,92,b)].
% 17.51/17.65 1897 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(109,b,92,b)].
% 17.81/17.94 1898 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 17.81/17.94 1899 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 17.81/17.94 1900 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(221,c,205,b)].
% 17.81/17.94 1901 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(222,c,205,b)].
% 17.81/17.94 1902 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 17.81/17.94 1903 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 17.81/17.94 1904 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 17.81/17.94 1905 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 17.81/17.94 1906 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(307,a,299,b)].
% 17.81/17.94 1907 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(308,a,299,b)].
% 17.81/17.94 1908 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 17.81/17.94 1909 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 17.81/17.94 1910 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 17.81/17.94 1911 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 17.81/17.94 1912 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(389,c,368,b)].
% 17.81/17.94 1913 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(390,c,368,b)].
% 17.81/17.94 1914 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 17.81/17.94 1915 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 17.81/17.94 1916 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 17.81/17.94 1917 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 17.81/17.94 1918 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1559,c,1549,b)].
% 17.81/17.94 1919 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1560,b,1549,b)].
% 17.81/17.94 1920 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1561,c,1549,b)].
% 17.81/17.94 1921 -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(1562,c,1549,b)].
% 17.81/17.94 1922 -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(1563,c,1549,b)].
% 17.81/17.94 1923 -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(1564,c,1549,b)].
% 17.81/17.94 1924 -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(1565,c,1549,b)].
% 17.81/17.97 1925 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1566,c,1549,b)].
% 17.81/17.97 1926 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(1567,b,1549,b)].
% 17.81/17.97 1927 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 17.81/17.97 1928 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1575,c,1549,b)].
% 17.81/17.97 1929 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1576,c,1549,b)].
% 17.81/17.97 1930 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 17.81/17.97 1931 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 17.81/17.97 1932 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 17.81/17.97 1933 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 17.81/17.97 1934 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 17.81/17.97 1935 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1627,c,1592,b)].
% 17.81/17.97 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1935,c,1872,a)].
% 17.81/17.97 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1935,c,1873,a)].
% 17.81/17.97 1936 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1628,c,1592,b)].
% 17.81/17.97 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1936,c,1872,a)].
% 17.81/17.97 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1936,c,1873,a)].
% 17.81/17.97 1937 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 17.81/17.97 1938 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 17.81/17.97 1939 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 17.81/17.97 1940 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1633,c,1592,b)].
% 17.81/17.97 1941 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1634,b,1592,b)].
% 17.81/17.97 1942 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1635,c,1592,b)].
% 17.81/17.97 1943 -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(1636,c,1592,b)].
% 17.81/17.97 1944 -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(1637,c,1592,b)].
% 17.81/17.97 1945 -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(1638,c,1592,b)].
% 17.81/17.97 1946 -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(1639,c,1592,b)].
% 17.81/17.97 1947 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1640,c,1592,b)].
% 18.12/18.25 1948 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(1641,b,1592,b)].
% 18.12/18.25 1949 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 18.12/18.25 1950 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1643,c,1592,b)].
% 18.12/18.25 1951 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1644,c,1592,b)].
% 18.12/18.25 1952 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 18.12/18.25 1953 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 18.12/18.25 1954 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 18.12/18.25 1955 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1955,b,1872,a)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(1955,b,1873,a)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1955,b,1875,b)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 18.12/18.25 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 18.12/18.25 1956 -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].
% 18.12/18.25 1957 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 18.12/18.25 1958 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 18.12/18.25 1959 -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].
% 18.12/18.25 1960 -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].
% 18.12/18.25 1961 -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].
% 18.12/18.25 1962 -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].
% 18.12/18.25 1963 -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].
% 18.12/18.25 1964 -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].
% 18.12/18.25 1965 -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].
% 18.12/18.25 1966 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 18.12/18.25 1967 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 18.22/18.30 1968 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(34,a,20,b)].
% 18.22/18.30 1969 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(35,a,20,b)].
% 18.22/18.30 1970 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(36,a,20,b)].
% 18.22/18.30 1971 -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(37,a,20,b)].
% 18.22/18.30 1972 -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(38,a,20,b)].
% 18.22/18.30 1973 -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(39,a,20,b)].
% 18.22/18.30 1974 -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(40,a,20,b)].
% 18.22/18.30 1975 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(41,a,20,b)].
% 18.22/18.30 1976 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(42,a,20,b)].
% 18.22/18.30 1977 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 18.22/18.30 1978 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 18.22/18.30 1979 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 18.22/18.30 1980 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(108,b,86,b)].
% 18.22/18.30 1981 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(109,b,86,b)].
% 18.22/18.30 1982 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 18.22/18.30 1983 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 18.22/18.30 1984 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(221,c,199,b)].
% 18.22/18.30 1985 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(222,c,199,b)].
% 18.22/18.30 1986 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 18.22/18.30 1987 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 18.22/18.30 1988 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 18.22/18.30 1989 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 18.22/18.30 1990 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(307,a,293,b)].
% 18.22/18.30 1991 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(308,a,293,b)].
% 18.22/18.30 1992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 18.36/18.42 1993 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 18.36/18.42 1994 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 18.36/18.42 1995 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 18.36/18.42 1996 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(389,c,362,b)].
% 18.36/18.42 1997 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(390,c,362,b)].
% 18.36/18.42 1998 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 18.36/18.42 1999 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 18.36/18.42 2000 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 18.36/18.42 2001 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 18.36/18.42 2002 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 18.36/18.42 2003 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 18.36/18.42 2004 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1164,c,1141,b)].
% 18.36/18.42 2005 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1165,b,1141,b)].
% 18.36/18.42 2006 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1166,c,1141,b)].
% 18.36/18.42 2007 -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(1167,c,1141,b)].
% 18.36/18.42 2008 -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(1168,c,1141,b)].
% 18.36/18.42 2009 -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(1169,c,1141,b)].
% 18.36/18.42 2010 -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(1170,c,1141,b)].
% 18.36/18.42 2011 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1171,c,1141,b)].
% 18.36/18.42 2012 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(1172,b,1141,b)].
% 18.36/18.42 2013 -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(1185,a,1178,b)].
% 18.36/18.42 2014 -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(1186,a,1178,b)].
% 18.36/18.42 2015 -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(1187,a,1178,b)].
% 18.36/18.42 2016 -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(1188,a,1178,b)].
% 18.36/18.42 2017 -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(1189,a,1178,b)].
% 18.36/18.45 2018 -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(1190,a,1178,b)].
% 18.36/18.45 2019 -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(1191,a,1178,b)].
% 18.36/18.45 2020 -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(1192,a,1178,b)].
% 18.36/18.45 2021 -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(1193,a,1178,b)].
% 18.36/18.45 2022 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1194,a,1178,b)].
% 18.36/18.45 2023 -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(1195,a,1178,b)].
% 18.36/18.45 2024 -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(1196,a,1178,b)].
% 18.36/18.45 2025 -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(1197,a,1178,b)].
% 18.36/18.45 2026 -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(1198,a,1178,b)].
% 18.36/18.45 2027 -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(1199,a,1178,b)].
% 18.36/18.45 2028 -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(1200,a,1178,b)].
% 18.36/18.45 2029 -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(1201,a,1178,b)].
% 18.36/18.45 2030 -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(1202,a,1178,b)].
% 18.36/18.45 2031 -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(1203,a,1178,b)].
% 18.36/18.45 2032 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1204,a,1178,b)].
% 18.36/18.45 2033 -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(1205,a,1178,b)].
% 18.36/18.45 2034 -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(1206,a,1178,b)].
% 18.36/18.45 2035 -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(1207,a,1178,b)].
% 18.41/18.48 2036 -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(1208,b,1178,b)].
% 18.41/18.48 2037 -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(1209,b,1178,b)].
% 18.41/18.48 2038 -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(1210,a,1178,b)].
% 18.41/18.48 2039 -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(1211,a,1178,b)].
% 18.41/18.48 2040 -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(1212,a,1178,b)].
% 18.41/18.48 2041 -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(1213,a,1178,b)].
% 18.41/18.48 2042 -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(1214,a,1178,b)].
% 18.41/18.48 2043 -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(1215,a,1178,b)].
% 18.41/18.48 2044 -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(1216,a,1178,b)].
% 18.41/18.48 2045 -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(1217,a,1178,b)].
% 18.41/18.48 2046 -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(1218,a,1178,b)].
% 18.41/18.48 2047 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 18.41/18.48 2048 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(1220,a,1178,b)].
% 18.41/18.48 2049 -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(1221,a,1178,b)].
% 18.41/18.48 2050 -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(1222,a,1178,b)].
% 18.41/18.48 2051 -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(1223,a,1178,b)].
% 18.41/18.48 2052 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 18.41/18.48 2053 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(1225,a,1178,b)].
% 18.41/18.48 2054 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(1226,a,1178,b)].
% 18.41/18.48 2055 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(1227,a,1178,b)].
% 18.41/18.48 2056 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(1228,a,1178,b)].
% 18.41/18.48 2057 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(1229,a,1178,b)].
% 18.41/18.48 2058 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1230,a,1178,b)].
% 18.41/18.48 2059 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1231,a,1178,b)].
% 18.41/18.48 2060 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1232,a,1178,b)].
% 18.41/18.53 2061 -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(1233,a,1178,b)].
% 18.41/18.53 2062 -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(1234,a,1178,b)].
% 18.41/18.53 2063 -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(1235,a,1178,b)].
% 18.41/18.53 2064 -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(1236,a,1178,b)].
% 18.41/18.53 2065 -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(1237,a,1178,b)].
% 18.41/18.53 2066 -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(1238,a,1178,b)].
% 18.41/18.53 2067 -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(1239,a,1178,b)].
% 18.41/18.53 2068 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1240,a,1178,b)].
% 18.41/18.53 2069 -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(1241,a,1178,b)].
% 18.41/18.53 2070 -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(1242,a,1178,b)].
% 18.41/18.53 2071 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 18.41/18.53 2072 -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(1362,a,1355,b)].
% 18.41/18.53 2073 -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(1363,a,1355,b)].
% 18.41/18.53 2074 -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(1364,a,1355,b)].
% 18.41/18.53 2075 -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(1365,a,1355,b)].
% 18.41/18.53 2076 -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(1366,a,1355,b)].
% 18.41/18.53 2077 -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(1367,a,1355,b)].
% 18.41/18.53 2078 -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(1368,a,1355,b)].
% 18.41/18.53 2079 -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(1369,a,1355,b)].
% 18.41/18.53 2080 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 18.41/18.53 2081 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 18.41/18.53 2082 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 18.41/18.53 2083 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 18.41/18.53 2084 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1389,c,1355,b)].
% 18.52/18.59 2085 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1390,b,1355,b)].
% 18.52/18.59 2086 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1391,c,1355,b)].
% 18.52/18.59 2087 -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(1392,c,1355,b)].
% 18.52/18.59 2088 -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(1393,c,1355,b)].
% 18.52/18.59 2089 -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(1394,c,1355,b)].
% 18.52/18.59 2090 -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(1395,c,1355,b)].
% 18.52/18.59 2091 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1396,c,1355,b)].
% 18.52/18.59 2092 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(1397,b,1355,b)].
% 18.52/18.59 2093 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1398,c,1355,b)].
% 18.52/18.59 2094 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1399,c,1355,b)].
% 18.52/18.59 2095 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 18.52/18.59 2096 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 18.52/18.59 2097 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 18.52/18.59 2098 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 18.52/18.59 2099 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1575,c,1543,b)].
% 18.52/18.59 2100 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1576,c,1543,b)].
% 18.52/18.59 2101 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 18.52/18.59 2102 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 18.52/18.59 2103 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 18.52/18.59 2104 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 18.52/18.59 2105 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 18.52/18.59 2106 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 18.52/18.59 2107 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1633,c,1586,b)].
% 18.52/18.59 2108 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1634,b,1586,b)].
% 18.52/18.59 2109 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1635,c,1586,b)].
% 18.52/18.59 2110 -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(1636,c,1586,b)].
% 18.52/18.62 2111 -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(1637,c,1586,b)].
% 18.52/18.62 2112 -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(1638,c,1586,b)].
% 18.52/18.62 2113 -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(1639,c,1586,b)].
% 18.52/18.62 2114 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1640,c,1586,b)].
% 18.52/18.62 2115 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(1641,b,1586,b)].
% 18.52/18.62 2116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 18.52/18.62 2117 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1643,c,1586,b)].
% 18.52/18.62 2118 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1644,c,1586,b)].
% 18.52/18.62 2119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 18.52/18.62 2120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 18.52/18.62 2121 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 18.52/18.62 2122 -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(1706,e,1651,b)].
% 18.52/18.62 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(2122,e,1957,a)].
% 18.52/18.62 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(2122,e,1958,a)].
% 18.52/18.62 2123 -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(1707,d,1651,b)].
% 18.52/18.62 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(2123,d,1957,a)].
% 18.52/18.62 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(2123,d,1958,a)].
% 18.52/18.62 2124 -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(1708,d,1651,b)].
% 18.52/18.62 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(2124,d,1957,a)].
% 18.52/18.62 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(2124,d,1958,a)].
% 18.52/18.62 2125 -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(1709,f,1651,b)].
% 18.56/18.63 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(2125,f,1957,a)].
% 18.56/18.63 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(2125,f,1958,a)].
% 18.56/18.63 2126 -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(1710,e,1651,b)].
% 18.56/18.63 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(2126,e,1957,a)].
% 18.56/18.63 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(2126,e,1958,a)].
% 18.56/18.63 2127 -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(1711,e,1651,b)].
% 18.56/18.63 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(2127,e,1957,a)].
% 18.56/18.63 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(2127,e,1958,a)].
% 18.56/18.63 2128 -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(1712,f,1651,b)].
% 18.56/18.63 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(2128,f,1957,a)].
% 18.56/18.63 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(2128,f,1958,a)].
% 18.56/18.63 2129 -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(1713,e,1651,b)].
% 18.56/18.63 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(2129,e,1957,a)].
% 18.56/18.63 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(2129,e,1958,a)].
% 18.56/18.63 2130 -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(1714,e,1651,b)].
% 18.56/18.63 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(2130,e,1957,a)].
% 18.56/18.63 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(2130,e,1958,a)].
% 18.56/18.63 2131 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1715,b,1651,b)].
% 18.56/18.63 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2131,b,1957,a)].
% 18.56/18.63 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2131,b,1958,a)].
% 18.56/18.63 2132 -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(1716,f,1651,b)].
% 18.56/18.63 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(2132,f,1957,a)].
% 18.56/18.63 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(2132,f,1958,a)].
% 18.56/18.63 2133 -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(1717,e,1651,b)].
% 18.56/18.63 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(2133,e,1957,a)].
% 18.56/18.63 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(2133,e,1958,a)].
% 18.56/18.63 2134 -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(1718,e,1651,b)].
% 18.56/18.63 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(2134,e,1957,a)].
% 18.56/18.63 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(2134,e,1958,a)].
% 18.56/18.63 2135 -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(1719,f,1651,b)].
% 18.56/18.63 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(2135,f,1957,a)].
% 18.56/18.63 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(2135,f,1958,a)].
% 18.56/18.63 2136 -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(1720,e,1651,b)].
% 18.56/18.63 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(2136,e,1957,a)].
% 18.56/18.63 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(2136,e,1958,a)].
% 18.56/18.63 2137 -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(1721,e,1651,b)].
% 18.56/18.63 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(2137,e,1957,a)].
% 18.58/18.64 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(2137,e,1958,a)].
% 18.58/18.64 2138 -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(1722,d,1651,b)].
% 18.58/18.64 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(2138,d,1957,a)].
% 18.58/18.64 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(2138,d,1958,a)].
% 18.58/18.64 2139 -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(1723,d,1651,b)].
% 18.58/18.64 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(2139,d,1957,a)].
% 18.58/18.64 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(2139,d,1958,a)].
% 18.58/18.64 2140 -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(1724,e,1651,b)].
% 18.58/18.64 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(2140,e,1957,a)].
% 18.58/18.64 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(2140,e,1958,a)].
% 18.58/18.64 2141 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1725,b,1651,b)].
% 18.58/18.64 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2141,b,1957,a)].
% 18.58/18.64 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2141,b,1958,a)].
% 18.58/18.64 2142 -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(1726,d,1651,b)].
% 18.58/18.64 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(2142,d,1957,a)].
% 18.58/18.64 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(2142,d,1958,a)].
% 18.58/18.64 2143 -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(1727,e,1651,b)].
% 18.58/18.64 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(2143,e,1957,a)].
% 18.58/18.64 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(2143,e,1958,a)].
% 18.58/18.64 2144 -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(1728,e,1651,b)].
% 18.58/18.64 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(2144,e,1957,a)].
% 18.58/18.64 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(2144,e,1958,a)].
% 18.58/18.66 2145 -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(1729,d,1651,b)].
% 18.58/18.66 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(2145,d,1957,a)].
% 18.58/18.66 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(2145,d,1958,a)].
% 18.58/18.66 2146 -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(1730,d,1651,b)].
% 18.58/18.66 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(2146,d,1957,a)].
% 18.58/18.66 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(2146,d,1958,a)].
% 18.58/18.66 2147 -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(1731,c,1651,b)].
% 18.58/18.66 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2147,c,1957,a)].
% 18.58/18.66 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2147,c,1958,a)].
% 18.58/18.66 2148 -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(1732,c,1651,b)].
% 18.58/18.66 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2148,c,1957,a)].
% 18.58/18.66 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2148,c,1958,a)].
% 18.58/18.66 2149 -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(1733,d,1651,b)].
% 18.58/18.66 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(2149,d,1957,a)].
% 18.58/18.66 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(2149,d,1958,a)].
% 18.58/18.66 2150 -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(1734,c,1651,b)].
% 18.58/18.66 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2150,c,1957,a)].
% 18.58/18.66 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2150,c,1958,a)].
% 18.58/18.66 2151 -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(1735,c,1651,b)].
% 18.58/18.66 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2151,c,1957,a)].
% 18.58/18.66 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2151,c,1958,a)].
% 18.58/18.66 2152 -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(1736,d,1651,b)].
% 18.58/18.66 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(2152,d,1957,a)].
% 18.58/18.66 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(2152,d,1958,a)].
% 18.58/18.66 2153 -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(1737,c,1651,b)].
% 18.58/18.66 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2153,c,1957,a)].
% 18.58/18.66 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2153,c,1958,a)].
% 18.58/18.66 2154 -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(1738,c,1651,b)].
% 18.58/18.67 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2154,c,1957,a)].
% 18.58/18.67 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2154,c,1958,a)].
% 18.58/18.67 2155 -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(1739,d,1651,b)].
% 18.58/18.67 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2155,d,1957,a)].
% 18.58/18.67 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(2155,d,1958,a)].
% 18.58/18.67 2156 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 18.58/18.67 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2156,b,1957,a)].
% 18.58/18.67 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2156,b,1958,a)].
% 18.58/18.67 2157 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(1741,b,1651,b)].
% 18.58/18.67 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(2157,b,1957,a)].
% 18.58/18.67 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2157,b,1958,a)].
% 18.58/18.67 2158 -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(1742,c,1651,b)].
% 18.58/18.67 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2158,c,1957,a)].
% 18.58/18.67 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2158,c,1958,a)].
% 18.58/18.67 2159 -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(1743,c,1651,b)].
% 18.58/18.67 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2159,c,1957,a)].
% 18.58/18.67 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2159,c,1958,a)].
% 18.58/18.67 2160 -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(1744,d,1651,b)].
% 18.58/18.67 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(2160,d,1957,a)].
% 18.58/18.67 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(2160,d,1958,a)].
% 18.58/18.67 2161 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 18.58/18.67 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2161,b,1957,a)].
% 18.58/18.67 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2161,b,1958,a)].
% 18.58/18.67 2162 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(1746,b,1651,b)].
% 18.58/18.67 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(2162,b,1957,a)].
% 18.58/18.67 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(2162,b,1958,a)].
% 18.58/18.67 2163 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(1747,b,1651,b)].
% 18.58/18.67 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(2163,b,1957,a)].
% 18.58/18.67 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2163,b,1958,a)].
% 18.58/18.68 2164 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(1748,b,1651,b)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(2164,b,1957,a)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2164,b,1958,a)].
% 18.58/18.68 2165 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(1749,b,1651,b)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(2165,b,1957,a)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2165,b,1958,a)].
% 18.58/18.68 2166 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(1750,b,1651,b)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(2166,b,1957,a)].
% 18.58/18.68 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2166,b,1958,a)].
% 18.58/18.68 2167 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1751,c,1651,b)].
% 18.58/18.68 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2167,c,1957,a)].
% 18.58/18.68 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2167,c,1958,a)].
% 18.58/18.68 2168 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1752,c,1651,b)].
% 18.58/18.68 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2168,c,1957,a)].
% 18.58/18.68 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2168,c,1958,a)].
% 18.58/18.68 2169 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1753,c,1651,b)].
% 18.58/18.68 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2169,c,1957,a)].
% 18.58/18.68 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2169,c,1958,a)].
% 18.58/18.68 2170 -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(1754,c,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2170,c,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2170,c,1958,a)].
% 18.58/18.68 2171 -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(1755,c,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2171,c,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(2171,c,1958,a)].
% 18.58/18.68 2172 -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(1756,c,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(2172,c,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(2172,c,1958,a)].
% 18.58/18.68 2173 -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(1757,d,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2173,d,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2173,d,1958,a)].
% 18.58/18.68 2174 -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(1758,d,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2174,d,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2174,d,1958,a)].
% 18.58/18.68 2175 -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(1759,c,1651,b)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2175,c,1957,a)].
% 18.58/18.68 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(2175,c,1958,a)].
% 18.58/18.68 2176 -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(1760,d,1651,b)].
% 18.58/18.68 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(2176,d,1957,a)].
% 18.58/18.68 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(2176,d,1958,a)].
% 18.58/18.68 2177 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1761,c,1651,b)].
% 18.58/18.68 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2177,c,1957,a)].
% 18.58/18.68 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2177,c,1958,a)].
% 18.58/18.68 2178 -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(1762,c,1651,b)].
% 18.58/18.68 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(2178,c,1957,a)].
% 18.58/18.68 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(2178,c,1958,a)].
% 18.58/18.69 2179 -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(1763,c,1651,b)].
% 18.58/18.69 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(2179,c,1957,a)].
% 18.58/18.69 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(2179,c,1958,a)].
% 18.58/18.69 2180 -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(1765,c,1651,b)].
% 18.58/18.69 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2180,c,1957,a)].
% 18.58/18.69 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2180,c,1958,a)].
% 18.58/18.69 2181 -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(1766,c,1651,b)].
% 18.58/18.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2181,c,1957,a)].
% 18.58/18.69 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2181,c,1958,a)].
% 18.58/18.69 2182 -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(1767,c,1651,b)].
% 18.58/18.69 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2182,c,1957,a)].
% 18.58/18.69 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2182,c,1958,a)].
% 18.58/18.69 2183 -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(1768,c,1651,b)].
% 18.58/18.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2183,c,1957,a)].
% 18.58/18.69 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2183,c,1958,a)].
% 18.58/18.69 2184 -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(1769,c,1651,b)].
% 18.58/18.69 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2184,c,1957,a)].
% 18.58/18.69 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(2184,c,1958,a)].
% 18.58/18.69 2185 -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(1770,c,1651,b)].
% 18.58/18.69 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2185,c,1957,a)].
% 18.58/18.69 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2185,c,1958,a)].
% 18.58/18.69 2186 -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(1771,c,1651,b)].
% 18.58/18.69 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2186,c,1957,a)].
% 18.58/18.69 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2186,c,1958,a)].
% 18.58/18.69 2187 -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(1772,c,1651,b)].
% 18.58/18.69 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2187,c,1957,a)].
% 18.58/18.69 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2187,c,1958,a)].
% 18.58/18.69 2188 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 18.58/18.71 2189 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1786,c,1651,b)].
% 18.58/18.71 2190 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1787,c,1651,b)].
% 18.58/18.71 2191 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 18.58/18.71 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2191,b,1957,a)].
% 18.58/18.71 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2191,b,1958,a)].
% 18.58/18.71 2192 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 18.58/18.71 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2192,b,1957,a)].
% 18.58/18.71 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2192,b,1958,a)].
% 18.58/18.71 2193 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 18.58/18.71 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2193,b,1957,a)].
% 18.58/18.71 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2193,b,1958,a)].
% 18.58/18.71 2194 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 18.58/18.71 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2194,b,1957,a)].
% 18.58/18.71 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2194,b,1958,a)].
% 18.58/18.71 2195 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 18.58/18.71 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2195,b,1957,a)].
% 18.58/18.71 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2195,b,1958,a)].
% 18.58/18.71 2196 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 18.58/18.71 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2196,b,1957,a)].
% 18.58/18.71 Derived: c_lessequals(A,A,tc_nat). [resolve(2196,b,1958,a)].
% 18.58/18.71 2197 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 18.58/18.71 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2197,b,1957,a)].
% 18.58/18.71 Derived: -c_less(A,A,tc_nat). [resolve(2197,b,1958,a)].
% 18.58/18.71 2198 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1800,c,1651,b)].
% 18.58/18.71 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2198,c,1957,a)].
% 18.58/18.71 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2198,c,1958,a)].
% 18.58/18.71 2199 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1801,b,1651,b)].
% 18.58/18.71 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2199,b,1957,a)].
% 18.58/18.71 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2199,b,1958,a)].
% 18.58/18.71 2200 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1802,c,1651,b)].
% 18.58/18.71 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2200,c,1957,a)].
% 18.58/18.71 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2200,c,1958,a)].
% 18.58/18.71 2201 -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(1803,c,1651,b)].
% 18.58/18.71 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(2201,c,1957,a)].
% 18.58/18.71 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(2201,c,1958,a)].
% 18.58/18.71 2202 -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(1804,c,1651,b)].
% 18.58/18.71 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(2202,c,1957,a)].
% 18.66/18.72 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(2202,c,1958,a)].
% 18.66/18.72 2203 -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(1805,c,1651,b)].
% 18.66/18.72 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(2203,c,1957,a)].
% 18.66/18.72 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(2203,c,1958,a)].
% 18.66/18.72 2204 -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(1806,c,1651,b)].
% 18.66/18.72 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(2204,c,1957,a)].
% 18.66/18.72 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(2204,c,1958,a)].
% 18.66/18.72 2205 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1807,c,1651,b)].
% 18.66/18.72 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2205,c,1957,a)].
% 18.66/18.72 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2205,c,1958,a)].
% 18.66/18.72 2206 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(1808,b,1651,b)].
% 18.66/18.72 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(2206,b,1957,a)].
% 18.66/18.72 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(2206,b,1958,a)].
% 18.66/18.72 2207 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 18.66/18.72 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2207,b,1957,a)].
% 18.66/18.72 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2207,b,1958,a)].
% 18.66/18.72 2208 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1810,c,1651,b)].
% 18.66/18.72 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(2208,c,1957,a)].
% 18.66/18.72 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(2208,c,1958,a)].
% 18.66/18.72 2209 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1811,c,1651,b)].
% 18.66/18.72 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(2209,c,1957,a)].
% 19.31/19.44 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(2209,c,1958,a)].
% 19.31/19.44 2210 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 19.31/19.44 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2210,b,1957,a)].
% 19.31/19.44 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2210,b,1958,a)].
% 19.31/19.44 2211 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 19.31/19.44 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2211,b,1957,a)].
% 19.31/19.44 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2211,b,1958,a)].
% 19.31/19.44 2212 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 19.31/19.44 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 19.31/19.44 Derived: class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 19.31/19.44 2213 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 19.31/19.44 2214 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 19.31/19.44 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(2214,b,1957,a)].
% 19.31/19.44 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(2214,b,1958,a)].
% 19.31/19.44 2215 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 19.31/19.44 2216 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 19.31/19.44 2217 -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].
% 19.31/19.44 2218 -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].
% 19.31/19.44 2219 -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].
% 19.31/19.44 2220 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 19.31/19.44 2221 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 19.31/19.44 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2220,a,2221,a)].
% 19.31/19.44 2222 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 19.31/19.44 2223 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 19.31/19.44 2224 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 19.31/19.44 2225 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 19.31/19.44 2226 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 19.31/19.44 2227 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 19.31/19.44 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 19.31/19.44 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 19.31/19.44 2228 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 19.41/19.48 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 19.41/19.48 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 19.41/19.48 2229 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 19.41/19.48 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 19.41/19.48 2230 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 19.41/19.48 2231 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 19.41/19.48 2232 -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].
% 19.41/19.48 2233 -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].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(2233,a,2221,a)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2233,a,2226,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2233,a,2227,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2233,a,2228,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2233,a,2229,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2233,a,2230,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2233,a,2231,b)].
% 19.41/19.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2233,a,2232,b)].
% 19.41/19.48 2234 -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].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2234,a,2221,a)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2234,a,2226,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2234,a,2227,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2234,a,2228,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2234,a,2229,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2234,a,2230,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2234,a,2231,b)].
% 19.41/19.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2234,a,2232,b)].
% 19.41/19.48 2235 -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].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2235,a,2221,a)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2235,a,2226,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2235,a,2227,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2235,a,2228,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2235,a,2229,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2235,a,2230,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2235,a,2231,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2235,a,2232,b)].
% 19.41/19.49 2236 -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].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2236,a,2221,a)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2236,a,2226,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2236,a,2227,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2236,a,2228,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2236,a,2229,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2236,a,2230,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2236,a,2231,b)].
% 19.41/19.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2236,a,2232,b)].
% 19.41/19.49 2237 -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].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2237,a,2221,a)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2237,a,2226,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2237,a,2227,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2237,a,2228,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2237,a,2229,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2237,a,2230,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2237,a,2231,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2237,a,2232,b)].
% 19.41/19.49 2238 -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].
% 19.41/19.49 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2238,a,2221,a)].
% 19.41/19.49 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2238,a,2226,b)].
% 19.41/19.49 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2238,a,2227,b)].
% 19.46/19.51 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2238,a,2228,b)].
% 19.46/19.51 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2238,a,2229,b)].
% 19.46/19.51 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2238,a,2230,b)].
% 19.46/19.51 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2238,a,2231,b)].
% 19.46/19.51 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2238,a,2232,b)].
% 19.46/19.51 2239 -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].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2239,a,2221,a)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2239,a,2226,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2239,a,2227,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2239,a,2228,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,a,2229,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2239,a,2230,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2239,a,2231,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2239,a,2232,b)].
% 19.46/19.51 2240 -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].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2240,a,2221,a)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2240,a,2226,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2240,a,2227,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2240,a,2228,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,a,2229,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2240,a,2230,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2240,a,2231,b)].
% 19.46/19.51 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2240,a,2232,b)].
% 19.46/19.51 2241 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 19.46/19.51 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2241,a,2221,a)].
% 19.46/19.51 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2241,a,2230,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 19.46/19.53 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 19.46/19.53 2242 -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].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2242,a,2221,a)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2242,a,2226,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2242,a,2227,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2242,a,2228,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2242,a,2229,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2242,a,2230,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2242,a,2231,b)].
% 19.46/19.53 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2242,a,2232,b)].
% 19.46/19.53 2243 -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].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2243,a,2221,a)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2243,a,2226,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2243,a,2227,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2243,a,2228,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2243,a,2229,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2243,a,2230,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2243,a,2231,b)].
% 19.46/19.53 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2243,a,2232,b)].
% 19.46/19.53 2244 -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].
% 19.46/19.53 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2244,a,2221,a)].
% 19.46/19.53 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 19.46/19.53 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 19.46/19.53 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 19.46/19.53 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 19.49/19.54 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2244,a,2230,b)].
% 19.49/19.54 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 19.49/19.54 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 19.49/19.54 2245 -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].
% 19.49/19.54 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(2245,a,2221,a)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2245,a,2226,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2245,a,2227,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2245,a,2228,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2245,a,2229,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2245,a,2230,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2245,a,2231,b)].
% 19.49/19.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2245,a,2232,b)].
% 19.49/19.54 2246 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2246,a,2221,a)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2246,a,2230,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 19.49/19.54 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 19.49/19.54 2247 -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].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2247,a,2221,a)].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2247,a,2226,b)].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2247,a,2227,b)].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2247,a,2228,b)].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2247,a,2229,b)].
% 19.49/19.54 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2247,a,2230,b)].
% 19.49/19.56 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2247,a,2231,b)].
% 19.49/19.56 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2247,a,2232,b)].
% 19.49/19.56 2248 -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].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2248,a,2221,a)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2248,a,2226,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2248,a,2227,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2248,a,2228,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2248,a,2229,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2248,a,2230,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2248,a,2231,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2248,a,2232,b)].
% 19.49/19.56 2249 -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].
% 19.49/19.56 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(2249,a,2221,a)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2249,a,2226,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2249,a,2227,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2249,a,2228,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2249,a,2229,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2249,a,2230,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2249,a,2231,b)].
% 19.49/19.56 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2249,a,2232,b)].
% 19.49/19.56 2250 -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].
% 19.49/19.56 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(2250,a,2221,a)].
% 19.49/19.56 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2250,a,2226,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2250,a,2227,b)].
% 19.49/19.56 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2250,a,2228,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2250,a,2229,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2250,a,2230,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2250,a,2231,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2250,a,2232,b)].
% 19.49/19.61 2251 -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].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2251,a,2221,a)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2251,a,2226,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2251,a,2227,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2251,a,2228,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2251,a,2229,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2251,a,2230,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2251,a,2231,b)].
% 19.49/19.61 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2251,a,2232,b)].
% 19.49/19.61 2252 -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].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2252,a,2221,a)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2252,a,2230,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 19.49/19.61 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 19.49/19.61 2253 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 19.49/19.61 2254 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 19.49/19.61 2255 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 19.49/19.61 2256 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(34,a,8,b)].
% 19.49/19.61 2257 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 19.49/19.61 2258 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(36,a,8,b)].
% 19.49/19.61 2259 -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(B). [resolve(37,a,8,b)].
% 19.49/19.61 2260 -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(C). [resolve(38,a,8,b)].
% 19.76/19.82 2261 -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(B). [resolve(39,a,8,b)].
% 19.76/19.82 2262 -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(C). [resolve(40,a,8,b)].
% 19.76/19.82 2263 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(41,a,8,b)].
% 19.76/19.82 2264 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(B). [resolve(42,a,8,b)].
% 19.76/19.82 2265 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 19.76/19.82 2266 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 19.76/19.82 2267 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 19.76/19.82 2268 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 19.76/19.82 2269 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 19.76/19.82 2270 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 19.76/19.82 2271 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 19.76/19.82 2272 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 19.76/19.82 2273 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 19.76/19.82 2274 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 19.76/19.82 2275 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 19.76/19.82 2276 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 19.76/19.82 2277 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1164,c,1134,b)].
% 19.76/19.82 2278 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 19.76/19.82 2279 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1166,c,1134,b)].
% 19.76/19.82 2280 -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(B). [resolve(1167,c,1134,b)].
% 19.76/19.82 2281 -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(C). [resolve(1168,c,1134,b)].
% 19.76/19.82 2282 -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(B). [resolve(1169,c,1134,b)].
% 19.76/19.82 2283 -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(C). [resolve(1170,c,1134,b)].
% 19.76/19.82 2284 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1171,c,1134,b)].
% 19.76/19.82 2285 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(B). [resolve(1172,b,1134,b)].
% 19.76/19.82 2286 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 19.76/19.82 2287 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 19.76/19.82 2288 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 19.76/19.82 2289 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1362,a,1346,b)].
% 19.76/19.82 2290 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1363,a,1346,b)].
% 20.07/20.15 2291 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1364,a,1346,b)].
% 20.07/20.15 2292 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1365,a,1346,b)].
% 20.07/20.15 2293 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1366,a,1346,b)].
% 20.07/20.15 2294 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1367,a,1346,b)].
% 20.07/20.15 2295 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1368,a,1346,b)].
% 20.07/20.15 2296 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1369,a,1346,b)].
% 20.07/20.15 2297 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 20.07/20.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 20.07/20.15 2298 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 20.07/20.15 2299 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 20.07/20.15 2300 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 20.07/20.15 2301 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1389,c,1346,b)].
% 20.07/20.15 2302 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 20.07/20.15 2303 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1391,c,1346,b)].
% 20.07/20.15 2304 -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(B). [resolve(1392,c,1346,b)].
% 20.07/20.15 2305 -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(C). [resolve(1393,c,1346,b)].
% 20.07/20.15 2306 -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(B). [resolve(1394,c,1346,b)].
% 20.07/20.15 2307 -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(C). [resolve(1395,c,1346,b)].
% 20.07/20.15 2308 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1396,c,1346,b)].
% 20.07/20.15 2309 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(B). [resolve(1397,b,1346,b)].
% 20.07/20.15 2310 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 20.07/20.15 2311 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 20.07/20.15 2312 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 20.07/20.15 2313 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 20.07/20.15 2314 -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].
% 20.07/20.15 2315 -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].
% 20.07/20.15 2316 -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].
% 20.07/20.15 2317 -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].
% 20.16/20.26 2318 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 20.16/20.26 2319 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 20.16/20.26 2320 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 20.16/20.26 2321 -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].
% 20.16/20.26 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2321,a,2315,b)].
% 20.16/20.26 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 20.16/20.26 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 20.16/20.26 2322 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 20.16/20.26 2323 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 20.16/20.26 2324 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 20.16/20.26 2325 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(34,a,30,b)].
% 20.16/20.26 2326 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(35,a,30,b)].
% 20.16/20.26 2327 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(36,a,30,b)].
% 20.16/20.26 2328 -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(37,a,30,b)].
% 20.16/20.26 2329 -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(38,a,30,b)].
% 20.16/20.26 2330 -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(39,a,30,b)].
% 20.16/20.26 2331 -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(40,a,30,b)].
% 20.16/20.26 2332 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(41,a,30,b)].
% 20.16/20.26 2333 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(42,a,30,b)].
% 20.16/20.26 2334 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 20.16/20.26 2335 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 20.16/20.26 2336 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 20.16/20.26 2337 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(108,b,96,b)].
% 20.16/20.26 2338 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(109,b,96,b)].
% 20.16/20.26 2339 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 20.16/20.26 2340 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 20.16/20.26 2341 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(221,c,209,b)].
% 20.16/20.28 2342 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(222,c,209,b)].
% 20.16/20.28 2343 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 20.16/20.28 2344 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 20.16/20.28 2345 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 20.16/20.28 2346 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 20.16/20.28 2347 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(307,a,302,b)].
% 20.16/20.28 2348 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(308,a,302,b)].
% 20.16/20.28 2349 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 20.16/20.28 2350 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 20.16/20.28 2351 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 20.16/20.28 2352 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 20.16/20.28 2353 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(389,c,371,b)].
% 20.16/20.28 2354 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(390,c,371,b)].
% 20.16/20.28 2355 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 20.16/20.28 2356 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 20.16/20.28 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 20.16/20.28 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2356,b,2315,b)].
% 20.16/20.28 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 20.16/20.28 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 20.16/20.28 2357 -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_Opordered__ring(A). [resolve(413,b,405,b)].
% 20.16/20.28 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(2357,c,2314,b)].
% 20.16/20.28 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__ring__strict(A). [resolve(2357,c,2317,b)].
% 20.16/20.28 2358 -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_Opordered__ring(A). [resolve(414,b,405,b)].
% 20.16/20.28 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(2358,c,2314,b)].
% 20.16/20.28 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__ring__strict(A). [resolve(2358,c,2317,b)].
% 20.16/20.28 2359 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(415,a,405,b)].
% 20.37/20.46 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(2359,b,2314,b)].
% 20.37/20.46 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2359,b,2317,b)].
% 20.37/20.46 2360 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(416,a,405,b)].
% 20.37/20.46 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(2360,b,2314,b)].
% 20.37/20.46 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2360,b,2317,b)].
% 20.37/20.46 2361 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(417,a,405,b)].
% 20.37/20.46 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(2361,b,2314,b)].
% 20.37/20.46 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2361,b,2317,b)].
% 20.37/20.46 2362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 20.37/20.46 2363 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(428,c,405,b)].
% 20.37/20.46 2364 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(429,c,405,b)].
% 20.37/20.46 2365 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 20.37/20.46 2366 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 20.37/20.46 2367 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 20.37/20.46 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 20.37/20.46 2368 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 20.37/20.46 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 20.37/20.46 2369 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 20.37/20.46 2370 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(442,c,405,b)].
% 20.37/20.46 2371 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(443,c,405,b)].
% 20.37/20.46 2372 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 20.37/20.46 2373 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 20.37/20.46 2374 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1362,a,1361,b)].
% 20.37/20.46 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(2374,c,2314,b)].
% 20.37/20.46 2375 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1363,a,1361,b)].
% 20.37/20.46 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(2375,c,2314,b)].
% 20.37/20.46 2376 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1364,a,1361,b)].
% 20.37/20.46 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(2376,c,2314,b)].
% 20.37/20.46 2377 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1365,a,1361,b)].
% 20.37/20.46 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(2377,c,2314,b)].
% 20.48/20.53 2378 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1366,a,1361,b)].
% 20.48/20.53 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(2378,c,2314,b)].
% 20.48/20.53 2379 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1367,a,1361,b)].
% 20.48/20.53 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(2379,c,2314,b)].
% 20.48/20.53 2380 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1368,a,1361,b)].
% 20.48/20.53 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(2380,c,2314,b)].
% 20.48/20.53 2381 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1369,a,1361,b)].
% 20.48/20.53 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(2381,c,2314,b)].
% 20.48/20.53 2382 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 20.48/20.53 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 20.48/20.53 2383 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 20.48/20.53 2384 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 20.48/20.53 2385 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 20.48/20.53 2386 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1389,c,1361,b)].
% 20.48/20.53 2387 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1390,b,1361,b)].
% 20.48/20.53 2388 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1391,c,1361,b)].
% 20.48/20.53 2389 -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(1392,c,1361,b)].
% 20.48/20.53 2390 -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(1393,c,1361,b)].
% 20.48/20.53 2391 -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(1394,c,1361,b)].
% 20.48/20.53 2392 -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(1395,c,1361,b)].
% 20.48/20.53 2393 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1396,c,1361,b)].
% 20.48/20.53 2394 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(1397,b,1361,b)].
% 20.48/20.53 2395 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1398,c,1361,b)].
% 20.48/20.53 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2395,c,2314,b)].
% 20.48/20.53 2396 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1399,c,1361,b)].
% 20.48/20.53 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2396,c,2314,b)].
% 20.48/20.53 2397 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 20.48/20.53 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 20.48/20.53 2398 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 20.48/20.53 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 20.48/20.53 2399 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1633,c,1596,b)].
% 20.48/20.55 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2399,c,2314,b)].
% 20.48/20.55 2400 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1634,b,1596,b)].
% 20.48/20.55 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2400,b,2314,b)].
% 20.48/20.55 2401 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1635,c,1596,b)].
% 20.48/20.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2401,c,2314,b)].
% 20.48/20.55 2402 -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(1636,c,1596,b)].
% 20.48/20.55 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(2402,c,2314,b)].
% 20.48/20.55 2403 -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(1637,c,1596,b)].
% 20.48/20.55 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(2403,c,2314,b)].
% 20.48/20.55 2404 -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(1638,c,1596,b)].
% 20.48/20.55 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(2404,c,2314,b)].
% 20.48/20.55 2405 -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(1639,c,1596,b)].
% 20.48/20.55 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(2405,c,2314,b)].
% 20.48/20.55 2406 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1640,c,1596,b)].
% 20.48/20.55 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2406,c,2314,b)].
% 20.48/20.55 2407 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(1641,b,1596,b)].
% 20.48/20.55 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(2407,b,2314,b)].
% 20.48/20.55 2408 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 20.48/20.55 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 20.48/20.55 2409 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1643,c,1596,b)].
% 20.48/20.55 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2409,c,2314,b)].
% 20.48/20.55 2410 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1644,c,1596,b)].
% 20.48/20.55 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2410,c,2314,b)].
% 20.77/20.84 2411 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 20.77/20.84 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 20.77/20.84 2412 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 20.77/20.84 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 20.77/20.84 2413 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 20.77/20.84 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 20.77/20.84 2414 -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].
% 20.77/20.84 2415 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 20.77/20.84 2416 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 20.77/20.84 2417 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 20.77/20.84 2418 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 20.77/20.84 2419 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 20.77/20.84 2420 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 20.77/20.84 2421 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 20.77/20.84 2422 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 20.77/20.84 2423 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 20.77/20.84 2424 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 20.77/20.84 2425 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 20.77/20.84 2426 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 20.77/20.84 2427 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 20.77/20.84 2428 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2414,a,2415,a)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2414,a,2416,a)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(2414,a,2417,a)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2414,a,2418,b)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2414,a,2419,b)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2414,a,2420,b)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2414,a,2421,b)].
% 20.77/20.84 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2414,a,2422,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2414,a,2423,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2414,a,2424,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2414,a,2425,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2414,a,2426,b)].
% 20.77/20.86 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(2414,a,2427,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2414,a,2428,b)].
% 20.77/20.86 2429 -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].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2429,a,2415,a)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2429,a,2416,a)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(2429,a,2417,a)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2429,a,2418,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2429,a,2419,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2429,a,2420,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2429,a,2421,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2429,a,2422,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2429,a,2423,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2429,a,2424,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2429,a,2425,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2429,a,2426,b)].
% 20.77/20.86 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(2429,a,2427,b)].
% 20.77/20.86 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2429,a,2428,b)].
% 20.77/20.86 2430 -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].
% 20.77/20.86 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(2430,a,2415,a)].
% 20.77/20.86 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(2430,a,2416,a)].
% 20.77/20.86 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(2430,a,2417,a)].
% 20.77/20.86 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__abs(C). [resolve(2430,a,2418,b)].
% 20.77/20.86 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(2430,a,2419,b)].
% 20.77/20.87 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(2430,a,2420,b)].
% 20.77/20.87 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(2430,a,2421,b)].
% 20.77/20.87 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(2430,a,2422,b)].
% 20.77/20.87 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(2430,a,2423,b)].
% 20.77/20.87 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(2430,a,2424,b)].
% 20.77/20.87 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__ring__strict(C). [resolve(2430,a,2425,b)].
% 20.77/20.87 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__semidom(C). [resolve(2430,a,2426,b)].
% 20.77/20.87 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(2430,a,2427,b)].
% 20.77/20.87 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2430,a,2428,b)].
% 20.77/20.87 2431 -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].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2431,a,2415,a)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2431,a,2416,a)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(2431,a,2417,a)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2431,a,2418,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2431,a,2419,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2431,a,2420,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2431,a,2421,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2431,a,2422,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2431,a,2423,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2431,a,2424,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2431,a,2425,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2431,a,2426,b)].
% 20.77/20.87 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(2431,a,2427,b)].
% 20.77/20.87 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2431,a,2428,b)].
% 20.77/20.87 2432 -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].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2432,a,2415,a)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2432,a,2416,a)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(2432,a,2417,a)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2432,a,2418,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2432,a,2419,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2432,a,2420,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2432,a,2421,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2432,a,2422,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2432,a,2423,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2432,a,2424,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2432,a,2425,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2432,a,2426,b)].
% 20.77/20.89 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(2432,a,2427,b)].
% 20.77/20.89 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2432,a,2428,b)].
% 20.77/20.89 2433 -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].
% 20.77/20.89 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2433,a,2415,a)].
% 20.77/20.89 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2433,a,2416,a)].
% 20.77/20.89 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(2433,a,2417,a)].
% 20.77/20.89 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__abs(C). [resolve(2433,a,2418,b)].
% 20.77/20.89 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(2433,a,2419,b)].
% 20.77/20.89 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(2433,a,2420,b)].
% 20.77/20.89 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(2433,a,2421,b)].
% 20.77/20.89 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2433,a,2422,b)].
% 20.77/20.89 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2433,a,2423,b)].
% 20.77/20.89 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2433,a,2424,b)].
% 20.77/20.89 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2433,a,2425,b)].
% 20.87/20.90 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__semidom(C). [resolve(2433,a,2426,b)].
% 20.87/20.90 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(2433,a,2427,b)].
% 20.87/20.90 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2433,a,2428,b)].
% 20.87/20.90 2434 -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].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2434,a,2415,a)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2434,a,2416,a)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(2434,a,2417,a)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2434,a,2418,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2434,a,2419,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2434,a,2420,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2434,a,2421,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2434,a,2422,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2434,a,2423,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2434,a,2424,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2434,a,2425,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2434,a,2426,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2434,a,2427,b)].
% 20.87/20.90 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2434,a,2428,b)].
% 20.87/20.90 2435 -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].
% 20.87/20.90 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2435,a,2415,a)].
% 20.87/20.90 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2435,a,2416,a)].
% 20.87/20.90 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(2435,a,2417,a)].
% 20.87/20.90 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2435,a,2418,b)].
% 20.87/20.90 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2435,a,2419,b)].
% 20.87/20.90 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2435,a,2420,b)].
% 20.87/20.90 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2435,a,2421,b)].
% 20.87/20.90 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2435,a,2422,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2435,a,2423,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2435,a,2424,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2435,a,2425,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2435,a,2426,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2435,a,2427,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2435,a,2428,b)].
% 20.87/20.92 2436 -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].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2436,a,2415,a)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2436,a,2416,a)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(2436,a,2417,a)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2436,a,2418,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2436,a,2419,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2436,a,2420,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2436,a,2421,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2436,a,2422,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2436,a,2423,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2436,a,2424,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2436,a,2425,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2436,a,2426,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2436,a,2427,b)].
% 20.87/20.92 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2436,a,2428,b)].
% 20.87/20.92 2437 -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].
% 20.87/20.92 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2437,a,2415,a)].
% 20.87/20.92 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2437,a,2416,a)].
% 20.87/20.92 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(2437,a,2417,a)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2437,a,2418,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2437,a,2419,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2437,a,2420,b)].
% 20.87/20.92 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2437,a,2421,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2437,a,2422,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2437,a,2423,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2437,a,2424,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2437,a,2425,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2437,a,2426,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2437,a,2427,b)].
% 20.87/20.94 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2437,a,2428,b)].
% 20.87/20.94 2438 -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].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2438,a,2415,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2438,a,2416,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(2438,a,2417,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2438,a,2418,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2438,a,2419,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2438,a,2420,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2438,a,2421,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2438,a,2422,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2438,a,2423,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2438,a,2424,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2438,a,2425,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2438,a,2426,b)].
% 20.87/20.94 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(2438,a,2427,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2438,a,2428,b)].
% 20.87/20.94 2439 -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].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2439,a,2415,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2439,a,2416,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(2439,a,2417,a)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2439,a,2418,b)].
% 20.87/20.94 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2439,a,2419,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2439,a,2420,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2439,a,2421,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2439,a,2422,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2439,a,2423,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2439,a,2424,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2439,a,2425,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2439,a,2426,b)].
% 20.87/20.95 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(2439,a,2427,b)].
% 20.87/20.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2439,a,2428,b)].
% 20.87/20.95 2440 -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].
% 20.87/20.95 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(2440,a,2415,a)].
% 20.87/20.95 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(2440,a,2416,a)].
% 20.87/20.95 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(2440,a,2417,a)].
% 20.87/20.95 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__abs(C). [resolve(2440,a,2418,b)].
% 20.87/20.95 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(2440,a,2419,b)].
% 20.87/20.95 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(2440,a,2420,b)].
% 20.87/20.95 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(2440,a,2421,b)].
% 20.87/20.95 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(2440,a,2422,b)].
% 20.87/20.95 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(2440,a,2423,b)].
% 20.87/20.95 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(2440,a,2424,b)].
% 20.87/20.95 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__ring__strict(C). [resolve(2440,a,2425,b)].
% 20.87/20.95 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__semidom(C). [resolve(2440,a,2426,b)].
% 20.87/20.95 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(2440,a,2427,b)].
% 20.87/20.95 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2440,a,2428,b)].
% 20.87/20.97 2441 -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].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2441,a,2415,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2441,a,2416,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(2441,a,2417,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2441,a,2418,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2441,a,2419,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2441,a,2420,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2441,a,2421,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2441,a,2422,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2441,a,2423,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2441,a,2424,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2441,a,2425,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2441,a,2426,b)].
% 20.87/20.97 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(2441,a,2427,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2441,a,2428,b)].
% 20.87/20.97 2442 -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].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2442,a,2415,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2442,a,2416,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(2442,a,2417,a)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2442,a,2418,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2442,a,2419,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2442,a,2420,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(2442,a,2421,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2442,a,2422,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2442,a,2423,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2442,a,2424,b)].
% 20.87/20.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2442,a,2425,b)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2442,a,2426,b)].
% 20.87/20.98 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(2442,a,2427,b)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2442,a,2428,b)].
% 20.87/20.98 2443 -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].
% 20.87/20.98 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(2443,a,2415,a)].
% 20.87/20.98 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(2443,a,2416,a)].
% 20.87/20.98 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(2443,a,2417,a)].
% 20.87/20.98 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__abs(C). [resolve(2443,a,2418,b)].
% 20.87/20.98 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(2443,a,2419,b)].
% 20.87/20.98 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(2443,a,2420,b)].
% 20.87/20.98 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(2443,a,2421,b)].
% 20.87/20.98 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(2443,a,2422,b)].
% 20.87/20.98 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(2443,a,2423,b)].
% 20.87/20.98 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(2443,a,2424,b)].
% 20.87/20.98 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__ring__strict(C). [resolve(2443,a,2425,b)].
% 20.87/20.98 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__semidom(C). [resolve(2443,a,2426,b)].
% 20.87/20.98 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(2443,a,2427,b)].
% 20.87/20.98 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2443,a,2428,b)].
% 20.87/20.98 2444 -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].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2444,a,2415,a)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2444,a,2416,a)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(2444,a,2417,a)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2444,a,2418,b)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2444,a,2419,b)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2444,a,2420,b)].
% 20.87/20.98 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2444,a,2421,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2444,a,2422,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2444,a,2423,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2444,a,2424,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2444,a,2425,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2444,a,2426,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2444,a,2427,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2444,a,2428,b)].
% 20.96/21.00 2445 -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].
% 20.96/21.00 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2445,a,2415,a)].
% 20.96/21.00 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2445,a,2416,a)].
% 20.96/21.00 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(2445,a,2417,a)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2445,a,2418,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2445,a,2419,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2445,a,2420,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2445,a,2421,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2445,a,2422,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2445,a,2423,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2445,a,2424,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2445,a,2425,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2445,a,2426,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2445,a,2427,b)].
% 20.96/21.00 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2445,a,2428,b)].
% 20.96/21.00 2446 -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].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2446,a,2415,a)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2446,a,2416,a)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(2446,a,2417,a)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2446,a,2418,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2446,a,2419,b)].
% 20.96/21.00 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2446,a,2420,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2446,a,2421,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2446,a,2422,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2446,a,2423,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2446,a,2424,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2446,a,2425,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2446,a,2426,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2446,a,2427,b)].
% 21.19/21.23 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2446,a,2428,b)].
% 21.19/21.23 2447 -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].
% 21.19/21.23 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2447,a,2415,a)].
% 21.19/21.23 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2447,a,2416,a)].
% 21.19/21.23 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(2447,a,2417,a)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2447,a,2418,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2447,a,2419,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2447,a,2420,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(2447,a,2421,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2447,a,2422,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2447,a,2423,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2447,a,2424,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2447,a,2425,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2447,a,2426,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2447,a,2427,b)].
% 21.19/21.23 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2447,a,2428,b)].
% 21.19/21.23 2448 class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 21.19/21.23 2449 class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 21.19/21.23 2450 class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 21.19/21.23 2451 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 21.19/21.23 2452 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 21.19/21.23 2453 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 21.19/21.23 2454 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 21.19/21.23 2455 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 21.19/21.23 2456 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 21.56/21.65 2457 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 21.56/21.65 2458 class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 21.56/21.65 2459 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 21.56/21.65 2460 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 21.56/21.65 2461 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 21.56/21.65 2462 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 21.56/21.65 2463 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 21.56/21.65 2464 class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 21.56/21.65 2465 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 21.56/21.65 2466 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 21.56/21.65 2467 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 21.56/21.65 2468 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 21.56/21.65 2469 class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 21.56/21.65 2470 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 21.56/21.65 2471 class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 21.56/21.65 2472 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 21.56/21.65 2473 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 21.56/21.65 2474 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 21.56/21.65 2475 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 21.56/21.65 2476 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 21.56/21.65 2477 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 21.56/21.65 2478 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 21.56/21.65 2479 class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 21.56/21.65 2480 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 21.56/21.65 2481 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 21.56/21.65 2482 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 21.56/21.65 2483 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 21.56/21.65 2484 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 21.56/21.65 2485 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 21.56/21.65 2486 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 21.56/21.65 2487 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 21.56/21.65 2488 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 21.56/21.65 2489 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 21.56/21.65 2490 class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 21.56/21.65 2491 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 21.56/21.65 2492 class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 21.56/21.65 2493 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 21.56/21.65 2494 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 21.56/21.65 2495 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 21.56/21.65 2496 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 21.56/21.65 2497 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 21.56/21.65 2498 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 21.56/21.65 2499 class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 21.56/21.65 2500 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 21.84/21.93 2501 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 21.84/21.93 2502 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 21.84/21.93 2503 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 21.84/21.93 2504 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 21.84/21.93 2505 class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 21.84/21.93 2506 class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 21.84/21.93 2507 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 21.84/21.93 2508 -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].
% 21.84/21.93 2509 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 21.84/21.93 2510 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 21.84/21.93 2511 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 21.84/21.93 2512 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 21.84/21.93 2513 -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].
% 21.84/21.93 2514 -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].
% 21.84/21.93 2515 -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].
% 21.84/21.93 2516 -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].
% 21.84/21.93 2517 -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].
% 21.84/21.93 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(2517,a,2509,a)].
% 21.84/21.93 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 21.84/21.93 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2517,a,2514,b)].
% 21.84/21.93 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 21.84/21.93 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 21.84/21.93 2518 -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].
% 21.84/21.93 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(2518,a,2509,a)].
% 21.84/21.93 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 21.84/21.93 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2518,a,2514,b)].
% 21.84/21.93 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 21.84/21.93 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 21.84/21.93 2519 -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].
% 21.84/21.93 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(2519,a,2509,a)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2519,a,2513,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2519,a,2514,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2519,a,2515,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2519,a,2516,b)].
% 21.84/21.95 2520 -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].
% 21.84/21.95 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2520,a,2509,a)].
% 21.84/21.95 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2520,a,2514,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 21.84/21.95 2521 -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].
% 21.84/21.95 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(2521,a,2509,a)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2521,a,2514,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 21.84/21.95 2522 -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].
% 21.84/21.95 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2522,a,2509,a)].
% 21.84/21.95 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 21.84/21.95 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2522,a,2514,b)].
% 21.84/21.95 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 21.84/21.95 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 21.84/21.95 2523 -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].
% 21.84/21.95 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(2523,a,2509,a)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2523,a,2513,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2523,a,2514,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2523,a,2515,b)].
% 21.84/21.95 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2523,a,2516,b)].
% 21.84/21.95 2524 -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].
% 21.84/21.95 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(2524,a,2509,a)].
% 21.84/21.95 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2524,a,2513,b)].
% 21.84/21.95 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2524,a,2514,b)].
% 21.93/21.97 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2524,a,2515,b)].
% 21.93/21.97 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2524,a,2516,b)].
% 21.93/21.97 2525 -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].
% 21.93/21.97 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2525,a,2509,a)].
% 21.93/21.97 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 21.93/21.97 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2525,a,2514,b)].
% 21.93/21.97 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 21.93/21.97 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2525,a,2516,b)].
% 21.93/21.97 2526 -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].
% 21.93/21.97 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(2526,a,2509,a)].
% 21.93/21.97 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2526,a,2513,b)].
% 21.93/21.97 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2526,a,2514,b)].
% 21.93/21.97 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2526,a,2515,b)].
% 21.93/21.97 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2526,a,2516,b)].
% 21.93/21.97 2527 -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].
% 21.93/21.97 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2527,a,2509,a)].
% 21.93/21.97 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 21.93/21.97 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2527,a,2514,b)].
% 21.93/21.97 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 21.93/21.97 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 21.93/21.97 2528 -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].
% 21.93/21.97 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(2528,a,2509,a)].
% 21.93/21.97 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2528,a,2513,b)].
% 21.93/21.97 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2528,a,2514,b)].
% 21.93/21.97 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2528,a,2515,b)].
% 21.93/21.97 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2528,a,2516,b)].
% 21.93/21.97 2529 -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].
% 21.93/21.97 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(2529,a,2509,a)].
% 21.93/21.97 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2529,a,2513,b)].
% 21.93/21.97 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2529,a,2514,b)].
% 21.93/21.97 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2529,a,2515,b)].
% 22.02/22.04 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2529,a,2516,b)].
% 22.02/22.04 2530 -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].
% 22.02/22.04 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2530,a,2509,a)].
% 22.02/22.04 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 22.02/22.04 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2530,a,2514,b)].
% 22.02/22.04 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 22.02/22.04 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2530,a,2516,b)].
% 22.02/22.04 2531 -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].
% 22.02/22.04 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(2531,a,2509,a)].
% 22.02/22.04 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2531,a,2513,b)].
% 22.02/22.04 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2531,a,2514,b)].
% 22.02/22.04 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2531,a,2515,b)].
% 22.02/22.04 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2531,a,2516,b)].
% 22.02/22.04 2532 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 22.02/22.04 2533 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 22.02/22.04 2534 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(34,a,9,b)].
% 22.02/22.04 2535 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(35,a,9,b)].
% 22.02/22.04 2536 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(36,a,9,b)].
% 22.02/22.04 2537 -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__abs(B). [resolve(37,a,9,b)].
% 22.02/22.04 2538 -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__abs(C). [resolve(38,a,9,b)].
% 22.02/22.04 2539 -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__abs(B). [resolve(39,a,9,b)].
% 22.02/22.04 2540 -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__abs(C). [resolve(40,a,9,b)].
% 22.02/22.04 2541 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(41,a,9,b)].
% 22.02/22.04 2542 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__abs(B). [resolve(42,a,9,b)].
% 22.02/22.04 2543 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 22.02/22.04 2544 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 22.02/22.04 2545 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 22.02/22.04 2546 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 22.02/22.04 2547 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(307,a,278,b)].
% 22.02/22.04 2548 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(308,a,278,b)].
% 22.15/22.22 2549 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 22.15/22.22 2550 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 22.15/22.22 2551 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 22.15/22.22 2552 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 22.15/22.22 2553 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 22.15/22.22 2554 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1164,c,1135,b)].
% 22.15/22.22 2555 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1165,b,1135,b)].
% 22.15/22.22 2556 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1166,c,1135,b)].
% 22.15/22.22 2557 -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__abs(B). [resolve(1167,c,1135,b)].
% 22.15/22.22 2558 -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__abs(C). [resolve(1168,c,1135,b)].
% 22.15/22.22 2559 -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__abs(B). [resolve(1169,c,1135,b)].
% 22.15/22.22 2560 -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__abs(C). [resolve(1170,c,1135,b)].
% 22.15/22.22 2561 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1171,c,1135,b)].
% 22.15/22.22 2562 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__abs(B). [resolve(1172,b,1135,b)].
% 22.15/22.22 2563 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1340,c,1311,b)].
% 22.15/22.22 2564 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1341,c,1311,b)].
% 22.15/22.22 2565 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 22.15/22.22 2566 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1362,a,1347,b)].
% 22.15/22.22 2567 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1363,a,1347,b)].
% 22.15/22.22 2568 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1364,a,1347,b)].
% 22.15/22.22 2569 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1365,a,1347,b)].
% 22.15/22.22 2570 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1366,a,1347,b)].
% 22.15/22.22 2571 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1367,a,1347,b)].
% 22.15/22.22 2572 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1368,a,1347,b)].
% 22.15/22.22 2573 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1369,a,1347,b)].
% 22.15/22.22 2574 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 22.15/22.22 2575 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 22.15/22.22 2576 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 22.15/22.22 2577 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1389,c,1347,b)].
% 22.32/22.40 2578 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1390,b,1347,b)].
% 22.32/22.40 2579 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1391,c,1347,b)].
% 22.32/22.40 2580 -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__abs(B). [resolve(1392,c,1347,b)].
% 22.32/22.40 2581 -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__abs(C). [resolve(1393,c,1347,b)].
% 22.32/22.40 2582 -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__abs(B). [resolve(1394,c,1347,b)].
% 22.32/22.40 2583 -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__abs(C). [resolve(1395,c,1347,b)].
% 22.32/22.40 2584 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1396,c,1347,b)].
% 22.32/22.40 2585 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__abs(B). [resolve(1397,b,1347,b)].
% 22.32/22.40 2586 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1398,c,1347,b)].
% 22.32/22.40 2587 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1399,c,1347,b)].
% 22.32/22.40 2588 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2233,a,2226,b)].
% 22.32/22.40 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(2588,c,2509,a)].
% 22.32/22.40 2589 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2234,a,2226,b)].
% 22.32/22.40 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2589,c,2509,a)].
% 22.32/22.40 2590 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2235,a,2226,b)].
% 22.32/22.40 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2590,c,2509,a)].
% 22.32/22.40 2591 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2236,a,2226,b)].
% 22.32/22.40 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2591,b,2509,a)].
% 22.32/22.40 2592 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2237,a,2226,b)].
% 22.32/22.40 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2592,c,2509,a)].
% 22.32/22.40 2593 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2238,a,2226,b)].
% 22.32/22.40 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2593,b,2509,a)].
% 22.32/22.40 2594 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2239,a,2226,b)].
% 22.32/22.40 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(2594,b,2509,a)].
% 22.32/22.40 2595 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2240,a,2226,b)].
% 22.32/22.40 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(2595,b,2509,a)].
% 22.32/22.40 2596 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 22.32/22.40 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2596,b,2509,a)].
% 22.32/22.43 2597 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2242,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2597,c,2509,a)].
% 22.32/22.43 2598 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2243,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2598,c,2509,a)].
% 22.32/22.43 2599 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 22.32/22.43 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2599,b,2509,a)].
% 22.32/22.43 2600 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2245,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2600,c,2509,a)].
% 22.32/22.43 2601 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 22.32/22.43 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2601,b,2509,a)].
% 22.32/22.43 2602 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2247,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2602,c,2509,a)].
% 22.32/22.43 2603 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2248,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2603,c,2509,a)].
% 22.32/22.43 2604 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2249,a,2226,b)].
% 22.32/22.43 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(2604,c,2509,a)].
% 22.32/22.43 2605 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2250,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(2605,c,2509,a)].
% 22.32/22.43 2606 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2251,a,2226,b)].
% 22.32/22.43 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2606,c,2509,a)].
% 22.32/22.43 2607 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 22.32/22.43 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2607,b,2509,a)].
% 22.32/22.43 2608 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2414,a,2418,b)].
% 22.32/22.43 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2608,c,2509,a)].
% 22.32/22.43 2609 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2429,a,2418,b)].
% 22.32/22.43 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2609,c,2509,a)].
% 22.32/22.43 2610 -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__abs(C). [resolve(2430,a,2418,b)].
% 22.32/22.43 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(2610,d,2509,a)].
% 22.32/22.43 2611 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2431,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2611,c,2509,a)].
% 22.42/22.47 2612 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2432,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2612,c,2509,a)].
% 22.42/22.47 2613 -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__abs(C). [resolve(2433,a,2418,b)].
% 22.42/22.47 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2613,d,2509,a)].
% 22.42/22.47 2614 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2434,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2614,c,2509,a)].
% 22.42/22.47 2615 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2435,a,2418,b)].
% 22.42/22.47 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2615,c,2509,a)].
% 22.42/22.47 2616 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2436,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2616,c,2509,a)].
% 22.42/22.47 2617 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2437,a,2418,b)].
% 22.42/22.47 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2617,c,2509,a)].
% 22.42/22.47 2618 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2438,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2618,c,2509,a)].
% 22.42/22.47 2619 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2439,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2619,c,2509,a)].
% 22.42/22.47 2620 -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__abs(C). [resolve(2440,a,2418,b)].
% 22.42/22.47 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2620,d,2509,a)].
% 22.42/22.47 2621 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2441,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2621,c,2509,a)].
% 22.42/22.47 2622 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__abs(D). [resolve(2442,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2622,c,2509,a)].
% 22.42/22.47 2623 -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__abs(C). [resolve(2443,a,2418,b)].
% 22.42/22.47 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(2623,d,2509,a)].
% 22.42/22.47 2624 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2444,a,2418,b)].
% 22.42/22.47 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2624,c,2509,a)].
% 22.62/22.68 2625 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2445,a,2418,b)].
% 22.62/22.68 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2625,c,2509,a)].
% 22.62/22.68 2626 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2446,a,2418,b)].
% 22.62/22.68 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2626,c,2509,a)].
% 22.62/22.68 2627 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(2447,a,2418,b)].
% 22.62/22.68 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2627,c,2509,a)].
% 22.62/22.68 2628 -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].
% 22.62/22.68 2629 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 22.62/22.68 2630 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 22.62/22.68 2631 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 22.62/22.68 2632 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 22.62/22.68 2633 -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].
% 22.62/22.68 2634 -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].
% 22.62/22.68 2635 -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].
% 22.62/22.68 2636 -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].
% 22.62/22.68 2637 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 22.62/22.68 2638 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 22.62/22.68 2639 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(34,a,11,b)].
% 22.62/22.68 2640 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(35,a,11,b)].
% 22.62/22.68 2641 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(36,a,11,b)].
% 22.62/22.68 2642 -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(37,a,11,b)].
% 22.62/22.68 2643 -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(38,a,11,b)].
% 22.62/22.68 2644 -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(39,a,11,b)].
% 22.62/22.68 2645 -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(40,a,11,b)].
% 22.62/22.68 2646 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(41,a,11,b)].
% 22.62/22.68 2647 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(42,a,11,b)].
% 22.77/22.87 2648 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 22.77/22.87 2649 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 22.77/22.87 2650 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 22.77/22.87 2651 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 22.77/22.87 2652 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(307,a,280,b)].
% 22.77/22.87 2653 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(308,a,280,b)].
% 22.77/22.87 2654 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 22.77/22.87 2655 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 22.77/22.87 2656 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 22.77/22.87 2657 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 22.77/22.87 2658 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 22.77/22.87 2659 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1164,c,1137,b)].
% 22.77/22.87 2660 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1165,b,1137,b)].
% 22.77/22.87 2661 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1166,c,1137,b)].
% 22.77/22.87 2662 -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(1167,c,1137,b)].
% 22.77/22.87 2663 -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(1168,c,1137,b)].
% 22.77/22.87 2664 -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(1169,c,1137,b)].
% 22.77/22.87 2665 -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(1170,c,1137,b)].
% 22.77/22.87 2666 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1171,c,1137,b)].
% 22.77/22.87 2667 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(1172,b,1137,b)].
% 22.77/22.87 2668 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1340,c,1313,b)].
% 22.77/22.87 2669 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1341,c,1313,b)].
% 22.77/22.87 2670 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 22.77/22.87 2671 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1362,a,1349,b)].
% 22.77/22.87 2672 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1363,a,1349,b)].
% 22.77/22.87 2673 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1364,a,1349,b)].
% 22.77/22.87 2674 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1365,a,1349,b)].
% 22.77/22.87 2675 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1366,a,1349,b)].
% 22.77/22.87 2676 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1367,a,1349,b)].
% 23.00/23.04 2677 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1368,a,1349,b)].
% 23.00/23.04 2678 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1369,a,1349,b)].
% 23.00/23.04 2679 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 23.00/23.04 2680 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 23.00/23.04 2681 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 23.00/23.04 2682 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1389,c,1349,b)].
% 23.00/23.04 2683 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1390,b,1349,b)].
% 23.00/23.04 2684 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1391,c,1349,b)].
% 23.00/23.04 2685 -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(1392,c,1349,b)].
% 23.00/23.04 2686 -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(1393,c,1349,b)].
% 23.00/23.04 2687 -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(1394,c,1349,b)].
% 23.00/23.04 2688 -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(1395,c,1349,b)].
% 23.00/23.04 2689 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1396,c,1349,b)].
% 23.00/23.04 2690 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(1397,b,1349,b)].
% 23.00/23.04 2691 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1398,c,1349,b)].
% 23.00/23.04 2692 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1399,c,1349,b)].
% 23.00/23.04 2693 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 23.00/23.04 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2693,a,2629,a)].
% 23.00/23.04 2694 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 23.00/23.04 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(2694,a,2629,a)].
% 23.00/23.04 2695 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2233,a,2228,b)].
% 23.00/23.04 2696 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2234,a,2228,b)].
% 23.00/23.04 2697 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2235,a,2228,b)].
% 23.00/23.04 2698 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2236,a,2228,b)].
% 23.00/23.04 2699 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2237,a,2228,b)].
% 23.00/23.04 2700 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2238,a,2228,b)].
% 23.00/23.04 2701 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2239,a,2228,b)].
% 23.00/23.04 2702 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2240,a,2228,b)].
% 23.00/23.04 2703 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 23.06/23.11 2704 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2242,a,2228,b)].
% 23.06/23.11 2705 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2243,a,2228,b)].
% 23.06/23.11 2706 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 23.06/23.11 2707 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2245,a,2228,b)].
% 23.06/23.11 2708 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 23.06/23.11 2709 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2247,a,2228,b)].
% 23.06/23.11 2710 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2248,a,2228,b)].
% 23.06/23.11 2711 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2249,a,2228,b)].
% 23.06/23.11 2712 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2250,a,2228,b)].
% 23.06/23.11 2713 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2251,a,2228,b)].
% 23.06/23.11 2714 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 23.06/23.11 2715 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2414,a,2420,b)].
% 23.06/23.11 2716 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2429,a,2420,b)].
% 23.06/23.11 2717 -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(2430,a,2420,b)].
% 23.06/23.11 2718 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2431,a,2420,b)].
% 23.06/23.11 2719 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2432,a,2420,b)].
% 23.06/23.11 2720 -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(2433,a,2420,b)].
% 23.06/23.11 2721 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2434,a,2420,b)].
% 23.06/23.11 2722 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2435,a,2420,b)].
% 23.06/23.11 2723 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2436,a,2420,b)].
% 23.06/23.11 2724 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2437,a,2420,b)].
% 23.06/23.11 2725 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2438,a,2420,b)].
% 23.06/23.11 2726 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2439,a,2420,b)].
% 23.06/23.11 2727 -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(2440,a,2420,b)].
% 23.06/23.11 2728 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2441,a,2420,b)].
% 23.06/23.11 2729 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(2442,a,2420,b)].
% 23.06/23.11 2730 -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(2443,a,2420,b)].
% 23.31/23.32 2731 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2444,a,2420,b)].
% 23.31/23.32 2732 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2445,a,2420,b)].
% 23.31/23.32 2733 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2446,a,2420,b)].
% 23.31/23.32 2734 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(2447,a,2420,b)].
% 23.31/23.32 2735 -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].
% 23.31/23.32 2736 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 23.31/23.32 2737 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 23.31/23.32 2738 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 23.31/23.32 2739 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 23.31/23.32 2740 -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].
% 23.31/23.32 2741 -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].
% 23.31/23.32 2742 -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].
% 23.31/23.32 2743 -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].
% 23.31/23.32 2744 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 23.31/23.32 2745 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 23.31/23.32 2746 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(34,a,10,b)].
% 23.31/23.32 2747 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(35,a,10,b)].
% 23.31/23.32 2748 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(36,a,10,b)].
% 23.31/23.32 2749 -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(37,a,10,b)].
% 23.31/23.32 2750 -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(38,a,10,b)].
% 23.31/23.32 2751 -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(39,a,10,b)].
% 23.31/23.32 2752 -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(40,a,10,b)].
% 23.31/23.32 2753 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(41,a,10,b)].
% 23.31/23.32 2754 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(42,a,10,b)].
% 23.31/23.32 2755 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 23.31/23.32 2756 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 23.48/23.50 2757 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 23.48/23.50 2758 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 23.48/23.50 2759 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(307,a,279,b)].
% 23.48/23.50 2760 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(308,a,279,b)].
% 23.48/23.50 2761 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 23.48/23.50 2762 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 23.48/23.50 2763 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 23.48/23.50 2764 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 23.48/23.50 2765 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 23.48/23.50 2766 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1164,c,1136,b)].
% 23.48/23.50 2767 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1165,b,1136,b)].
% 23.48/23.50 2768 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1166,c,1136,b)].
% 23.48/23.50 2769 -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(1167,c,1136,b)].
% 23.48/23.50 2770 -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(1168,c,1136,b)].
% 23.48/23.50 2771 -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(1169,c,1136,b)].
% 23.48/23.50 2772 -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(1170,c,1136,b)].
% 23.48/23.50 2773 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1171,c,1136,b)].
% 23.48/23.50 2774 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(1172,b,1136,b)].
% 23.48/23.50 2775 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1340,c,1312,b)].
% 23.48/23.50 2776 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1341,c,1312,b)].
% 23.48/23.50 2777 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 23.48/23.50 2778 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1362,a,1348,b)].
% 23.48/23.50 2779 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1363,a,1348,b)].
% 23.48/23.50 2780 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1364,a,1348,b)].
% 23.48/23.50 2781 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1365,a,1348,b)].
% 23.48/23.50 2782 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1366,a,1348,b)].
% 23.48/23.50 2783 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1367,a,1348,b)].
% 23.48/23.50 2784 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1368,a,1348,b)].
% 23.48/23.50 2785 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1369,a,1348,b)].
% 23.60/23.67 2786 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 23.60/23.67 2787 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 23.60/23.67 2788 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 23.60/23.67 2789 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1389,c,1348,b)].
% 23.60/23.67 2790 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1390,b,1348,b)].
% 23.60/23.67 2791 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1391,c,1348,b)].
% 23.60/23.67 2792 -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(1392,c,1348,b)].
% 23.60/23.67 2793 -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(1393,c,1348,b)].
% 23.60/23.67 2794 -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(1394,c,1348,b)].
% 23.60/23.67 2795 -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(1395,c,1348,b)].
% 23.60/23.67 2796 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1396,c,1348,b)].
% 23.60/23.67 2797 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(1397,b,1348,b)].
% 23.60/23.67 2798 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1398,c,1348,b)].
% 23.60/23.67 2799 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1399,c,1348,b)].
% 23.60/23.67 2800 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 23.60/23.67 2801 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 23.60/23.67 2802 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2233,a,2227,b)].
% 23.60/23.67 2803 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2234,a,2227,b)].
% 23.60/23.67 2804 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2235,a,2227,b)].
% 23.60/23.67 2805 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2236,a,2227,b)].
% 23.60/23.67 2806 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2237,a,2227,b)].
% 23.60/23.67 2807 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2238,a,2227,b)].
% 23.60/23.67 2808 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2239,a,2227,b)].
% 23.60/23.67 2809 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2240,a,2227,b)].
% 23.60/23.67 2810 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 23.60/23.67 2811 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2242,a,2227,b)].
% 23.60/23.67 2812 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2243,a,2227,b)].
% 23.60/23.67 2813 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 23.67/23.73 2814 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2245,a,2227,b)].
% 23.67/23.73 2815 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 23.67/23.73 2816 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2247,a,2227,b)].
% 23.67/23.73 2817 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2248,a,2227,b)].
% 23.67/23.73 2818 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2249,a,2227,b)].
% 23.67/23.73 2819 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2250,a,2227,b)].
% 23.67/23.73 2820 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2251,a,2227,b)].
% 23.67/23.73 2821 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 23.67/23.73 2822 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2414,a,2419,b)].
% 23.67/23.73 2823 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2429,a,2419,b)].
% 23.67/23.73 2824 -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(2430,a,2419,b)].
% 23.67/23.73 2825 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2431,a,2419,b)].
% 23.67/23.73 2826 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2432,a,2419,b)].
% 23.67/23.73 2827 -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(2433,a,2419,b)].
% 23.67/23.73 2828 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2434,a,2419,b)].
% 23.67/23.73 2829 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2435,a,2419,b)].
% 23.67/23.73 2830 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2436,a,2419,b)].
% 23.67/23.73 2831 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2437,a,2419,b)].
% 23.67/23.73 2832 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2438,a,2419,b)].
% 23.67/23.73 2833 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2439,a,2419,b)].
% 23.67/23.73 2834 -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(2440,a,2419,b)].
% 23.67/23.73 2835 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2441,a,2419,b)].
% 23.67/23.73 2836 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(2442,a,2419,b)].
% 23.67/23.73 2837 -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(2443,a,2419,b)].
% 23.67/23.73 2838 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2444,a,2419,b)].
% 23.67/23.73 2839 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2445,a,2419,b)].
% 23.67/23.73 2840 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2446,a,2419,b)].
% 23.91/23.94 2841 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(2447,a,2419,b)].
% 23.91/23.94 2842 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 23.91/23.94 2843 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 23.91/23.94 2844 -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].
% 23.91/23.94 2845 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 23.91/23.94 2846 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 23.91/23.94 2847 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 23.91/23.94 2848 -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].
% 23.91/23.94 2849 -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].
% 23.91/23.94 2850 -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].
% 23.91/23.94 2851 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 23.91/23.94 2852 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 23.91/23.94 2853 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(34,a,19,b)].
% 23.91/23.94 2854 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(35,a,19,b)].
% 23.91/23.94 2855 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(36,a,19,b)].
% 23.91/23.94 2856 -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(37,a,19,b)].
% 23.91/23.94 2857 -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(38,a,19,b)].
% 23.91/23.94 2858 -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(39,a,19,b)].
% 23.91/23.94 2859 -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(40,a,19,b)].
% 23.91/23.94 2860 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(41,a,19,b)].
% 23.91/23.94 2861 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(42,a,19,b)].
% 23.91/23.94 2862 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 23.91/23.94 2863 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 23.91/23.94 2864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 23.91/23.94 2865 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(108,b,85,b)].
% 23.91/23.94 2866 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(109,b,85,b)].
% 23.91/23.97 2867 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 23.91/23.97 2868 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 23.91/23.97 2869 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(221,c,198,b)].
% 23.91/23.97 2870 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(222,c,198,b)].
% 23.91/23.97 2871 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 23.91/23.97 2872 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 23.91/23.97 2873 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 23.91/23.97 2874 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 23.91/23.97 2875 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(307,a,292,b)].
% 23.91/23.97 2876 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(308,a,292,b)].
% 23.91/23.97 2877 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 23.91/23.97 2878 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 23.91/23.97 2879 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 23.91/23.97 2880 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 23.91/23.97 2881 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(389,c,361,b)].
% 23.91/23.97 2882 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(390,c,361,b)].
% 23.91/23.97 2883 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 23.91/23.97 2884 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 23.91/23.97 2885 -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(413,b,400,b)].
% 23.91/23.97 2886 -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(414,b,400,b)].
% 23.91/23.97 2887 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(415,a,400,b)].
% 23.91/23.97 2888 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(416,a,400,b)].
% 23.91/23.97 2889 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(417,a,400,b)].
% 23.91/23.97 2890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 23.91/23.97 2891 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(428,c,400,b)].
% 23.91/23.97 2892 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(429,c,400,b)].
% 23.91/23.97 2893 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 23.91/23.97 2894 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 23.91/23.97 2895 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 24.09/24.12 2896 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 24.09/24.12 2897 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 24.09/24.12 2898 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(442,c,400,b)].
% 24.09/24.12 2899 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(443,c,400,b)].
% 24.09/24.12 2900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 24.09/24.12 2901 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 24.09/24.12 2902 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 24.09/24.12 2903 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 24.09/24.12 2904 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 24.09/24.12 2905 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1164,c,1140,b)].
% 24.09/24.12 2906 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1165,b,1140,b)].
% 24.09/24.12 2907 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1166,c,1140,b)].
% 24.09/24.12 2908 -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(1167,c,1140,b)].
% 24.09/24.12 2909 -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(1168,c,1140,b)].
% 24.09/24.12 2910 -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(1169,c,1140,b)].
% 24.09/24.12 2911 -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(1170,c,1140,b)].
% 24.09/24.12 2912 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1171,c,1140,b)].
% 24.09/24.12 2913 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(1172,b,1140,b)].
% 24.09/24.12 2914 -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(1362,a,1354,b)].
% 24.09/24.12 2915 -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(1363,a,1354,b)].
% 24.09/24.12 2916 -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(1364,a,1354,b)].
% 24.09/24.12 2917 -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(1365,a,1354,b)].
% 24.09/24.12 2918 -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(1366,a,1354,b)].
% 24.09/24.12 2919 -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(1367,a,1354,b)].
% 24.09/24.12 2920 -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(1368,a,1354,b)].
% 24.09/24.12 2921 -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(1369,a,1354,b)].
% 24.09/24.12 2922 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 24.09/24.12 2923 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 24.09/24.12 2924 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 24.09/24.12 2925 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1389,c,1354,b)].
% 24.21/24.27 2926 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1390,b,1354,b)].
% 24.21/24.27 2927 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1391,c,1354,b)].
% 24.21/24.27 2928 -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(1392,c,1354,b)].
% 24.21/24.27 2929 -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(1393,c,1354,b)].
% 24.21/24.27 2930 -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(1394,c,1354,b)].
% 24.21/24.27 2931 -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(1395,c,1354,b)].
% 24.21/24.27 2932 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1396,c,1354,b)].
% 24.21/24.27 2933 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(1397,b,1354,b)].
% 24.21/24.27 2934 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1398,c,1354,b)].
% 24.21/24.27 2935 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1399,c,1354,b)].
% 24.21/24.27 2936 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 24.21/24.27 2937 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 24.21/24.27 2938 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1633,c,1585,b)].
% 24.21/24.27 2939 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1634,b,1585,b)].
% 24.21/24.27 2940 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1635,c,1585,b)].
% 24.21/24.27 2941 -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(1636,c,1585,b)].
% 24.21/24.27 2942 -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(1637,c,1585,b)].
% 24.21/24.27 2943 -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(1638,c,1585,b)].
% 24.21/24.27 2944 -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(1639,c,1585,b)].
% 24.21/24.27 2945 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1640,c,1585,b)].
% 24.21/24.27 2946 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(1641,b,1585,b)].
% 24.21/24.27 2947 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 24.21/24.27 2948 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(1643,c,1585,b)].
% 24.21/24.27 2949 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(1644,c,1585,b)].
% 24.21/24.27 2950 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 24.21/24.27 2951 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 24.21/24.27 2952 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 24.21/24.29 2953 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2233,a,2229,b)].
% 24.21/24.29 2954 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2234,a,2229,b)].
% 24.21/24.29 2955 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2235,a,2229,b)].
% 24.21/24.29 2956 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2236,a,2229,b)].
% 24.21/24.29 2957 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2237,a,2229,b)].
% 24.21/24.29 2958 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2238,a,2229,b)].
% 24.21/24.29 2959 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2239,a,2229,b)].
% 24.21/24.29 2960 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2240,a,2229,b)].
% 24.21/24.29 2961 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 24.21/24.29 2962 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2242,a,2229,b)].
% 24.21/24.29 2963 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2243,a,2229,b)].
% 24.21/24.29 2964 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 24.21/24.29 2965 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2245,a,2229,b)].
% 24.21/24.29 2966 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 24.21/24.29 2967 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2247,a,2229,b)].
% 24.21/24.29 2968 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2248,a,2229,b)].
% 24.21/24.29 2969 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2249,a,2229,b)].
% 24.21/24.29 2970 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2250,a,2229,b)].
% 24.21/24.29 2971 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2251,a,2229,b)].
% 24.21/24.29 2972 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 24.21/24.29 2973 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 24.21/24.29 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2973,b,2843,a)].
% 24.21/24.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2973,b,2848,b)].
% 24.21/24.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 24.21/24.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 24.21/24.29 2974 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 24.21/24.29 2975 -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(2357,c,2314,b)].
% 24.21/24.29 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(2975,c,2843,a)].
% 24.21/24.29 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(2975,c,2848,b)].
% 24.21/24.29 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(2975,c,2849,b)].
% 24.21/24.29 2976 -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(2358,c,2314,b)].
% 24.21/24.29 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(2976,c,2843,a)].
% 24.21/24.29 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(2976,c,2848,b)].
% 24.21/24.29 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(2976,c,2849,b)].
% 24.21/24.29 2977 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2359,b,2314,b)].
% 24.21/24.29 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(2977,b,2843,a)].
% 24.21/24.29 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(2977,b,2848,b)].
% 24.21/24.29 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(2977,b,2849,b)].
% 24.21/24.29 2978 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2360,b,2314,b)].
% 24.21/24.29 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(2978,b,2843,a)].
% 24.21/24.29 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(2978,b,2848,b)].
% 24.21/24.29 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(2978,b,2849,b)].
% 24.21/24.29 2979 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2361,b,2314,b)].
% 24.21/24.29 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(2979,b,2843,a)].
% 24.21/24.29 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(2979,b,2848,b)].
% 24.21/24.29 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(2979,b,2849,b)].
% 24.21/24.29 2980 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 24.21/24.29 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2980,b,2843,a)].
% 24.21/24.29 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2980,b,2848,b)].
% 24.21/24.29 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 24.21/24.29 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 24.21/24.29 2981 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 24.21/24.29 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2981,b,2843,a)].
% 24.21/24.29 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2981,b,2848,b)].
% 24.21/24.29 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 24.21/24.30 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 24.21/24.30 2982 -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(2374,c,2314,b)].
% 24.21/24.30 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(2982,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2982,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2982,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2982,c,2850,b)].
% 24.21/24.30 2983 -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(2375,c,2314,b)].
% 24.21/24.30 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(2983,c,2843,a)].
% 24.21/24.30 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(2983,c,2848,b)].
% 24.21/24.30 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(2983,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2983,c,2850,b)].
% 24.21/24.30 2984 -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(2376,c,2314,b)].
% 24.21/24.30 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(2984,c,2843,a)].
% 24.21/24.30 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(2984,c,2848,b)].
% 24.21/24.30 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(2984,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2984,c,2850,b)].
% 24.21/24.30 2985 -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(2377,c,2314,b)].
% 24.21/24.30 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(2985,c,2843,a)].
% 24.21/24.30 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(2985,c,2848,b)].
% 24.21/24.30 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(2985,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2985,c,2850,b)].
% 24.21/24.30 2986 -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(2378,c,2314,b)].
% 24.21/24.30 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(2986,c,2843,a)].
% 24.21/24.30 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(2986,c,2848,b)].
% 24.21/24.30 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(2986,c,2849,b)].
% 24.21/24.30 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2986,c,2850,b)].
% 24.21/24.30 2987 -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(2379,c,2314,b)].
% 24.21/24.30 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(2987,c,2843,a)].
% 24.21/24.30 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(2987,c,2848,b)].
% 24.21/24.30 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(2987,c,2849,b)].
% 24.21/24.30 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2987,c,2850,b)].
% 24.21/24.30 2988 -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(2380,c,2314,b)].
% 24.21/24.30 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(2988,c,2843,a)].
% 24.21/24.30 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(2988,c,2848,b)].
% 24.21/24.30 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(2988,c,2849,b)].
% 24.21/24.30 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2988,c,2850,b)].
% 24.21/24.30 2989 -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(2381,c,2314,b)].
% 24.21/24.30 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(2989,c,2843,a)].
% 24.21/24.30 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(2989,c,2848,b)].
% 24.21/24.30 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(2989,c,2849,b)].
% 24.21/24.30 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2989,c,2850,b)].
% 24.21/24.30 2990 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 24.21/24.30 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(2990,b,2843,a)].
% 24.21/24.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2990,b,2848,b)].
% 24.21/24.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 24.21/24.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 24.21/24.30 2991 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2395,c,2314,b)].
% 24.21/24.30 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2991,c,2843,a)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2991,c,2848,b)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2991,c,2849,b)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2991,c,2850,b)].
% 24.21/24.30 2992 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2396,c,2314,b)].
% 24.21/24.30 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2992,c,2843,a)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2992,c,2848,b)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2992,c,2849,b)].
% 24.21/24.30 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2992,c,2850,b)].
% 24.21/24.30 2993 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 24.21/24.30 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2993,b,2843,a)].
% 24.21/24.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2993,b,2848,b)].
% 24.21/24.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 24.21/24.30 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 24.21/24.30 2994 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 24.21/24.30 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2994,b,2843,a)].
% 24.21/24.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2994,b,2848,b)].
% 24.21/24.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 24.21/24.30 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 24.21/24.30 2995 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2399,c,2314,b)].
% 24.21/24.30 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2995,c,2843,a)].
% 24.21/24.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2995,c,2848,b)].
% 24.21/24.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2995,c,2849,b)].
% 24.21/24.30 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2995,c,2850,b)].
% 24.21/24.30 2996 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2400,b,2314,b)].
% 24.21/24.30 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2996,b,2843,a)].
% 24.21/24.30 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2996,b,2848,b)].
% 24.21/24.30 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2996,b,2849,b)].
% 24.21/24.30 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2996,b,2850,b)].
% 24.21/24.30 2997 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2401,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2997,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2997,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2997,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2997,c,2850,b)].
% 24.21/24.30 2998 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2402,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2998,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2998,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2998,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2998,c,2850,b)].
% 24.21/24.30 2999 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2403,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2999,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2999,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2999,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2999,c,2850,b)].
% 24.21/24.30 3000 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2404,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3000,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3000,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3000,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3000,c,2850,b)].
% 24.21/24.30 3001 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2405,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3001,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3001,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3001,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3001,c,2850,b)].
% 24.21/24.30 3002 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2406,c,2314,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3002,c,2843,a)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(3002,c,2848,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3002,c,2849,b)].
% 24.21/24.30 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3002,c,2850,b)].
% 24.21/24.30 3003 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2407,b,2314,b)].
% 24.21/24.30 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3003,b,2843,a)].
% 24.21/24.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3003,b,2848,b)].
% 24.21/24.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3003,b,2849,b)].
% 24.21/24.30 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3003,b,2850,b)].
% 24.21/24.30 3004 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 24.21/24.30 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3004,b,2843,a)].
% 24.31/24.31 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3004,b,2848,b)].
% 24.31/24.31 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 24.31/24.31 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 24.31/24.31 3005 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(2409,c,2314,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3005,c,2843,a)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3005,c,2848,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3005,c,2849,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3005,c,2850,b)].
% 24.31/24.31 3006 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(2410,c,2314,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3006,c,2843,a)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3006,c,2848,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3006,c,2849,b)].
% 24.31/24.31 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3006,c,2850,b)].
% 24.31/24.31 3007 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 24.31/24.31 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3007,b,2843,a)].
% 24.31/24.31 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3007,b,2848,b)].
% 24.31/24.31 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 24.31/24.31 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 24.31/24.31 3008 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 24.31/24.31 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3008,b,2843,a)].
% 24.31/24.31 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3008,b,2848,b)].
% 24.31/24.31 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 24.31/24.31 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 24.31/24.31 3009 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2414,a,2422,b)].
% 24.31/24.35 3010 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2429,a,2422,b)].
% 24.31/24.35 3011 -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(2430,a,2422,b)].
% 24.31/24.35 3012 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2431,a,2422,b)].
% 24.31/24.35 3013 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2432,a,2422,b)].
% 24.31/24.35 3014 -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(2433,a,2422,b)].
% 24.31/24.35 3015 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2434,a,2422,b)].
% 24.31/24.35 3016 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2435,a,2422,b)].
% 24.31/24.35 3017 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2436,a,2422,b)].
% 24.31/24.35 3018 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2437,a,2422,b)].
% 24.31/24.35 3019 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2438,a,2422,b)].
% 24.31/24.35 3020 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2439,a,2422,b)].
% 24.31/24.35 3021 -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(2440,a,2422,b)].
% 24.31/24.35 3022 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2441,a,2422,b)].
% 24.31/24.35 3023 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2442,a,2422,b)].
% 24.31/24.35 3024 -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(2443,a,2422,b)].
% 24.31/24.35 3025 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2444,a,2422,b)].
% 24.31/24.35 3026 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2445,a,2422,b)].
% 24.31/24.35 3027 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2446,a,2422,b)].
% 24.31/24.35 3028 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2447,a,2422,b)].
% 24.31/24.35 3029 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 24.31/24.35 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3029,c,2843,a)].
% 24.31/24.35 3030 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 24.31/24.35 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3030,b,2843,a)].
% 24.31/24.35 3031 c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2519,a,2513,b)].
% 24.31/24.35 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(3031,b,2843,a)].
% 24.31/24.35 3032 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 24.31/24.35 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3032,c,2843,a)].
% 24.31/24.35 3033 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 24.31/24.35 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3033,b,2843,a)].
% 24.31/24.35 3034 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 25.02/25.08 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3034,b,2843,a)].
% 25.02/25.08 3035 c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2523,a,2513,b)].
% 25.02/25.08 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3035,b,2843,a)].
% 25.02/25.08 3036 -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2524,a,2513,b)].
% 25.02/25.08 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3036,c,2843,a)].
% 25.02/25.08 3037 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 25.02/25.08 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3037,b,2843,a)].
% 25.02/25.08 3038 c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2526,a,2513,b)].
% 25.02/25.08 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3038,b,2843,a)].
% 25.02/25.08 3039 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 25.02/25.08 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3039,b,2843,a)].
% 25.02/25.08 3040 -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2528,a,2513,b)].
% 25.02/25.08 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3040,c,2843,a)].
% 25.02/25.08 3041 -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2529,a,2513,b)].
% 25.02/25.08 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3041,c,2843,a)].
% 25.02/25.08 3042 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 25.02/25.08 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3042,b,2843,a)].
% 25.02/25.08 3043 c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2531,a,2513,b)].
% 25.02/25.08 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3043,c,2843,a)].
% 25.02/25.08 3044 -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].
% 25.02/25.08 3045 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 25.02/25.08 3046 -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].
% 25.02/25.08 3047 -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].
% 25.02/25.08 3048 -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].
% 25.02/25.08 3049 -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].
% 25.02/25.08 3050 -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].
% 25.02/25.08 3051 -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].
% 25.02/25.08 3052 -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].
% 25.02/25.08 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(3052,b,3045,a)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3052,b,3046,b)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3052,b,3047,b)].
% 25.02/25.09 3053 -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].
% 25.02/25.09 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(3053,b,3045,a)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3053,b,3046,b)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3053,b,3047,b)].
% 25.02/25.09 3054 -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].
% 25.02/25.09 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(3054,b,3045,a)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3054,b,3046,b)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3054,b,3047,b)].
% 25.02/25.09 3055 -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].
% 25.02/25.09 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(3055,b,3045,a)].
% 25.02/25.09 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3055,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3055,b,3047,b)].
% 25.02/25.10 3056 -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].
% 25.02/25.10 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(3056,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3056,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3056,b,3047,b)].
% 25.02/25.10 3057 -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].
% 25.02/25.10 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(3057,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3057,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3057,b,3047,b)].
% 25.02/25.10 3058 -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].
% 25.02/25.10 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(3058,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3058,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3058,b,3047,b)].
% 25.02/25.10 3059 -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].
% 25.02/25.10 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(3059,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3059,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3059,b,3047,b)].
% 25.02/25.10 3060 -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].
% 25.02/25.10 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(3060,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3060,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3060,b,3047,b)].
% 25.02/25.10 3061 -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].
% 25.02/25.10 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(3061,b,3045,a)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3061,b,3046,b)].
% 25.02/25.10 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3061,b,3047,b)].
% 25.02/25.10 3062 -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].
% 25.02/25.11 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(3062,b,3045,a)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3062,b,3046,b)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3062,b,3047,b)].
% 25.02/25.11 3063 -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].
% 25.02/25.11 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(3063,b,3045,a)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3063,b,3046,b)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3063,b,3047,b)].
% 25.02/25.11 3064 -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].
% 25.02/25.11 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(3064,b,3045,a)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3064,b,3046,b)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3064,b,3047,b)].
% 25.02/25.11 3065 -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].
% 25.02/25.11 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(3065,b,3045,a)].
% 25.02/25.11 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3065,b,3046,b)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3065,b,3047,b)].
% 25.12/25.12 3066 -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].
% 25.12/25.12 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(3066,b,3045,a)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3066,b,3046,b)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3066,b,3047,b)].
% 25.12/25.12 3067 -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].
% 25.12/25.12 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(3067,b,3045,a)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3067,b,3046,b)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3067,b,3047,b)].
% 25.12/25.12 3068 -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].
% 25.12/25.12 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(3068,b,3045,a)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3068,b,3046,b)].
% 25.12/25.12 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3068,b,3047,b)].
% 25.12/25.13 3069 -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].
% 25.12/25.13 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(3069,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3069,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3069,b,3047,b)].
% 25.12/25.13 3070 -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].
% 25.12/25.13 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(3070,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3070,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3070,b,3047,b)].
% 25.12/25.13 3071 -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].
% 25.12/25.13 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(3071,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3071,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3071,b,3047,b)].
% 25.12/25.13 3072 -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].
% 25.12/25.13 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(3072,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3072,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3072,b,3047,b)].
% 25.12/25.13 3073 -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].
% 25.12/25.13 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(3073,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3073,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3073,b,3047,b)].
% 25.12/25.13 3074 -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].
% 25.12/25.13 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(3074,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3074,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3074,b,3047,b)].
% 25.12/25.13 3075 -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].
% 25.12/25.13 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(3075,b,3045,a)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3075,b,3046,b)].
% 25.12/25.13 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3075,b,3047,b)].
% 25.20/25.20 3076 -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].
% 25.20/25.20 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(3076,a,3045,a)].
% 25.20/25.20 Derived: c_times(A,B,C) != c_0 | B = c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(C). [resolve(3076,a,3046,b)].
% 25.20/25.20 Derived: c_times(A,B,C) != c_0 | B = c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(C). [resolve(3076,a,3047,b)].
% 25.20/25.20 3077 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 25.20/25.20 3078 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 25.20/25.20 3079 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(34,a,23,b)].
% 25.20/25.20 3080 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(35,a,23,b)].
% 25.20/25.20 3081 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(36,a,23,b)].
% 25.20/25.20 3082 -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__ring__strict(B). [resolve(37,a,23,b)].
% 25.20/25.20 3083 -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__ring__strict(C). [resolve(38,a,23,b)].
% 25.20/25.20 3084 -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__ring__strict(B). [resolve(39,a,23,b)].
% 25.20/25.20 3085 -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__ring__strict(C). [resolve(40,a,23,b)].
% 25.20/25.20 3086 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(41,a,23,b)].
% 25.20/25.20 3087 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__ring__strict(B). [resolve(42,a,23,b)].
% 25.20/25.20 3088 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 25.20/25.20 3089 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 25.20/25.20 3090 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 25.20/25.20 3091 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(108,b,89,b)].
% 25.20/25.20 3092 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(109,b,89,b)].
% 25.20/25.20 3093 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 25.20/25.20 3094 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 25.20/25.20 3095 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(221,c,202,b)].
% 25.20/25.20 3096 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(222,c,202,b)].
% 25.20/25.20 3097 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 25.28/25.29 3098 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 25.28/25.29 3099 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 25.28/25.29 3100 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 25.28/25.29 3101 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(307,a,296,b)].
% 25.28/25.29 3102 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(308,a,296,b)].
% 25.28/25.29 3103 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 25.28/25.29 3104 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 25.28/25.29 3105 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 25.28/25.29 3106 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 25.28/25.29 3107 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(389,c,365,b)].
% 25.28/25.29 3108 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(390,c,365,b)].
% 25.28/25.29 3109 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 25.28/25.29 3110 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 25.28/25.29 3111 -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__ring__strict(A). [resolve(413,b,403,b)].
% 25.28/25.29 3112 -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__ring__strict(A). [resolve(414,b,403,b)].
% 25.28/25.29 3113 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(415,a,403,b)].
% 25.28/25.29 3114 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(416,a,403,b)].
% 25.28/25.29 3115 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(417,a,403,b)].
% 25.28/25.29 3116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 25.28/25.29 3117 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(428,c,403,b)].
% 25.28/25.29 3118 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(429,c,403,b)].
% 25.28/25.29 3119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 25.28/25.29 3120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 25.28/25.29 3121 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 25.28/25.29 3122 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 25.28/25.29 3123 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 25.28/25.29 3124 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(442,c,403,b)].
% 25.28/25.29 3125 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(443,c,403,b)].
% 25.28/25.29 3126 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 25.28/25.29 3127 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 25.33/25.32 3128 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 25.33/25.32 3129 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 25.33/25.32 3130 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 25.33/25.32 3131 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1164,c,1144,b)].
% 25.33/25.32 3132 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1165,b,1144,b)].
% 25.33/25.32 3133 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1166,c,1144,b)].
% 25.33/25.32 3134 -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__ring__strict(B). [resolve(1167,c,1144,b)].
% 25.33/25.32 3135 -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__ring__strict(C). [resolve(1168,c,1144,b)].
% 25.33/25.32 3136 -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__ring__strict(B). [resolve(1169,c,1144,b)].
% 25.33/25.32 3137 -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__ring__strict(C). [resolve(1170,c,1144,b)].
% 25.33/25.32 3138 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1171,c,1144,b)].
% 25.33/25.32 3139 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__ring__strict(B). [resolve(1172,b,1144,b)].
% 25.33/25.32 3140 -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__ring__strict(C). [resolve(1185,a,1181,b)].
% 25.33/25.32 3141 -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__ring__strict(B). [resolve(1186,a,1181,b)].
% 25.33/25.32 3142 -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__ring__strict(B). [resolve(1187,a,1181,b)].
% 25.33/25.32 3143 -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__ring__strict(C). [resolve(1188,a,1181,b)].
% 25.33/25.32 3144 -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__ring__strict(B). [resolve(1189,a,1181,b)].
% 25.33/25.32 3145 -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__ring__strict(B). [resolve(1190,a,1181,b)].
% 25.33/25.32 3146 -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__ring__strict(C). [resolve(1191,a,1181,b)].
% 25.33/25.32 3147 -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__ring__strict(B). [resolve(1192,a,1181,b)].
% 25.33/25.32 3148 -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__ring__strict(B). [resolve(1193,a,1181,b)].
% 25.33/25.32 3149 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1194,a,1181,b)].
% 25.33/25.32 3150 -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__ring__strict(C). [resolve(1195,a,1181,b)].
% 25.35/25.35 3151 -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__ring__strict(B). [resolve(1196,a,1181,b)].
% 25.35/25.35 3152 -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__ring__strict(B). [resolve(1197,a,1181,b)].
% 25.35/25.35 3153 -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__ring__strict(C). [resolve(1198,a,1181,b)].
% 25.35/25.35 3154 -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__ring__strict(B). [resolve(1199,a,1181,b)].
% 25.35/25.35 3155 -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__ring__strict(B). [resolve(1200,a,1181,b)].
% 25.35/25.35 3156 -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__ring__strict(B). [resolve(1201,a,1181,b)].
% 25.35/25.35 3157 -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__ring__strict(B). [resolve(1202,a,1181,b)].
% 25.35/25.35 3158 -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__ring__strict(C). [resolve(1203,a,1181,b)].
% 25.35/25.35 3159 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1204,a,1181,b)].
% 25.35/25.35 3160 -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__ring__strict(B). [resolve(1205,a,1181,b)].
% 25.35/25.35 3161 -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__ring__strict(C). [resolve(1206,a,1181,b)].
% 25.35/25.35 3162 -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__ring__strict(C). [resolve(1207,a,1181,b)].
% 25.35/25.35 3163 -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__ring__strict(A). [resolve(1208,b,1181,b)].
% 25.35/25.35 3164 -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__ring__strict(A). [resolve(1209,b,1181,b)].
% 25.35/25.35 3165 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1210,a,1181,b)].
% 25.35/25.35 3166 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1211,a,1181,b)].
% 25.35/25.35 3167 -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__ring__strict(C). [resolve(1212,a,1181,b)].
% 25.35/25.35 3168 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1213,a,1181,b)].
% 25.35/25.35 3169 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1214,a,1181,b)].
% 25.35/25.35 3170 -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__ring__strict(C). [resolve(1215,a,1181,b)].
% 25.35/25.35 3171 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1216,a,1181,b)].
% 25.35/25.35 3172 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1217,a,1181,b)].
% 25.35/25.38 3173 -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__ring__strict(C). [resolve(1218,a,1181,b)].
% 25.35/25.38 3174 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 25.35/25.38 3175 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1220,a,1181,b)].
% 25.35/25.38 3176 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1221,a,1181,b)].
% 25.35/25.38 3177 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1222,a,1181,b)].
% 25.35/25.38 3178 -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__ring__strict(C). [resolve(1223,a,1181,b)].
% 25.35/25.38 3179 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 25.35/25.38 3180 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1225,a,1181,b)].
% 25.35/25.38 3181 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1226,a,1181,b)].
% 25.35/25.38 3182 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1227,a,1181,b)].
% 25.35/25.38 3183 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1228,a,1181,b)].
% 25.35/25.38 3184 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1229,a,1181,b)].
% 25.35/25.38 3185 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1230,a,1181,b)].
% 25.35/25.38 3186 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1231,a,1181,b)].
% 25.35/25.38 3187 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1232,a,1181,b)].
% 25.35/25.38 3188 -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__ring__strict(B). [resolve(1233,a,1181,b)].
% 25.35/25.38 3189 -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__ring__strict(C). [resolve(1234,a,1181,b)].
% 25.35/25.38 3190 -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__ring__strict(C). [resolve(1235,a,1181,b)].
% 25.35/25.38 3191 -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__ring__strict(C). [resolve(1236,a,1181,b)].
% 25.35/25.38 3192 -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__ring__strict(C). [resolve(1237,a,1181,b)].
% 25.35/25.38 3193 -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__ring__strict(C). [resolve(1238,a,1181,b)].
% 25.35/25.38 3194 -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__ring__strict(C). [resolve(1239,a,1181,b)].
% 25.35/25.38 3195 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1240,a,1181,b)].
% 25.43/25.44 3196 -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__ring__strict(B). [resolve(1241,a,1181,b)].
% 25.43/25.44 3197 -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__ring__strict(C). [resolve(1242,a,1181,b)].
% 25.43/25.44 3198 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1362,a,1358,b)].
% 25.43/25.44 3199 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1363,a,1358,b)].
% 25.43/25.44 3200 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1364,a,1358,b)].
% 25.43/25.44 3201 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1365,a,1358,b)].
% 25.43/25.44 3202 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1366,a,1358,b)].
% 25.43/25.44 3203 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1367,a,1358,b)].
% 25.43/25.44 3204 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1368,a,1358,b)].
% 25.43/25.44 3205 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1369,a,1358,b)].
% 25.43/25.44 3206 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 25.43/25.44 3207 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 25.43/25.44 3208 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 25.43/25.44 3209 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1389,c,1358,b)].
% 25.43/25.44 3210 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1390,b,1358,b)].
% 25.43/25.44 3211 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1391,c,1358,b)].
% 25.43/25.44 3212 -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__ring__strict(B). [resolve(1392,c,1358,b)].
% 25.43/25.44 3213 -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__ring__strict(C). [resolve(1393,c,1358,b)].
% 25.43/25.44 3214 -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__ring__strict(B). [resolve(1394,c,1358,b)].
% 25.43/25.44 3215 -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__ring__strict(C). [resolve(1395,c,1358,b)].
% 25.43/25.44 3216 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1396,c,1358,b)].
% 25.43/25.44 3217 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__ring__strict(B). [resolve(1397,b,1358,b)].
% 25.43/25.44 3218 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1398,c,1358,b)].
% 25.43/25.44 3219 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1399,c,1358,b)].
% 25.43/25.44 3220 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 25.43/25.44 3221 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 25.43/25.44 3222 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 25.43/25.44 3223 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 25.43/25.46 3224 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 25.43/25.46 3225 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1633,c,1589,b)].
% 25.43/25.46 3226 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1634,b,1589,b)].
% 25.43/25.46 3227 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1635,c,1589,b)].
% 25.43/25.46 3228 -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__ring__strict(B). [resolve(1636,c,1589,b)].
% 25.43/25.46 3229 -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__ring__strict(C). [resolve(1637,c,1589,b)].
% 25.43/25.46 3230 -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__ring__strict(B). [resolve(1638,c,1589,b)].
% 25.43/25.46 3231 -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__ring__strict(C). [resolve(1639,c,1589,b)].
% 25.43/25.46 3232 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1640,c,1589,b)].
% 25.43/25.46 3233 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__ring__strict(B). [resolve(1641,b,1589,b)].
% 25.43/25.46 3234 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 25.43/25.46 3235 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1643,c,1589,b)].
% 25.43/25.46 3236 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1644,c,1589,b)].
% 25.43/25.46 3237 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 25.43/25.46 3238 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 25.43/25.46 3239 -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__ring__strict(C). [resolve(1706,e,1654,b)].
% 25.43/25.46 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(3239,e,3046,b)].
% 25.43/25.46 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(3239,e,3047,b)].
% 25.43/25.46 3240 -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__ring__strict(B). [resolve(1707,d,1654,b)].
% 25.43/25.46 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(3240,d,3046,b)].
% 25.43/25.46 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(3240,d,3047,b)].
% 25.43/25.46 3241 -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__ring__strict(B). [resolve(1708,d,1654,b)].
% 25.43/25.46 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(3241,d,3046,b)].
% 25.43/25.47 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(3241,d,3047,b)].
% 25.43/25.47 3242 -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__ring__strict(C). [resolve(1709,f,1654,b)].
% 25.43/25.47 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(3242,f,3046,b)].
% 25.43/25.47 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(3242,f,3047,b)].
% 25.43/25.47 3243 -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__ring__strict(B). [resolve(1710,e,1654,b)].
% 25.43/25.47 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(3243,e,3046,b)].
% 25.43/25.47 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(3243,e,3047,b)].
% 25.43/25.47 3244 -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__ring__strict(B). [resolve(1711,e,1654,b)].
% 25.43/25.47 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(3244,e,3046,b)].
% 25.43/25.47 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(3244,e,3047,b)].
% 25.43/25.47 3245 -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__ring__strict(C). [resolve(1712,f,1654,b)].
% 25.43/25.47 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(3245,f,3046,b)].
% 25.43/25.47 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(3245,f,3047,b)].
% 25.43/25.47 3246 -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__ring__strict(B). [resolve(1713,e,1654,b)].
% 25.43/25.47 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(3246,e,3046,b)].
% 25.43/25.47 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(3246,e,3047,b)].
% 25.43/25.47 3247 -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__ring__strict(B). [resolve(1714,e,1654,b)].
% 25.43/25.47 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(3247,e,3046,b)].
% 25.49/25.48 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(3247,e,3047,b)].
% 25.49/25.48 3248 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1715,b,1654,b)].
% 25.49/25.48 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3248,b,3046,b)].
% 25.49/25.48 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3248,b,3047,b)].
% 25.49/25.48 3249 -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__ring__strict(C). [resolve(1716,f,1654,b)].
% 25.49/25.48 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(3249,f,3046,b)].
% 25.49/25.48 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(3249,f,3047,b)].
% 25.49/25.48 3250 -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__ring__strict(B). [resolve(1717,e,1654,b)].
% 25.49/25.48 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(3250,e,3046,b)].
% 25.49/25.48 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(3250,e,3047,b)].
% 25.49/25.48 3251 -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__ring__strict(B). [resolve(1718,e,1654,b)].
% 25.49/25.48 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(3251,e,3046,b)].
% 25.49/25.48 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(3251,e,3047,b)].
% 25.49/25.48 3252 -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__ring__strict(C). [resolve(1719,f,1654,b)].
% 25.49/25.48 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(3252,f,3046,b)].
% 25.49/25.48 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(3252,f,3047,b)].
% 25.49/25.48 3253 -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__ring__strict(B). [resolve(1720,e,1654,b)].
% 25.49/25.48 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(3253,e,3046,b)].
% 25.49/25.48 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(3253,e,3047,b)].
% 25.49/25.48 3254 -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__ring__strict(B). [resolve(1721,e,1654,b)].
% 25.49/25.49 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__field(B). [resolve(3254,e,3046,b)].
% 25.49/25.49 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__idom(B). [resolve(3254,e,3047,b)].
% 25.49/25.49 3255 -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__ring__strict(B). [resolve(1722,d,1654,b)].
% 25.49/25.49 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__field(B). [resolve(3255,d,3046,b)].
% 25.49/25.49 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__idom(B). [resolve(3255,d,3047,b)].
% 25.49/25.49 3256 -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__ring__strict(B). [resolve(1723,d,1654,b)].
% 25.49/25.49 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__field(B). [resolve(3256,d,3046,b)].
% 25.49/25.49 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__idom(B). [resolve(3256,d,3047,b)].
% 25.49/25.49 3257 -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__ring__strict(C). [resolve(1724,e,1654,b)].
% 25.49/25.49 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__field(C). [resolve(3257,e,3046,b)].
% 25.49/25.49 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__idom(C). [resolve(3257,e,3047,b)].
% 25.49/25.49 3258 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1725,b,1654,b)].
% 25.49/25.49 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3258,b,3046,b)].
% 25.49/25.49 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3258,b,3047,b)].
% 25.49/25.49 3259 -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__ring__strict(B). [resolve(1726,d,1654,b)].
% 25.49/25.49 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__field(B). [resolve(3259,d,3046,b)].
% 25.49/25.49 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__idom(B). [resolve(3259,d,3047,b)].
% 25.49/25.49 3260 -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__ring__strict(C). [resolve(1727,e,1654,b)].
% 25.49/25.49 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__field(C). [resolve(3260,e,3046,b)].
% 25.49/25.49 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__idom(C). [resolve(3260,e,3047,b)].
% 25.49/25.49 3261 -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__ring__strict(C). [resolve(1728,e,1654,b)].
% 25.49/25.50 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(3261,e,3046,b)].
% 25.49/25.50 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(3261,e,3047,b)].
% 25.49/25.50 3262 -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__ring__strict(A). [resolve(1729,d,1654,b)].
% 25.49/25.50 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(3262,d,3046,b)].
% 25.49/25.50 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(3262,d,3047,b)].
% 25.49/25.50 3263 -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__ring__strict(A). [resolve(1730,d,1654,b)].
% 25.49/25.50 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(3263,d,3046,b)].
% 25.49/25.50 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(3263,d,3047,b)].
% 25.49/25.50 3264 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1731,c,1654,b)].
% 25.49/25.50 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3264,c,3046,b)].
% 25.49/25.50 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3264,c,3047,b)].
% 25.49/25.50 3265 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1732,c,1654,b)].
% 25.49/25.50 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3265,c,3046,b)].
% 25.49/25.50 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3265,c,3047,b)].
% 25.49/25.50 3266 -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__ring__strict(C). [resolve(1733,d,1654,b)].
% 25.49/25.50 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(3266,d,3046,b)].
% 25.49/25.50 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(3266,d,3047,b)].
% 25.49/25.50 3267 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1734,c,1654,b)].
% 25.49/25.50 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3267,c,3046,b)].
% 25.49/25.50 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3267,c,3047,b)].
% 25.49/25.50 3268 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1735,c,1654,b)].
% 25.49/25.50 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3268,c,3046,b)].
% 25.49/25.50 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3268,c,3047,b)].
% 25.49/25.50 3269 -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__ring__strict(C). [resolve(1736,d,1654,b)].
% 25.49/25.50 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__field(C). [resolve(3269,d,3046,b)].
% 25.49/25.50 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__idom(C). [resolve(3269,d,3047,b)].
% 25.49/25.51 3270 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1737,c,1654,b)].
% 25.49/25.51 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3270,c,3046,b)].
% 25.49/25.51 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3270,c,3047,b)].
% 25.49/25.51 3271 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1738,c,1654,b)].
% 25.49/25.51 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3271,c,3046,b)].
% 25.49/25.51 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3271,c,3047,b)].
% 25.49/25.51 3272 -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__ring__strict(C). [resolve(1739,d,1654,b)].
% 25.49/25.51 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(3272,d,3046,b)].
% 25.49/25.51 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(3272,d,3047,b)].
% 25.49/25.51 3273 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 25.49/25.51 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3273,b,3046,b)].
% 25.49/25.51 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 25.49/25.51 3274 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1741,b,1654,b)].
% 25.49/25.51 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(3274,b,3046,b)].
% 25.49/25.51 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(3274,b,3047,b)].
% 25.49/25.51 3275 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1742,c,1654,b)].
% 25.49/25.51 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3275,c,3046,b)].
% 25.49/25.51 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3275,c,3047,b)].
% 25.49/25.51 3276 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1743,c,1654,b)].
% 25.49/25.51 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3276,c,3046,b)].
% 25.49/25.51 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3276,c,3047,b)].
% 25.49/25.51 3277 -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__ring__strict(C). [resolve(1744,d,1654,b)].
% 25.49/25.51 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(3277,d,3046,b)].
% 25.49/25.51 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(3277,d,3047,b)].
% 25.49/25.51 3278 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 25.49/25.51 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3278,b,3046,b)].
% 25.49/25.51 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 25.49/25.51 3279 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1746,b,1654,b)].
% 25.49/25.52 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(3279,b,3046,b)].
% 25.49/25.52 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(3279,b,3047,b)].
% 25.49/25.52 3280 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1747,b,1654,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3280,b,3046,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3280,b,3047,b)].
% 25.49/25.52 3281 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1748,b,1654,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3281,b,3046,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3281,b,3047,b)].
% 25.49/25.52 3282 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1749,b,1654,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3282,b,3046,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3282,b,3047,b)].
% 25.49/25.52 3283 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1750,b,1654,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3283,b,3046,b)].
% 25.49/25.52 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3283,b,3047,b)].
% 25.49/25.52 3284 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1751,c,1654,b)].
% 25.49/25.52 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3284,c,3046,b)].
% 25.49/25.52 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3284,c,3047,b)].
% 25.49/25.52 3285 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1752,c,1654,b)].
% 25.49/25.52 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3285,c,3046,b)].
% 25.49/25.52 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3285,c,3047,b)].
% 25.49/25.52 3286 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1753,c,1654,b)].
% 25.49/25.52 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3286,c,3046,b)].
% 25.49/25.52 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3286,c,3047,b)].
% 25.49/25.52 3287 -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__ring__strict(B). [resolve(1754,c,1654,b)].
% 25.49/25.52 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(3287,c,3046,b)].
% 25.49/25.52 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(3287,c,3047,b)].
% 25.49/25.52 3288 -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__ring__strict(C). [resolve(1755,c,1654,b)].
% 25.49/25.52 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(3288,c,3046,b)].
% 25.49/25.52 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(3288,c,3047,b)].
% 25.49/25.52 3289 -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__ring__strict(C). [resolve(1756,c,1654,b)].
% 25.49/25.52 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(3289,c,3046,b)].
% 25.49/25.52 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(3289,c,3047,b)].
% 25.49/25.52 3290 -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__ring__strict(C). [resolve(1757,d,1654,b)].
% 25.49/25.52 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(3290,d,3046,b)].
% 25.49/25.52 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(3290,d,3047,b)].
% 25.49/25.52 3291 -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__ring__strict(C). [resolve(1758,d,1654,b)].
% 25.49/25.52 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(3291,d,3046,b)].
% 25.49/25.52 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(3291,d,3047,b)].
% 25.49/25.52 3292 -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__ring__strict(C). [resolve(1759,c,1654,b)].
% 25.49/25.52 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(3292,c,3046,b)].
% 25.49/25.52 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(3292,c,3047,b)].
% 25.49/25.52 3293 -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__ring__strict(C). [resolve(1760,d,1654,b)].
% 25.49/25.52 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(3293,d,3046,b)].
% 25.49/25.52 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(3293,d,3047,b)].
% 25.49/25.54 3294 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1761,c,1654,b)].
% 25.49/25.54 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3294,c,3046,b)].
% 25.49/25.54 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3294,c,3047,b)].
% 25.49/25.54 3295 -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__ring__strict(B). [resolve(1762,c,1654,b)].
% 25.49/25.54 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(3295,c,3046,b)].
% 25.49/25.54 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(3295,c,3047,b)].
% 25.49/25.54 3296 -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__ring__strict(C). [resolve(1763,c,1654,b)].
% 25.49/25.54 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(3296,c,3046,b)].
% 25.49/25.54 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(3296,c,3047,b)].
% 25.49/25.54 3297 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1765,c,1654,b)].
% 25.49/25.54 3298 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1766,c,1654,b)].
% 25.49/25.54 3299 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1767,c,1654,b)].
% 25.49/25.54 3300 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1768,c,1654,b)].
% 25.49/25.54 3301 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1769,c,1654,b)].
% 25.49/25.54 3302 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1770,c,1654,b)].
% 25.49/25.54 3303 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1771,c,1654,b)].
% 25.49/25.54 3304 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1772,c,1654,b)].
% 25.49/25.54 3305 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 25.49/25.54 3306 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1786,c,1654,b)].
% 25.49/25.54 3307 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1787,c,1654,b)].
% 25.49/25.54 3308 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 25.49/25.54 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3308,b,3046,b)].
% 25.49/25.54 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 25.49/25.54 3309 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 25.49/25.54 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3309,b,3046,b)].
% 25.49/25.54 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 25.49/25.54 3310 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 25.49/25.54 3311 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 25.60/25.60 3312 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 25.60/25.60 3313 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 25.60/25.60 3314 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 25.60/25.60 3315 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1800,c,1654,b)].
% 25.60/25.60 3316 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1801,b,1654,b)].
% 25.60/25.60 3317 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1802,c,1654,b)].
% 25.60/25.60 3318 -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__ring__strict(B). [resolve(1803,c,1654,b)].
% 25.60/25.60 3319 -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__ring__strict(C). [resolve(1804,c,1654,b)].
% 25.60/25.60 3320 -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__ring__strict(B). [resolve(1805,c,1654,b)].
% 25.60/25.60 3321 -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__ring__strict(C). [resolve(1806,c,1654,b)].
% 25.60/25.60 3322 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1807,c,1654,b)].
% 25.60/25.60 3323 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__ring__strict(B). [resolve(1808,b,1654,b)].
% 25.60/25.60 3324 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 25.60/25.60 3325 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1810,c,1654,b)].
% 25.60/25.60 3326 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1811,c,1654,b)].
% 25.60/25.60 3327 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 25.60/25.60 3328 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 25.60/25.60 3329 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2233,a,2232,b)].
% 25.60/25.60 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3329,c,3046,b)].
% 25.60/25.60 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3329,c,3047,b)].
% 25.60/25.60 3330 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2234,a,2232,b)].
% 25.60/25.60 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3330,c,3046,b)].
% 25.60/25.60 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3330,c,3047,b)].
% 25.60/25.60 3331 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2235,a,2232,b)].
% 25.60/25.60 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3331,c,3046,b)].
% 25.60/25.60 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3331,c,3047,b)].
% 25.60/25.60 3332 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2236,a,2232,b)].
% 25.60/25.61 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3332,b,3046,b)].
% 25.60/25.61 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3332,b,3047,b)].
% 25.60/25.61 3333 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2237,a,2232,b)].
% 25.60/25.61 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3333,c,3046,b)].
% 25.60/25.61 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3333,c,3047,b)].
% 25.60/25.61 3334 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2238,a,2232,b)].
% 25.60/25.61 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3334,b,3046,b)].
% 25.60/25.61 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3334,b,3047,b)].
% 25.60/25.61 3335 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2239,a,2232,b)].
% 25.60/25.61 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3335,b,3046,b)].
% 25.60/25.61 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3335,b,3047,b)].
% 25.60/25.61 3336 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2240,a,2232,b)].
% 25.60/25.61 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3336,b,3046,b)].
% 25.60/25.61 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3336,b,3047,b)].
% 25.60/25.61 3337 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 25.60/25.61 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3337,b,3046,b)].
% 25.60/25.61 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 25.60/25.61 3338 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2242,a,2232,b)].
% 25.60/25.61 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3338,c,3046,b)].
% 25.60/25.61 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3338,c,3047,b)].
% 25.60/25.61 3339 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2243,a,2232,b)].
% 25.60/25.61 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3339,c,3046,b)].
% 25.60/25.61 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3339,c,3047,b)].
% 25.60/25.61 3340 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 25.60/25.61 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3340,b,3046,b)].
% 25.60/25.61 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 25.60/25.61 3341 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2245,a,2232,b)].
% 25.60/25.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3341,c,3046,b)].
% 25.60/25.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3341,c,3047,b)].
% 25.60/25.62 3342 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 25.60/25.62 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3342,b,3046,b)].
% 25.60/25.62 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 25.60/25.62 3343 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2247,a,2232,b)].
% 25.60/25.62 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3343,c,3046,b)].
% 25.60/25.62 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3343,c,3047,b)].
% 25.60/25.62 3344 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2248,a,2232,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3344,c,3046,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3344,c,3047,b)].
% 25.60/25.62 3345 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2249,a,2232,b)].
% 25.60/25.62 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3345,c,3046,b)].
% 25.60/25.62 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3345,c,3047,b)].
% 25.60/25.62 3346 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2250,a,2232,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3346,c,3046,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3346,c,3047,b)].
% 25.60/25.62 3347 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2251,a,2232,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3347,c,3046,b)].
% 25.60/25.62 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3347,c,3047,b)].
% 25.60/25.62 3348 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 25.60/25.62 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3348,b,3046,b)].
% 25.60/25.62 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 25.60/25.62 3349 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 25.60/25.62 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3349,b,3046,b)].
% 25.60/25.62 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 25.60/25.62 3350 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 25.60/25.62 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3350,b,3046,b)].
% 25.60/25.62 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 25.60/25.62 3351 -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__ring__strict(A). [resolve(2357,c,2317,b)].
% 25.60/25.62 3352 -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__ring__strict(A). [resolve(2358,c,2317,b)].
% 25.64/25.63 3353 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2359,b,2317,b)].
% 25.64/25.63 3354 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2360,b,2317,b)].
% 25.64/25.63 3355 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2361,b,2317,b)].
% 25.64/25.63 3356 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2414,a,2425,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3356,c,3046,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3356,c,3047,b)].
% 25.64/25.63 3357 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2429,a,2425,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3357,c,3046,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3357,c,3047,b)].
% 25.64/25.63 3358 -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__ring__strict(C). [resolve(2430,a,2425,b)].
% 25.64/25.63 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_Oordered__field(C). [resolve(3358,d,3046,b)].
% 25.64/25.63 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_Oordered__idom(C). [resolve(3358,d,3047,b)].
% 25.64/25.63 3359 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2431,a,2425,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3359,c,3046,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3359,c,3047,b)].
% 25.64/25.63 3360 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2432,a,2425,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3360,c,3046,b)].
% 25.64/25.63 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3360,c,3047,b)].
% 25.64/25.63 3361 -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__ring__strict(C). [resolve(2433,a,2425,b)].
% 25.64/25.63 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_Oordered__field(C). [resolve(3361,d,3046,b)].
% 25.64/25.64 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(3361,d,3047,b)].
% 25.64/25.64 3362 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2434,a,2425,b)].
% 25.64/25.64 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3362,c,3046,b)].
% 25.64/25.64 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3362,c,3047,b)].
% 25.64/25.64 3363 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2435,a,2425,b)].
% 25.64/25.64 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3363,c,3046,b)].
% 25.66/25.65 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3363,c,3047,b)].
% 25.66/25.65 3364 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2436,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3364,c,3046,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3364,c,3047,b)].
% 25.66/25.65 3365 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2437,a,2425,b)].
% 25.66/25.65 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3365,c,3046,b)].
% 25.66/25.65 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3365,c,3047,b)].
% 25.66/25.65 3366 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2438,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3366,c,3046,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3366,c,3047,b)].
% 25.66/25.65 3367 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2439,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3367,c,3046,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3367,c,3047,b)].
% 25.66/25.65 3368 -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__ring__strict(C). [resolve(2440,a,2425,b)].
% 25.66/25.65 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(3368,d,3046,b)].
% 25.66/25.65 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(3368,d,3047,b)].
% 25.66/25.65 3369 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2441,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3369,c,3046,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3369,c,3047,b)].
% 25.66/25.65 3370 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2442,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3370,c,3046,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3370,c,3047,b)].
% 25.66/25.65 3371 -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__ring__strict(C). [resolve(2443,a,2425,b)].
% 25.66/25.65 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(3371,d,3046,b)].
% 25.66/25.65 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(3371,d,3047,b)].
% 25.66/25.65 3372 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2444,a,2425,b)].
% 25.66/25.65 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3372,c,3046,b)].
% 25.66/25.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3372,c,3047,b)].
% 25.66/25.67 3373 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2445,a,2425,b)].
% 25.66/25.67 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3373,c,3046,b)].
% 25.66/25.67 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3373,c,3047,b)].
% 25.66/25.67 3374 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2446,a,2425,b)].
% 25.66/25.67 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3374,c,3046,b)].
% 25.66/25.67 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3374,c,3047,b)].
% 25.66/25.67 3375 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2447,a,2425,b)].
% 25.66/25.67 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3375,c,3046,b)].
% 25.66/25.67 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3375,c,3047,b)].
% 25.66/25.67 3376 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 25.66/25.67 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3376,c,3046,b)].
% 25.66/25.67 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 25.66/25.67 3377 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 25.66/25.67 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3377,b,3046,b)].
% 25.66/25.67 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 25.66/25.67 3378 c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2519,a,2516,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3378,b,3046,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3378,b,3047,b)].
% 25.66/25.67 3379 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3379,c,3046,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 25.66/25.67 3380 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3380,b,3046,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 25.66/25.67 3381 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 25.66/25.67 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3381,b,3046,b)].
% 25.66/25.67 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 25.66/25.67 3382 c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2523,a,2516,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3382,b,3046,b)].
% 25.66/25.67 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3382,b,3047,b)].
% 25.66/25.67 3383 -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2524,a,2516,b)].
% 25.66/25.69 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3383,c,3046,b)].
% 25.66/25.69 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3383,c,3047,b)].
% 25.66/25.69 3384 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2525,a,2516,b)].
% 25.66/25.69 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3384,b,3046,b)].
% 25.66/25.69 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 25.66/25.69 3385 c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2526,a,2516,b)].
% 25.66/25.69 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3385,b,3046,b)].
% 25.66/25.69 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3385,b,3047,b)].
% 25.66/25.69 3386 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 25.66/25.69 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3386,b,3046,b)].
% 25.66/25.69 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 25.66/25.69 3387 -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2528,a,2516,b)].
% 25.66/25.69 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3387,c,3046,b)].
% 25.66/25.69 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3387,c,3047,b)].
% 25.66/25.69 3388 -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2529,a,2516,b)].
% 25.66/25.69 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3388,c,3046,b)].
% 25.66/25.69 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3388,c,3047,b)].
% 25.66/25.69 3389 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2530,a,2516,b)].
% 25.66/25.69 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3389,b,3046,b)].
% 25.66/25.69 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 25.66/25.69 3390 c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2531,a,2516,b)].
% 25.66/25.69 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3390,c,3046,b)].
% 25.66/25.69 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3390,c,3047,b)].
% 25.66/25.69 3391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 25.66/25.69 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3391,b,3045,a)].
% 25.66/25.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3391,b,3046,b)].
% 25.66/25.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 25.66/25.69 3392 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 25.66/25.69 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3392,b,3045,a)].
% 25.66/25.69 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3392,b,3046,b)].
% 25.66/25.69 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 25.66/25.69 3393 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 25.66/25.69 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3393,b,3045,a)].
% 25.66/25.69 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3393,b,3046,b)].
% 25.66/25.69 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 25.66/25.69 3394 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2982,c,2850,b)].
% 25.66/25.69 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(3394,c,3045,a)].
% 25.66/25.69 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(3394,c,3046,b)].
% 25.66/25.69 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(3394,c,3047,b)].
% 25.66/25.69 3395 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2983,c,2850,b)].
% 25.66/25.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3395,c,3045,a)].
% 25.66/25.69 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(3395,c,3046,b)].
% 25.66/25.69 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(3395,c,3047,b)].
% 25.66/25.69 3396 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2984,c,2850,b)].
% 25.66/25.69 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3396,c,3045,a)].
% 25.66/25.69 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(3396,c,3046,b)].
% 25.66/25.69 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(3396,c,3047,b)].
% 25.66/25.69 3397 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2985,c,2850,b)].
% 25.66/25.69 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3397,c,3045,a)].
% 25.66/25.69 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(3397,c,3046,b)].
% 25.66/25.69 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(3397,c,3047,b)].
% 25.66/25.69 3398 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2986,c,2850,b)].
% 25.66/25.69 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(3398,c,3045,a)].
% 25.66/25.69 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(3398,c,3046,b)].
% 25.66/25.69 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(3398,c,3047,b)].
% 25.66/25.69 3399 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2987,c,2850,b)].
% 25.66/25.69 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3399,c,3045,a)].
% 25.66/25.69 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(3399,c,3046,b)].
% 25.66/25.69 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(3399,c,3047,b)].
% 25.66/25.69 3400 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2988,c,2850,b)].
% 25.66/25.69 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3400,c,3045,a)].
% 25.66/25.69 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(3400,c,3046,b)].
% 25.66/25.69 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(3400,c,3047,b)].
% 25.66/25.70 3401 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2989,c,2850,b)].
% 25.66/25.70 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(3401,c,3045,a)].
% 25.66/25.70 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(3401,c,3046,b)].
% 25.66/25.70 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(3401,c,3047,b)].
% 25.66/25.70 3402 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 25.66/25.70 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(3402,b,3045,a)].
% 25.66/25.70 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3402,b,3046,b)].
% 25.66/25.70 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 25.66/25.70 3403 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2991,c,2850,b)].
% 25.66/25.70 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(3403,c,3045,a)].
% 25.66/25.70 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(3403,c,3046,b)].
% 25.66/25.70 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(3403,c,3047,b)].
% 25.66/25.70 3404 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2992,c,2850,b)].
% 25.66/25.70 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(3404,c,3045,a)].
% 25.66/25.70 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(3404,c,3046,b)].
% 25.66/25.70 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(3404,c,3047,b)].
% 25.66/25.70 3405 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 25.66/25.70 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3405,b,3045,a)].
% 25.66/25.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3405,b,3046,b)].
% 25.66/25.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 25.66/25.70 3406 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 25.66/25.70 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(3406,b,3045,a)].
% 25.66/25.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3406,b,3046,b)].
% 25.66/25.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 25.66/25.70 3407 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2995,c,2850,b)].
% 25.66/25.70 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3407,c,3045,a)].
% 25.66/25.70 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(3407,c,3046,b)].
% 25.66/25.70 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3407,c,3047,b)].
% 25.66/25.70 3408 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2996,b,2850,b)].
% 25.66/25.70 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3408,b,3045,a)].
% 25.66/25.70 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3408,b,3046,b)].
% 25.66/25.70 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3408,b,3047,b)].
% 25.66/25.70 3409 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2997,c,2850,b)].
% 25.66/25.71 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3409,c,3045,a)].
% 25.66/25.71 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(3409,c,3046,b)].
% 25.66/25.71 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3409,c,3047,b)].
% 25.66/25.71 3410 -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__ring__strict(B). [resolve(2998,c,2850,b)].
% 25.66/25.71 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(3410,c,3045,a)].
% 25.66/25.71 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(3410,c,3046,b)].
% 25.66/25.71 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(3410,c,3047,b)].
% 25.66/25.71 3411 -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__ring__strict(C). [resolve(2999,c,2850,b)].
% 25.66/25.71 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(3411,c,3045,a)].
% 25.66/25.71 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(3411,c,3046,b)].
% 25.66/25.71 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(3411,c,3047,b)].
% 25.66/25.71 3412 -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__ring__strict(B). [resolve(3000,c,2850,b)].
% 25.66/25.71 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(3412,c,3045,a)].
% 25.66/25.71 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(3412,c,3046,b)].
% 25.66/25.71 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(3412,c,3047,b)].
% 25.66/25.71 3413 -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__ring__strict(C). [resolve(3001,c,2850,b)].
% 25.66/25.71 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(3413,c,3045,a)].
% 25.66/25.71 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(3413,c,3046,b)].
% 25.66/25.71 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(3413,c,3047,b)].
% 25.66/25.71 3414 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3002,c,2850,b)].
% 25.66/25.71 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3414,c,3045,a)].
% 25.66/25.71 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(3414,c,3046,b)].
% 25.66/25.71 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3414,c,3047,b)].
% 25.66/25.71 3415 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__ring__strict(B). [resolve(3003,b,2850,b)].
% 25.91/25.90 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(3415,b,3045,a)].
% 25.91/25.90 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(3415,b,3046,b)].
% 25.91/25.90 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(3415,b,3047,b)].
% 25.91/25.90 3416 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 25.91/25.90 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3416,b,3045,a)].
% 25.91/25.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3416,b,3046,b)].
% 25.91/25.90 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 25.91/25.90 3417 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3005,c,2850,b)].
% 25.91/25.90 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(3417,c,3045,a)].
% 25.91/25.90 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3417,c,3046,b)].
% 25.91/25.90 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3417,c,3047,b)].
% 25.91/25.90 3418 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3006,c,2850,b)].
% 25.91/25.90 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(3418,c,3045,a)].
% 25.91/25.90 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3418,c,3046,b)].
% 25.91/25.90 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3418,c,3047,b)].
% 25.91/25.90 3419 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 25.91/25.90 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3419,b,3045,a)].
% 25.91/25.90 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3419,b,3046,b)].
% 25.91/25.90 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 25.91/25.90 3420 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 25.91/25.90 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3420,b,3045,a)].
% 25.91/25.90 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3420,b,3046,b)].
% 25.91/25.90 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 25.91/25.90 3421 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 25.91/25.93 3422 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 25.91/25.93 3423 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 25.91/25.93 3424 -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].
% 25.91/25.93 3425 -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].
% 25.91/25.93 3426 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 25.91/25.93 3427 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 25.91/25.93 3428 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 25.91/25.93 3429 -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].
% 25.91/25.93 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(3429,a,3422,a)].
% 25.91/25.93 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(3429,a,3423,a)].
% 25.91/25.93 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3429,a,3424,b)].
% 25.91/25.93 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 25.91/25.93 3430 -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].
% 25.91/25.93 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(3430,a,3422,a)].
% 25.91/25.93 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(3430,a,3423,a)].
% 25.91/25.93 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3430,a,3424,b)].
% 25.91/25.93 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 25.91/25.93 3431 -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].
% 25.91/25.93 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3431,a,3422,a)].
% 25.91/25.93 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(3431,a,3423,a)].
% 25.91/25.93 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3431,a,3424,b)].
% 25.91/25.93 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 25.91/25.93 3432 -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].
% 25.91/25.93 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(3432,a,3422,a)].
% 25.91/25.93 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat). [resolve(3432,a,3423,a)].
% 25.91/25.93 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,B),B) | c_less(c_0,A,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(3432,a,3424,b)].
% 25.91/25.93 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,B),B) | c_less(c_0,A,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3432,a,3425,b)].
% 25.91/25.93 3433 -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].
% 25.91/25.93 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3433,a,3422,a)].
% 25.91/25.93 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(3433,a,3423,a)].
% 25.96/25.94 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3433,a,3424,b)].
% 25.96/25.94 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3433,a,3425,b)].
% 25.96/25.94 3434 -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].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3434,a,3422,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(3434,a,3423,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3434,a,3424,b)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 25.96/25.94 3435 -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].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(3435,a,3422,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(3435,a,3423,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3435,a,3424,b)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 25.96/25.94 3436 -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].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(3436,a,3422,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(3436,a,3423,a)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,B) != c_NatArith_Oof__nat(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3436,a,3424,b)].
% 25.96/25.94 Derived: c_NatArith_Oof__nat(A,B) != c_NatArith_Oof__nat(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3436,a,3425,b)].
% 25.96/25.94 3437 -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].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3437,a,3422,a)].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(3437,a,3423,a)].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3437,a,3424,b)].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3437,a,3425,b)].
% 25.96/25.94 3438 -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].
% 25.96/25.94 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3438,a,3422,a)].
% 25.96/25.94 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(3438,a,3423,a)].
% 25.96/25.94 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3438,a,3424,b)].
% 25.96/25.94 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3438,a,3425,b)].
% 25.96/25.94 3439 -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].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_nat). [resolve(3439,a,3422,a)].
% 25.96/25.94 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(3439,a,3423,a)].
% 25.96/25.94 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_lessequals(A,C,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(3439,a,3424,b)].
% 25.96/25.97 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_lessequals(A,C,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3439,a,3425,b)].
% 25.96/25.97 3440 -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].
% 25.96/25.97 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(3440,a,3422,a)].
% 25.96/25.97 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(3440,a,3423,a)].
% 25.96/25.97 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3440,a,3424,b)].
% 25.96/25.97 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3440,a,3425,b)].
% 25.96/25.97 3441 -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].
% 25.96/25.97 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3441,a,3422,a)].
% 25.96/25.97 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3441,a,3424,b)].
% 25.96/25.97 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 25.96/25.97 3442 -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].
% 25.96/25.97 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(3442,a,3422,a)].
% 25.96/25.97 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(3442,a,3423,a)].
% 25.96/25.97 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_less(A,C,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(3442,a,3424,b)].
% 25.96/25.97 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_less(A,C,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3442,a,3425,b)].
% 25.96/25.97 3443 -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].
% 25.96/25.97 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(3443,a,3422,a)].
% 25.96/25.97 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(3443,a,3423,a)].
% 25.96/25.97 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3443,a,3424,b)].
% 25.96/25.97 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3443,a,3425,b)].
% 25.96/25.97 3444 -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].
% 25.96/25.97 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(3444,b,3422,a)].
% 25.96/25.97 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(3444,b,3423,a)].
% 25.96/25.97 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3444,b,3424,b)].
% 25.96/25.98 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3444,b,3425,b)].
% 25.96/25.98 3445 -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].
% 25.96/25.98 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(3445,b,3422,a)].
% 25.96/25.98 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(3445,b,3423,a)].
% 25.96/25.98 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3445,b,3424,b)].
% 25.96/25.98 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3445,b,3425,b)].
% 25.96/25.98 3446 -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].
% 25.96/25.98 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(3446,b,3422,a)].
% 25.96/25.98 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(3446,b,3423,a)].
% 25.96/25.98 Derived: -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D | -class_Ring__and__Field_Oordered__field(A). [resolve(3446,b,3424,b)].
% 25.96/25.98 Derived: -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D | -class_Ring__and__Field_Oordered__idom(A). [resolve(3446,b,3425,b)].
% 25.96/25.98 3447 -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].
% 25.96/25.98 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(3447,b,3422,a)].
% 25.96/25.98 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(3447,b,3423,a)].
% 25.96/25.98 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3447,b,3424,b)].
% 25.96/25.98 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3447,b,3425,b)].
% 25.96/25.98 3448 -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].
% 25.96/25.98 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(3448,b,3422,a)].
% 25.96/25.98 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(3448,b,3423,a)].
% 25.96/26.03 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3448,b,3424,b)].
% 25.96/26.03 Derived: -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3448,b,3425,b)].
% 25.96/26.03 3449 -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].
% 25.96/26.03 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(3449,a,3422,a)].
% 25.96/26.03 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(3449,a,3423,a)].
% 25.96/26.03 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3449,a,3424,b)].
% 25.96/26.03 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 25.96/26.03 3450 -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].
% 25.96/26.03 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(3450,a,3422,a)].
% 25.96/26.03 Derived: -c_less(c_1,c_0,tc_nat). [resolve(3450,a,3423,a)].
% 25.96/26.03 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3450,a,3424,b)].
% 25.96/26.03 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 25.96/26.03 3451 -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].
% 25.96/26.03 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(3451,a,3422,a)].
% 25.96/26.03 Derived: c_less(c_0,c_1,tc_nat). [resolve(3451,a,3423,a)].
% 25.96/26.03 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3451,a,3424,b)].
% 25.96/26.03 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 25.96/26.03 3452 -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].
% 25.96/26.03 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(3452,a,3422,a)].
% 25.96/26.03 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(3452,a,3423,a)].
% 25.96/26.03 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3452,a,3424,b)].
% 25.96/26.03 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 25.96/26.03 3453 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 25.96/26.03 3454 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 25.96/26.03 3455 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(34,a,24,b)].
% 25.96/26.03 3456 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(35,a,24,b)].
% 25.96/26.03 3457 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(36,a,24,b)].
% 25.96/26.03 3458 -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__semidom(B). [resolve(37,a,24,b)].
% 25.96/26.03 3459 -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__semidom(C). [resolve(38,a,24,b)].
% 25.96/26.03 3460 -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__semidom(B). [resolve(39,a,24,b)].
% 25.96/26.03 3461 -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__semidom(C). [resolve(40,a,24,b)].
% 25.96/26.03 3462 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(41,a,24,b)].
% 25.96/26.03 3463 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__semidom(B). [resolve(42,a,24,b)].
% 26.07/26.06 3464 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(43,a,58,b)].
% 26.07/26.06 3465 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(63,a,58,b)].
% 26.07/26.06 3466 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(64,a,58,b)].
% 26.07/26.06 3467 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(65,a,58,b)].
% 26.07/26.06 3468 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(66,a,58,b)].
% 26.07/26.06 3469 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(67,a,58,b)].
% 26.07/26.06 3470 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(68,a,58,b)].
% 26.07/26.06 3471 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(69,a,58,b)].
% 26.07/26.06 3472 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(70,a,58,b)].
% 26.07/26.06 3473 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 26.07/26.06 3474 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 26.07/26.06 3475 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 26.07/26.06 3476 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(108,b,90,b)].
% 26.07/26.06 3477 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(109,b,90,b)].
% 26.07/26.06 3478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 26.07/26.06 3479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 26.07/26.06 3480 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(221,c,203,b)].
% 26.07/26.06 3481 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(222,c,203,b)].
% 26.07/26.06 3482 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 26.07/26.06 3483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 26.07/26.06 3484 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 26.07/26.06 3485 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 26.07/26.06 3486 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 26.07/26.06 3487 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(307,a,297,b)].
% 26.07/26.06 3488 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(308,a,297,b)].
% 26.07/26.06 3489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 26.13/26.11 3490 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 26.13/26.11 3491 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 26.13/26.11 3492 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 26.13/26.11 3493 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(389,c,366,b)].
% 26.13/26.11 3494 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(390,c,366,b)].
% 26.13/26.11 3495 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 26.13/26.11 3496 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 26.13/26.11 3497 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 26.13/26.11 3498 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 26.13/26.11 3499 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(637,d,623,b)].
% 26.13/26.11 3500 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(638,d,623,b)].
% 26.13/26.11 3501 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(639,d,623,b)].
% 26.13/26.11 3502 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(640,d,623,b)].
% 26.13/26.11 3503 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(641,d,623,b)].
% 26.13/26.11 3504 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(642,d,623,b)].
% 26.13/26.11 3505 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(643,d,623,b)].
% 26.13/26.11 3506 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(644,d,623,b)].
% 26.13/26.11 3507 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(645,d,623,b)].
% 26.13/26.11 3508 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 26.13/26.11 3509 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 26.13/26.11 3510 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 26.13/26.11 3511 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 26.13/26.11 3512 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 26.13/26.11 3513 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 26.13/26.11 3514 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 26.13/26.11 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(3514,b,3423,a)].
% 26.13/26.11 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3514,b,3424,b)].
% 26.13/26.11 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 26.13/26.11 3515 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 26.13/26.11 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(3515,b,3423,a)].
% 26.13/26.11 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3515,b,3424,b)].
% 26.13/26.11 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 26.13/26.13 3516 -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__semidom(B). [resolve(871,a,868,b)].
% 26.13/26.13 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(3516,d,3423,a)].
% 26.13/26.13 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(3516,d,3424,b)].
% 26.13/26.13 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(3516,d,3425,b)].
% 26.13/26.13 3517 -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__semidom(B). [resolve(872,a,868,b)].
% 26.13/26.13 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(3517,d,3423,a)].
% 26.13/26.13 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(3517,d,3424,b)].
% 26.13/26.13 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(3517,d,3425,b)].
% 26.13/26.13 3518 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(873,a,868,b)].
% 26.13/26.13 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(3518,b,3423,a)].
% 26.13/26.13 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3518,b,3424,b)].
% 26.13/26.13 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3518,b,3425,b)].
% 26.13/26.13 3519 c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(874,a,868,b)].
% 26.13/26.13 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(3519,b,3423,a)].
% 26.13/26.13 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(3519,b,3424,b)].
% 26.13/26.13 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(3519,b,3425,b)].
% 26.13/26.13 3520 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 26.13/26.13 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(3520,b,3423,a)].
% 26.13/26.13 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3520,b,3424,b)].
% 26.13/26.13 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 26.13/26.13 3521 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__semidom(C). [resolve(876,a,868,b)].
% 26.13/26.13 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(3521,b,3423,a)].
% 26.13/26.13 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(3521,b,3424,b)].
% 26.13/26.13 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(3521,b,3425,b)].
% 26.13/26.13 3522 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__semidom(C). [resolve(877,a,868,b)].
% 26.13/26.13 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(3522,b,3423,a)].
% 26.13/26.13 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(3522,b,3424,b)].
% 26.19/26.17 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(3522,b,3425,b)].
% 26.19/26.17 3523 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 26.19/26.17 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(3523,b,3423,a)].
% 26.19/26.17 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3523,b,3424,b)].
% 26.19/26.17 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 26.19/26.17 3524 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 26.19/26.17 3525 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 26.19/26.17 3526 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 26.19/26.17 3527 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 26.19/26.17 3528 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1164,c,1145,b)].
% 26.19/26.17 3529 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1165,b,1145,b)].
% 26.19/26.17 3530 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1166,c,1145,b)].
% 26.19/26.17 3531 -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__semidom(B). [resolve(1167,c,1145,b)].
% 26.19/26.17 3532 -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__semidom(C). [resolve(1168,c,1145,b)].
% 26.19/26.17 3533 -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__semidom(B). [resolve(1169,c,1145,b)].
% 26.19/26.17 3534 -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__semidom(C). [resolve(1170,c,1145,b)].
% 26.19/26.17 3535 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1171,c,1145,b)].
% 26.19/26.17 3536 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__semidom(B). [resolve(1172,b,1145,b)].
% 26.19/26.17 3537 -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__semidom(C). [resolve(1185,a,1182,b)].
% 26.19/26.17 3538 -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__semidom(B). [resolve(1186,a,1182,b)].
% 26.19/26.17 3539 -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__semidom(B). [resolve(1187,a,1182,b)].
% 26.19/26.17 3540 -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__semidom(C). [resolve(1188,a,1182,b)].
% 26.19/26.17 3541 -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__semidom(B). [resolve(1189,a,1182,b)].
% 26.19/26.17 3542 -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__semidom(B). [resolve(1190,a,1182,b)].
% 26.19/26.17 3543 -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__semidom(C). [resolve(1191,a,1182,b)].
% 26.19/26.17 3544 -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__semidom(B). [resolve(1192,a,1182,b)].
% 26.19/26.20 3545 -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__semidom(B). [resolve(1193,a,1182,b)].
% 26.19/26.20 3546 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1194,a,1182,b)].
% 26.19/26.20 3547 -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__semidom(C). [resolve(1195,a,1182,b)].
% 26.19/26.20 3548 -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__semidom(B). [resolve(1196,a,1182,b)].
% 26.19/26.20 3549 -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__semidom(B). [resolve(1197,a,1182,b)].
% 26.19/26.20 3550 -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__semidom(C). [resolve(1198,a,1182,b)].
% 26.19/26.20 3551 -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__semidom(B). [resolve(1199,a,1182,b)].
% 26.19/26.20 3552 -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__semidom(B). [resolve(1200,a,1182,b)].
% 26.19/26.20 3553 -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__semidom(B). [resolve(1201,a,1182,b)].
% 26.19/26.20 3554 -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__semidom(B). [resolve(1202,a,1182,b)].
% 26.19/26.20 3555 -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__semidom(C). [resolve(1203,a,1182,b)].
% 26.19/26.20 3556 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1204,a,1182,b)].
% 26.19/26.20 3557 -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__semidom(B). [resolve(1205,a,1182,b)].
% 26.19/26.20 3558 -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__semidom(C). [resolve(1206,a,1182,b)].
% 26.19/26.20 3559 -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__semidom(C). [resolve(1207,a,1182,b)].
% 26.19/26.20 3560 -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__semidom(A). [resolve(1208,b,1182,b)].
% 26.19/26.20 3561 -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__semidom(A). [resolve(1209,b,1182,b)].
% 26.19/26.20 3562 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1210,a,1182,b)].
% 26.19/26.20 3563 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1211,a,1182,b)].
% 26.19/26.20 3564 -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__semidom(C). [resolve(1212,a,1182,b)].
% 26.19/26.20 3565 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1213,a,1182,b)].
% 26.19/26.22 3566 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1214,a,1182,b)].
% 26.19/26.22 3567 -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__semidom(C). [resolve(1215,a,1182,b)].
% 26.19/26.22 3568 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1216,a,1182,b)].
% 26.19/26.22 3569 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1217,a,1182,b)].
% 26.19/26.22 3570 -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__semidom(C). [resolve(1218,a,1182,b)].
% 26.19/26.22 3571 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 26.19/26.22 3572 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1220,a,1182,b)].
% 26.19/26.22 3573 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1221,a,1182,b)].
% 26.19/26.22 3574 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1222,a,1182,b)].
% 26.19/26.22 3575 -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__semidom(C). [resolve(1223,a,1182,b)].
% 26.19/26.22 3576 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 26.19/26.22 3577 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1225,a,1182,b)].
% 26.19/26.22 3578 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1226,a,1182,b)].
% 26.19/26.22 3579 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1227,a,1182,b)].
% 26.19/26.22 3580 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1228,a,1182,b)].
% 26.19/26.22 3581 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1229,a,1182,b)].
% 26.19/26.22 3582 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1230,a,1182,b)].
% 26.19/26.22 3583 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1231,a,1182,b)].
% 26.19/26.22 3584 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1232,a,1182,b)].
% 26.19/26.22 3585 -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__semidom(B). [resolve(1233,a,1182,b)].
% 26.19/26.22 3586 -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__semidom(C). [resolve(1234,a,1182,b)].
% 26.19/26.22 3587 -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__semidom(C). [resolve(1235,a,1182,b)].
% 26.19/26.22 3588 -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__semidom(C). [resolve(1236,a,1182,b)].
% 26.19/26.22 3589 -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__semidom(C). [resolve(1237,a,1182,b)].
% 26.19/26.22 3590 -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__semidom(C). [resolve(1238,a,1182,b)].
% 26.29/26.27 3591 -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__semidom(C). [resolve(1239,a,1182,b)].
% 26.29/26.27 3592 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1240,a,1182,b)].
% 26.29/26.27 3593 -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__semidom(B). [resolve(1241,a,1182,b)].
% 26.29/26.27 3594 -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__semidom(C). [resolve(1242,a,1182,b)].
% 26.29/26.27 3595 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1362,a,1359,b)].
% 26.29/26.27 3596 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1363,a,1359,b)].
% 26.29/26.27 3597 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1364,a,1359,b)].
% 26.29/26.27 3598 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1365,a,1359,b)].
% 26.29/26.27 3599 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1366,a,1359,b)].
% 26.29/26.27 3600 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1367,a,1359,b)].
% 26.29/26.27 3601 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1368,a,1359,b)].
% 26.29/26.27 3602 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1369,a,1359,b)].
% 26.29/26.27 3603 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 26.29/26.27 3604 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 26.29/26.27 3605 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 26.29/26.27 3606 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1389,c,1359,b)].
% 26.29/26.27 3607 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1390,b,1359,b)].
% 26.29/26.27 3608 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1391,c,1359,b)].
% 26.29/26.27 3609 -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__semidom(B). [resolve(1392,c,1359,b)].
% 26.29/26.27 3610 -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__semidom(C). [resolve(1393,c,1359,b)].
% 26.29/26.27 3611 -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__semidom(B). [resolve(1394,c,1359,b)].
% 26.29/26.27 3612 -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__semidom(C). [resolve(1395,c,1359,b)].
% 26.29/26.27 3613 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1396,c,1359,b)].
% 26.29/26.27 3614 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__semidom(B). [resolve(1397,b,1359,b)].
% 26.29/26.27 3615 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1398,c,1359,b)].
% 26.29/26.27 3616 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1399,c,1359,b)].
% 26.29/26.27 3617 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 26.29/26.27 3618 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 26.29/26.30 3619 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 26.29/26.30 3620 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1575,c,1547,b)].
% 26.29/26.30 3621 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1576,c,1547,b)].
% 26.29/26.30 3622 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 26.29/26.30 3623 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 26.29/26.30 3624 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 26.29/26.30 3625 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 26.29/26.30 3626 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1633,c,1590,b)].
% 26.29/26.30 3627 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1634,b,1590,b)].
% 26.29/26.30 3628 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1635,c,1590,b)].
% 26.29/26.30 3629 -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__semidom(B). [resolve(1636,c,1590,b)].
% 26.29/26.30 3630 -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__semidom(C). [resolve(1637,c,1590,b)].
% 26.29/26.30 3631 -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__semidom(B). [resolve(1638,c,1590,b)].
% 26.29/26.30 3632 -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__semidom(C). [resolve(1639,c,1590,b)].
% 26.29/26.30 3633 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1640,c,1590,b)].
% 26.29/26.30 3634 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__semidom(B). [resolve(1641,b,1590,b)].
% 26.29/26.30 3635 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 26.29/26.30 3636 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1643,c,1590,b)].
% 26.29/26.30 3637 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1644,c,1590,b)].
% 26.29/26.30 3638 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 26.29/26.30 3639 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 26.29/26.30 3640 -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__semidom(C). [resolve(1706,e,1655,b)].
% 26.29/26.30 3641 -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__semidom(B). [resolve(1707,d,1655,b)].
% 26.29/26.30 3642 -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__semidom(B). [resolve(1708,d,1655,b)].
% 26.29/26.30 3643 -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__semidom(C). [resolve(1709,f,1655,b)].
% 26.33/26.32 3644 -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__semidom(B). [resolve(1710,e,1655,b)].
% 26.33/26.32 3645 -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__semidom(B). [resolve(1711,e,1655,b)].
% 26.33/26.32 3646 -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__semidom(C). [resolve(1712,f,1655,b)].
% 26.33/26.32 3647 -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__semidom(B). [resolve(1713,e,1655,b)].
% 26.33/26.32 3648 -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__semidom(B). [resolve(1714,e,1655,b)].
% 26.33/26.32 3649 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1715,b,1655,b)].
% 26.33/26.32 3650 -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__semidom(C). [resolve(1716,f,1655,b)].
% 26.33/26.32 3651 -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__semidom(B). [resolve(1717,e,1655,b)].
% 26.33/26.32 3652 -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__semidom(B). [resolve(1718,e,1655,b)].
% 26.33/26.32 3653 -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__semidom(C). [resolve(1719,f,1655,b)].
% 26.33/26.32 3654 -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__semidom(B). [resolve(1720,e,1655,b)].
% 26.33/26.32 3655 -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__semidom(B). [resolve(1721,e,1655,b)].
% 26.33/26.32 3656 -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__semidom(B). [resolve(1722,d,1655,b)].
% 26.33/26.32 3657 -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__semidom(B). [resolve(1723,d,1655,b)].
% 26.33/26.32 3658 -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__semidom(C). [resolve(1724,e,1655,b)].
% 26.33/26.32 3659 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1725,b,1655,b)].
% 26.33/26.32 3660 -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__semidom(B). [resolve(1726,d,1655,b)].
% 26.33/26.32 3661 -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__semidom(C). [resolve(1727,e,1655,b)].
% 26.33/26.32 3662 -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__semidom(C). [resolve(1728,e,1655,b)].
% 26.33/26.32 3663 -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__semidom(A). [resolve(1729,d,1655,b)].
% 26.38/26.34 3664 -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__semidom(A). [resolve(1730,d,1655,b)].
% 26.38/26.34 3665 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1731,c,1655,b)].
% 26.38/26.34 3666 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1732,c,1655,b)].
% 26.38/26.34 3667 -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__semidom(C). [resolve(1733,d,1655,b)].
% 26.38/26.34 3668 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1734,c,1655,b)].
% 26.38/26.34 3669 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1735,c,1655,b)].
% 26.38/26.34 3670 -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__semidom(C). [resolve(1736,d,1655,b)].
% 26.38/26.34 3671 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1737,c,1655,b)].
% 26.38/26.34 3672 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(1738,c,1655,b)].
% 26.38/26.34 3673 -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__semidom(C). [resolve(1739,d,1655,b)].
% 26.38/26.34 3674 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 26.38/26.34 3675 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1741,b,1655,b)].
% 26.38/26.34 3676 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1742,c,1655,b)].
% 26.38/26.34 3677 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1743,c,1655,b)].
% 26.38/26.34 3678 -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__semidom(C). [resolve(1744,d,1655,b)].
% 26.38/26.34 3679 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 26.38/26.34 3680 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1746,b,1655,b)].
% 26.38/26.34 3681 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1747,b,1655,b)].
% 26.38/26.34 3682 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1748,b,1655,b)].
% 26.38/26.34 3683 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1749,b,1655,b)].
% 26.38/26.34 3684 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1750,b,1655,b)].
% 26.38/26.34 3685 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1751,c,1655,b)].
% 26.38/26.34 3686 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1752,c,1655,b)].
% 26.38/26.34 3687 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1753,c,1655,b)].
% 26.38/26.34 3688 -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__semidom(B). [resolve(1754,c,1655,b)].
% 26.38/26.34 3689 -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__semidom(C). [resolve(1755,c,1655,b)].
% 26.38/26.34 3690 -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__semidom(C). [resolve(1756,c,1655,b)].
% 26.38/26.37 3691 -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__semidom(C). [resolve(1757,d,1655,b)].
% 26.38/26.37 3692 -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__semidom(C). [resolve(1758,d,1655,b)].
% 26.38/26.37 3693 -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__semidom(C). [resolve(1759,c,1655,b)].
% 26.38/26.37 3694 -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__semidom(C). [resolve(1760,d,1655,b)].
% 26.38/26.37 3695 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1761,c,1655,b)].
% 26.38/26.37 3696 -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__semidom(B). [resolve(1762,c,1655,b)].
% 26.38/26.37 3697 -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__semidom(C). [resolve(1763,c,1655,b)].
% 26.38/26.37 3698 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1765,c,1655,b)].
% 26.38/26.37 3699 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1766,c,1655,b)].
% 26.38/26.37 3700 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1767,c,1655,b)].
% 26.38/26.37 3701 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1768,c,1655,b)].
% 26.38/26.37 3702 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1769,c,1655,b)].
% 26.38/26.37 3703 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1770,c,1655,b)].
% 26.38/26.37 3704 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1771,c,1655,b)].
% 26.38/26.37 3705 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1772,c,1655,b)].
% 26.38/26.37 3706 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 26.38/26.37 3707 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1786,c,1655,b)].
% 26.38/26.37 3708 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1787,c,1655,b)].
% 26.38/26.37 3709 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 26.38/26.37 3710 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 26.38/26.37 3711 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 26.38/26.37 3712 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 26.38/26.37 3713 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 26.38/26.37 3714 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 26.38/26.37 3715 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 26.38/26.37 3716 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1800,c,1655,b)].
% 26.38/26.37 3717 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1801,b,1655,b)].
% 26.38/26.43 3718 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1802,c,1655,b)].
% 26.38/26.43 3719 -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__semidom(B). [resolve(1803,c,1655,b)].
% 26.38/26.43 3720 -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__semidom(C). [resolve(1804,c,1655,b)].
% 26.38/26.43 3721 -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__semidom(B). [resolve(1805,c,1655,b)].
% 26.38/26.43 3722 -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__semidom(C). [resolve(1806,c,1655,b)].
% 26.38/26.43 3723 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1807,c,1655,b)].
% 26.38/26.43 3724 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__semidom(B). [resolve(1808,b,1655,b)].
% 26.38/26.43 3725 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 26.38/26.43 3726 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1810,c,1655,b)].
% 26.38/26.43 3727 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1811,c,1655,b)].
% 26.38/26.43 3728 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 26.38/26.43 3729 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 26.38/26.43 3730 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 26.38/26.43 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3730,b,3424,b)].
% 26.38/26.43 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 26.38/26.43 3731 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2414,a,2426,b)].
% 26.38/26.43 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3731,c,3423,a)].
% 26.38/26.43 3732 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2429,a,2426,b)].
% 26.38/26.43 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3732,c,3423,a)].
% 26.38/26.43 3733 -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__semidom(C). [resolve(2430,a,2426,b)].
% 26.38/26.43 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(3733,d,3423,a)].
% 26.38/26.43 3734 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2431,a,2426,b)].
% 26.38/26.43 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3734,c,3423,a)].
% 26.38/26.43 3735 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2432,a,2426,b)].
% 26.38/26.43 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3735,c,3423,a)].
% 26.38/26.43 3736 -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__semidom(C). [resolve(2433,a,2426,b)].
% 26.38/26.43 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(3736,d,3423,a)].
% 26.71/26.70 3737 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2434,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3737,c,3423,a)].
% 26.71/26.70 3738 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2435,a,2426,b)].
% 26.71/26.70 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3738,c,3423,a)].
% 26.71/26.70 3739 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2436,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3739,c,3423,a)].
% 26.71/26.70 3740 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2437,a,2426,b)].
% 26.71/26.70 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3740,c,3423,a)].
% 26.71/26.70 3741 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2438,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3741,c,3423,a)].
% 26.71/26.70 3742 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2439,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3742,c,3423,a)].
% 26.71/26.70 3743 -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__semidom(C). [resolve(2440,a,2426,b)].
% 26.71/26.70 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(3743,d,3423,a)].
% 26.71/26.70 3744 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2441,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3744,c,3423,a)].
% 26.71/26.70 3745 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semidom(D). [resolve(2442,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3745,c,3423,a)].
% 26.71/26.70 3746 -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__semidom(C). [resolve(2443,a,2426,b)].
% 26.71/26.70 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(3746,d,3423,a)].
% 26.71/26.70 3747 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2444,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3747,c,3423,a)].
% 26.71/26.70 3748 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2445,a,2426,b)].
% 26.71/26.70 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3748,c,3423,a)].
% 26.71/26.70 3749 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2446,a,2426,b)].
% 26.71/26.70 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3749,c,3423,a)].
% 26.71/26.70 3750 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2447,a,2426,b)].
% 26.71/26.70 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3750,c,3423,a)].
% 26.71/26.70 3751 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 26.71/26.70 3752 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 26.71/26.70 3753 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 26.78/26.76 3754 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 26.78/26.76 3755 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 26.78/26.76 3756 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 26.78/26.76 3757 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 26.78/26.76 3758 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 26.78/26.76 3759 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 26.78/26.76 3760 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(43,a,55,b)].
% 26.78/26.76 3761 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(63,a,55,b)].
% 26.78/26.76 3762 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(64,a,55,b)].
% 26.78/26.76 3763 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(65,a,55,b)].
% 26.78/26.76 3764 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(66,a,55,b)].
% 26.78/26.76 3765 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(67,a,55,b)].
% 26.78/26.76 3766 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(68,a,55,b)].
% 26.78/26.76 3767 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(69,a,55,b)].
% 26.78/26.76 3768 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(70,a,55,b)].
% 26.78/26.76 3769 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 26.78/26.76 3770 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 26.78/26.76 3771 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 26.78/26.76 3772 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(108,b,84,b)].
% 26.78/26.76 3773 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(109,b,84,b)].
% 26.78/26.76 3774 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 26.78/26.76 3775 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 26.78/26.76 3776 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(221,c,197,b)].
% 26.78/26.76 3777 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(222,c,197,b)].
% 26.78/26.76 3778 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 26.78/26.79 3779 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 26.78/26.79 3780 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 26.78/26.79 3781 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 26.78/26.79 3782 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 26.78/26.79 3783 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 26.78/26.79 3784 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 26.78/26.79 3785 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 26.78/26.79 3786 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 26.78/26.79 3787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 26.78/26.79 3788 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 26.78/26.79 3789 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 26.78/26.79 3790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 26.78/26.79 3791 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 26.78/26.79 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 26.78/26.79 3792 -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(413,b,399,b)].
% 26.78/26.79 3793 -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(414,b,399,b)].
% 26.78/26.79 3794 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(415,a,399,b)].
% 26.78/26.79 3795 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(416,a,399,b)].
% 26.78/26.79 3796 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(417,a,399,b)].
% 26.78/26.79 3797 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 26.78/26.79 3798 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(428,c,399,b)].
% 26.78/26.79 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3798,c,3753,b)].
% 26.78/26.79 3799 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(429,c,399,b)].
% 26.78/26.79 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3799,c,3753,b)].
% 26.78/26.79 3800 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 26.78/26.79 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 26.78/26.79 3801 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 26.78/26.79 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 26.78/26.79 3802 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 26.78/26.79 3803 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 26.78/26.79 3804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 26.78/26.79 3805 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 26.78/26.82 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 26.78/26.82 3806 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 26.78/26.82 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 26.78/26.82 3807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 26.78/26.82 3808 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 26.78/26.82 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3808,b,3753,b)].
% 26.78/26.82 3809 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 26.78/26.82 3810 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 26.78/26.82 3811 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 26.78/26.82 3812 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(637,d,620,b)].
% 26.78/26.82 3813 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(638,d,620,b)].
% 26.78/26.82 3814 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(639,d,620,b)].
% 26.78/26.82 3815 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(640,d,620,b)].
% 26.78/26.82 3816 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(641,d,620,b)].
% 26.78/26.82 3817 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(642,d,620,b)].
% 26.78/26.82 3818 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(643,d,620,b)].
% 26.78/26.82 3819 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(644,d,620,b)].
% 26.78/26.82 3820 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(645,d,620,b)].
% 26.78/26.82 3821 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 26.78/26.82 3822 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 26.78/26.82 3823 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 26.78/26.82 3824 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 26.78/26.82 3825 -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(830,c,789,b)].
% 26.78/26.82 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(3825,c,3753,b)].
% 26.78/26.82 3826 -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(831,c,789,b)].
% 26.78/26.82 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(3826,c,3753,b)].
% 26.78/26.82 3827 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B). [resolve(832,b,789,b)].
% 26.78/26.82 Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3827,b,3753,b)].
% 26.87/26.83 3828 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(833,b,789,b)].
% 26.87/26.83 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3828,b,3753,b)].
% 26.87/26.83 3829 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(834,b,789,b)].
% 26.87/26.83 Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3829,b,3753,b)].
% 26.87/26.83 3830 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(837,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3830,d,3753,b)].
% 26.87/26.83 3831 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(838,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3831,d,3753,b)].
% 26.87/26.83 3832 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(839,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3832,d,3753,b)].
% 26.87/26.83 3833 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(840,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3833,d,3753,b)].
% 26.87/26.83 3834 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(841,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3834,d,3753,b)].
% 26.87/26.83 3835 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(842,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3835,d,3753,b)].
% 26.87/26.83 3836 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(843,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3836,d,3753,b)].
% 26.87/26.83 3837 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(844,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3837,d,3753,b)].
% 26.87/26.83 3838 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(845,d,789,b)].
% 26.87/26.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3838,d,3753,b)].
% 26.87/26.83 3839 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 26.87/26.83 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 26.87/26.83 3840 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 26.87/26.85 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 26.87/26.85 3841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 26.87/26.85 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3841,b,3753,b)].
% 26.87/26.85 3842 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 26.87/26.85 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 26.87/26.85 3843 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 26.87/26.85 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 26.87/26.85 3844 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 26.87/26.85 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 26.87/26.85 3845 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 26.87/26.85 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 26.87/26.85 3846 -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_Oidom(B). [resolve(871,a,865,b)].
% 26.87/26.85 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(3846,d,3753,b)].
% 26.87/26.85 3847 -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_Oidom(B). [resolve(872,a,865,b)].
% 26.87/26.85 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(3847,d,3753,b)].
% 26.87/26.85 3848 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 26.87/26.85 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 26.87/26.85 3849 c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oidom(B). [resolve(874,a,865,b)].
% 26.87/26.85 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(3849,b,3753,b)].
% 26.87/26.85 3850 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 26.87/26.85 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 26.87/26.85 3851 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_Oidom(C). [resolve(876,a,865,b)].
% 26.87/26.85 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(3851,b,3753,b)].
% 26.87/26.85 3852 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_Oidom(C). [resolve(877,a,865,b)].
% 26.87/26.85 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(3852,b,3753,b)].
% 26.87/26.85 3853 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 26.87/26.85 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 26.87/26.85 3854 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 26.87/26.85 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3854,b,3752,a)].
% 26.87/26.85 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 26.87/26.85 3855 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 26.87/26.85 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3855,b,3752,a)].
% 26.87/26.85 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 26.87/26.85 3856 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(947,a,942,b)].
% 26.87/26.85 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3856,d,3752,a)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3856,d,3753,b)].
% 26.87/26.86 3857 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(948,a,942,b)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_minus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3857,d,3752,a)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3857,d,3753,b)].
% 26.87/26.86 3858 -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(949,a,942,b)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_uminus(A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3858,c,3752,a)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3858,c,3753,b)].
% 26.87/26.86 3859 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oidom(B). [resolve(950,a,942,b)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3859,d,3752,a)].
% 26.87/26.86 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3859,d,3753,b)].
% 26.87/26.86 3860 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(3860,b,3752,a)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 26.87/26.86 3861 c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(952,a,942,b)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3861,b,3752,a)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3861,b,3753,b)].
% 26.87/26.86 3862 c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(953,a,942,b)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3862,b,3752,a)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3862,b,3753,b)].
% 26.87/26.86 3863 c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oidom(B). [resolve(954,a,942,b)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(3863,b,3752,a)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3863,b,3753,b)].
% 26.87/26.86 3864 c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(955,a,942,b)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3864,b,3752,a)].
% 26.87/26.86 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3864,b,3753,b)].
% 26.87/26.86 3865 c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(956,a,942,b)].
% 26.87/26.87 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3865,b,3752,a)].
% 26.87/26.87 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3865,b,3753,b)].
% 26.87/26.87 3866 c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oidom(B). [resolve(957,a,942,b)].
% 26.87/26.87 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(3866,b,3752,a)].
% 26.87/26.87 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3866,b,3753,b)].
% 26.87/26.87 3867 -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oidom(C). [resolve(958,a,942,b)].
% 26.87/26.87 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),tc_IntDef_Oint) = c_minus(c_NatArith_Oof__nat(B,tc_IntDef_Oint),c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3867,c,3752,a)].
% 26.87/26.87 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3867,c,3753,b)].
% 26.87/26.87 3868 -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oidom(A). [resolve(959,b,942,b)].
% 26.87/26.87 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(c_uminus(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint) = c_Nat_Opower(A,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint). [resolve(3868,c,3752,a)].
% 26.87/26.87 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Ofield(A). [resolve(3868,c,3753,b)].
% 26.87/26.87 3869 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(960,b,942,b)].
% 26.87/26.87 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(3869,d,3752,a)].
% 26.87/26.87 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3869,d,3753,b)].
% 26.87/26.87 3870 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(961,b,942,b)].
% 26.87/26.87 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint). [resolve(3870,d,3752,a)].
% 26.87/26.87 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3870,d,3753,b)].
% 26.87/26.87 3871 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oidom(A). [resolve(962,b,942,b)].
% 26.87/26.87 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Nat_Opower(B,A,tc_IntDef_Oint). [resolve(3871,d,3752,a)].
% 27.33/27.31 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3871,d,3753,b)].
% 27.33/27.31 3872 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(963,b,942,b)].
% 27.33/27.31 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_Nat_Opower(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3872,d,3752,a)].
% 27.33/27.31 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3872,d,3753,b)].
% 27.33/27.31 3873 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 27.33/27.31 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3873,b,3753,b)].
% 27.33/27.31 3874 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 27.33/27.31 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3874,b,3753,b)].
% 27.33/27.31 3875 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 27.33/27.31 3876 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_58) # label(axiom). [assumption].
% 27.33/27.31 3877 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__idom(A) # label(clsrel_Ring__and__Field_Oordered__field_34) # label(axiom). [assumption].
% 27.33/27.31 3878 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_21) # label(axiom). [assumption].
% 27.33/27.31 3879 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 27.33/27.31 3880 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_28) # label(axiom). [assumption].
% 27.33/27.31 3881 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 27.33/27.31 3882 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_54) # label(axiom). [assumption].
% 27.33/27.31 3883 -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].
% 27.33/27.31 Derived: -class_Numeral_Onumber__ring(tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(3883,b,3876,a)].
% 27.33/27.31 Derived: -class_Numeral_Onumber__ring(A) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3883,b,3877,b)].
% 27.33/27.31 3884 -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].
% 27.33/27.31 Derived: -class_Numeral_Onumber__ring(tc_IntDef_Oint) | -class_Power_Orecpower(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(3884,c,3876,a)].
% 27.33/27.31 Derived: -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A),A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3884,c,3877,b)].
% 27.33/27.31 3885 -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].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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(3885,b,3876,a)].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3885,b,3877,b)].
% 27.36/27.32 3886 -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].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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(3886,b,3876,a)].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3886,b,3877,b)].
% 27.36/27.32 3887 -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].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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(3887,b,3876,a)].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3887,b,3877,b)].
% 27.36/27.32 3888 -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].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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(3888,b,3876,a)].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3888,b,3877,b)].
% 27.36/27.32 3889 -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].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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(3889,b,3876,a)].
% 27.36/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3889,b,3877,b)].
% 27.37/27.32 3890 -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].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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(3890,b,3876,a)].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3890,b,3877,b)].
% 27.37/27.32 3891 -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].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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(3891,b,3876,a)].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3891,b,3877,b)].
% 27.37/27.32 3892 -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].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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(3892,b,3876,a)].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3892,b,3877,b)].
% 27.37/27.32 3893 -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].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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(3893,b,3876,a)].
% 27.37/27.32 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3893,b,3877,b)].
% 27.37/27.32 3894 -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].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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(3894,b,3876,a)].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3894,b,3877,b)].
% 27.37/27.33 3895 -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].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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(3895,b,3876,a)].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3895,b,3877,b)].
% 27.37/27.33 3896 -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].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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(3896,b,3876,a)].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3896,b,3877,b)].
% 27.37/27.33 3897 -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].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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(3897,b,3876,a)].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3897,b,3877,b)].
% 27.37/27.33 3898 -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].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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(3898,b,3876,a)].
% 27.37/27.33 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3898,b,3877,b)].
% 27.37/27.34 3899 -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].
% 27.37/27.34 Derived: -class_Numeral_Onumber__ring(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(3899,b,3876,a)].
% 27.37/27.34 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3899,b,3877,b)].
% 27.37/27.34 3900 -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].
% 27.37/27.34 Derived: -class_Numeral_Onumber__ring(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(3900,b,3876,a)].
% 27.37/27.34 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3900,b,3877,b)].
% 27.37/27.34 3901 -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_IntDef_Oof__int(B,A) | c_0 = B # label(cls_IntDef_Oof__int__0__eq__iff_0) # label(axiom). [assumption].
% 27.37/27.34 Derived: c_0 != c_IntDef_Oof__int(A,tc_IntDef_Oint) | c_0 = A. [resolve(3901,a,3876,a)].
% 27.37/27.34 Derived: c_0 != c_IntDef_Oof__int(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3901,a,3877,b)].
% 27.37/27.34 3902 -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_IntDef_Oof__int(c_0,A) # label(cls_IntDef_Oof__int__0__eq__iff_1) # label(axiom). [assumption].
% 27.37/27.34 Derived: c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint). [resolve(3902,a,3876,a)].
% 27.37/27.34 Derived: c_0 = c_IntDef_Oof__int(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3902,a,3877,b)].
% 27.37/27.34 3903 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,c_IntDef_Oof__int(B,A),A) | c_lessequals(c_0,B,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__0__le__iff_0) # label(axiom). [assumption].
% 27.37/27.34 Derived: -c_lessequals(c_0,c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3903,a,3876,a)].
% 27.37/27.34 Derived: -c_lessequals(c_0,c_IntDef_Oof__int(A,B),B) | c_lessequals(c_0,A,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3903,a,3877,b)].
% 27.37/27.34 3904 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_IntDef_Oof__int(B,A),A) # label(cls_IntDef_Oof__int__0__le__iff_1) # label(axiom). [assumption].
% 27.37/27.34 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3904,a,3876,a)].
% 27.37/27.34 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3904,a,3877,b)].
% 27.37/27.34 3905 -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_IntDef_Oof__int(B,A),A) | c_less(c_0,B,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__0__less__iff_0) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_less(c_0,c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_IntDef_Oint). [resolve(3905,a,3876,a)].
% 27.37/27.35 Derived: -c_less(c_0,c_IntDef_Oof__int(A,B),B) | c_less(c_0,A,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3905,a,3877,b)].
% 27.37/27.35 3906 -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,tc_IntDef_Oint) | c_less(c_0,c_IntDef_Oof__int(B,A),A) # label(cls_IntDef_Oof__int__0__less__iff_1) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3906,a,3876,a)].
% 27.37/27.35 Derived: -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3906,a,3877,b)].
% 27.37/27.35 3907 -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(B,A) != c_0 | B = c_0 # label(cls_IntDef_Oof__int__eq__0__iff_0) # label(axiom). [assumption].
% 27.37/27.35 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3907,a,3876,a)].
% 27.37/27.35 Derived: c_IntDef_Oof__int(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3907,a,3877,b)].
% 27.37/27.35 3908 -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_0,A) = c_0 # label(cls_IntDef_Oof__int__eq__0__iff_1) # label(axiom). [assumption].
% 27.37/27.35 Derived: c_IntDef_Oof__int(c_0,tc_IntDef_Oint) = c_0. [resolve(3908,a,3876,a)].
% 27.37/27.35 Derived: c_IntDef_Oof__int(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3908,a,3877,b)].
% 27.37/27.35 3909 -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(B,A) != c_IntDef_Oof__int(C,A) | B = C # label(cls_IntDef_Oof__int__eq__iff_0) # label(axiom). [assumption].
% 27.37/27.35 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_IntDef_Oof__int(B,tc_IntDef_Oint) | A = B. [resolve(3909,a,3876,a)].
% 27.37/27.35 Derived: c_IntDef_Oof__int(A,B) != c_IntDef_Oof__int(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(3909,a,3877,b)].
% 27.37/27.35 3910 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_IntDef_Oof__int(B,A),c_0,A) | c_lessequals(B,c_0,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__le__0__iff_0) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_lessequals(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3910,a,3876,a)].
% 27.37/27.35 Derived: -c_lessequals(c_IntDef_Oof__int(A,B),c_0,B) | c_lessequals(A,c_0,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3910,a,3877,b)].
% 27.37/27.35 3911 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(B,A),c_0,A) # label(cls_IntDef_Oof__int__le__0__iff_1) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3911,a,3876,a)].
% 27.37/27.35 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3911,a,3877,b)].
% 27.37/27.35 3912 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) | c_lessequals(B,C,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__le__iff_0) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_lessequals(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3912,a,3876,a)].
% 27.37/27.35 Derived: -c_lessequals(c_IntDef_Oof__int(A,B),c_IntDef_Oof__int(C,B),B) | c_lessequals(A,C,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3912,a,3877,b)].
% 27.37/27.35 3913 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__le__iff_1) # label(axiom). [assumption].
% 27.37/27.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3913,a,3876,a)].
% 27.37/27.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3913,a,3877,b)].
% 27.37/27.38 3914 -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_IntDef_Oof__int(B,A),c_0,A) | c_less(B,c_0,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__less__0__iff_0) # label(axiom). [assumption].
% 27.37/27.38 Derived: -c_less(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(3914,a,3876,a)].
% 27.37/27.38 Derived: -c_less(c_IntDef_Oof__int(A,B),c_0,B) | c_less(A,c_0,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3914,a,3877,b)].
% 27.37/27.38 3915 -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_0,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(B,A),c_0,A) # label(cls_IntDef_Oof__int__less__0__iff_1) # label(axiom). [assumption].
% 27.37/27.38 Derived: -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3915,a,3876,a)].
% 27.37/27.38 Derived: -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3915,a,3877,b)].
% 27.37/27.38 3916 -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) | c_less(B,C,tc_IntDef_Oint) # label(cls_IntDef_Oof__int__less__iff_0) # label(axiom). [assumption].
% 27.37/27.38 Derived: -c_less(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(3916,a,3876,a)].
% 27.37/27.38 Derived: -c_less(c_IntDef_Oof__int(A,B),c_IntDef_Oof__int(C,B),B) | c_less(A,C,tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(B). [resolve(3916,a,3877,b)].
% 27.37/27.38 3917 -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__less__iff_1) # label(axiom). [assumption].
% 27.37/27.38 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3917,a,3876,a)].
% 27.37/27.38 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3917,a,3877,b)].
% 27.37/27.38 3918 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3918,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3918,b,3877,b)].
% 27.37/27.38 3919 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3919,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3919,b,3877,b)].
% 27.37/27.38 3920 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3920,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3920,b,3877,b)].
% 27.37/27.38 3921 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3921,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3921,b,3877,b)].
% 27.37/27.38 3922 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3922,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3922,b,3877,b)].
% 27.37/27.38 3923 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3923,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3923,b,3877,b)].
% 27.37/27.38 3924 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3924,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3924,b,3877,b)].
% 27.37/27.38 3925 -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].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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(3925,b,3876,a)].
% 27.37/27.38 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3925,b,3877,b)].
% 27.37/27.39 3926 -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].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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(3926,b,3876,a)].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3926,b,3877,b)].
% 27.37/27.39 3927 -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].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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(3927,b,3876,a)].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB1),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3927,b,3877,b)].
% 27.37/27.39 3928 -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].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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(3928,b,3876,a)].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3928,b,3877,b)].
% 27.37/27.39 3929 -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].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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(3929,b,3876,a)].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(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) | -class_Ring__and__Field_Oordered__field(A). [resolve(3929,b,3877,b)].
% 27.37/27.39 3930 -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].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3930,b,3876,a)].
% 27.37/27.39 Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3930,b,3877,b)].
% 27.37/27.39 3931 -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_0,A) # label(cls_Numeral_Obin__rel__simps__8_0) # label(axiom). [assumption].
% 27.37/27.39 Derived: -c_IntDef_Oneg(c_0,tc_IntDef_Oint). [resolve(3931,a,3876,a)].
% 27.37/27.40 Derived: -c_IntDef_Oneg(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3931,a,3877,b)].
% 27.37/27.40 3932 -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_1,A) # label(cls_Numeral_Obin__rel__simps__9_0) # label(axiom). [assumption].
% 27.37/27.40 Derived: -c_IntDef_Oneg(c_1,tc_IntDef_Oint). [resolve(3932,a,3876,a)].
% 27.37/27.40 Derived: -c_IntDef_Oneg(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3932,a,3877,b)].
% 27.37/27.40 3933 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A) != c_0 | B = c_0 # label(cls_Parity_Opower__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 27.37/27.40 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3933,b,3876,a)].
% 27.37/27.40 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A) != c_0 | B = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3933,b,3877,b)].
% 27.37/27.40 3934 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A) != c_0 | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) # label(cls_Parity_Opower__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 27.37/27.40 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint) != c_0 | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat). [resolve(3934,b,3876,a)].
% 27.37/27.40 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A) != c_0 | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | -class_Ring__and__Field_Oordered__field(A). [resolve(3934,b,3877,b)].
% 27.37/27.40 3935 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A) = c_0 # label(cls_Parity_Opower__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 27.37/27.40 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_Nat_Opower(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_0. [resolve(3935,b,3876,a)].
% 27.37/27.40 Derived: -class_Power_Orecpower(A) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3935,b,3877,b)].
% 27.37/27.40 3936 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Nat_Opower(c_HOL_Oabs(C,A),c_Numeral_Onumber__of(B,tc_nat),A) = c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A) # label(cls_Parity_Opower__even__abs__number__of_0) # label(axiom). [assumption].
% 27.37/27.40 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_Nat_Opower(c_HOL_Oabs(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint). [resolve(3936,b,3876,a)].
% 27.37/27.40 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Nat_Opower(c_HOL_Oabs(C,A),c_Numeral_Onumber__of(B,tc_nat),A) = c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3936,b,3877,b)].
% 27.37/27.40 3937 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(C,tc_nat) != c_0 # label(cls_Parity_Opower__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 27.37/27.40 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_Numeral_Onumber__of(B,tc_nat) != c_0. [resolve(3937,b,3876,a)].
% 27.37/27.40 Derived: -class_Power_Orecpower(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(C,tc_nat) != c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3937,b,3877,b)].
% 27.37/27.40 3938 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) | C = c_0 # label(cls_Parity_Opower__le__zero__eq__number__of_1) # label(axiom). [assumption].
% 27.45/27.41 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | B = c_0. [resolve(3938,b,3876,a)].
% 27.45/27.41 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) | C = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3938,b,3877,b)].
% 27.45/27.41 3939 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(B,c_0,A) # label(cls_Parity_Opower__le__zero__eq__number__of_2) # label(axiom). [assumption].
% 27.45/27.41 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3939,b,3876,a)].
% 27.45/27.41 Derived: -class_Power_Orecpower(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3939,b,3877,b)].
% 27.45/27.41 3940 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_lessequals(B,c_0,A) | B = c_0 # label(cls_Parity_Opower__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 27.45/27.41 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint) | A = c_0. [resolve(3940,b,3876,a)].
% 27.45/27.41 Derived: -class_Power_Orecpower(A) | -c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_lessequals(B,c_0,A) | B = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3940,b,3877,b)].
% 27.45/27.41 3941 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(C,tc_nat) = c_0 # label(cls_Parity_Opower__le__zero__eq__number__of_4) # label(axiom). [assumption].
% 27.45/27.41 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_Numeral_Onumber__of(B,tc_nat) = c_0. [resolve(3941,b,3876,a)].
% 27.45/27.41 Derived: -class_Power_Orecpower(A) | -c_lessequals(B,c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(C,tc_nat) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3941,b,3877,b)].
% 27.45/27.41 3942 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 # label(cls_Parity_Opower__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 27.45/27.41 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_nat) = c_0. [resolve(3942,b,3876,a)].
% 27.45/27.41 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3942,b,3877,b)].
% 27.45/27.42 3943 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_less(c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) # label(cls_Parity_Opower__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_less(c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3943,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_less(c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3943,b,3877,b)].
% 27.45/27.42 3944 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_less(B,c_0,A) # label(cls_Parity_Opower__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(3944,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_less(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3944,b,3877,b)].
% 27.45/27.42 3945 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) # label(cls_Parity_Opower__less__zero__eq__number__of_2) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3945,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_less(B,c_0,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3945,b,3877,b)].
% 27.45/27.42 3946 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_0,B,A) # label(cls_Parity_Ozero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(c_0,c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3946,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_lessequals(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_0,B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3946,b,3877,b)].
% 27.45/27.42 3947 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) # label(cls_Parity_Ozero__le__power__eq__number__of_1) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3947,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3947,b,3877,b)].
% 27.45/27.42 3948 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) # label(cls_Parity_Ozero__le__power__eq__number__of_2) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3948,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_lessequals(c_0,B,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3948,b,3877,b)].
% 27.45/27.42 3949 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_0,B,A) | c_Numeral_Onumber__of(C,tc_nat) = c_0 # label(cls_Parity_Ozero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_0,A,tc_IntDef_Oint) | c_Numeral_Onumber__of(B,tc_nat) = c_0. [resolve(3949,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_0,B,A) | c_Numeral_Onumber__of(C,tc_nat) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3949,b,3877,b)].
% 27.45/27.42 3950 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 # label(cls_Parity_Ozero__less__power__eq__number__of_1) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_nat) = c_0. [resolve(3950,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3950,b,3877,b)].
% 27.45/27.42 3951 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),A) | c_less(c_0,c_0,A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 # label(cls_Parity_Ozero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_0,tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_nat) = c_0. [resolve(3951,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | -c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(B,tc_nat),A),A) | c_less(c_0,c_0,A) | c_Numeral_Onumber__of(B,tc_nat) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3951,b,3877,b)].
% 27.45/27.42 3952 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_Numeral_Onumber__of(B,tc_nat) != c_0 | c_less(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) # label(cls_Parity_Ozero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 27.45/27.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_nat) != c_0 | c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3952,b,3876,a)].
% 27.45/27.42 Derived: -class_Power_Orecpower(A) | c_Numeral_Onumber__of(B,tc_nat) != c_0 | c_less(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3952,b,3877,b)].
% 27.45/27.42 3953 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) | C = c_0 # label(cls_Parity_Ozero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) | B = c_0. [resolve(3953,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(C,c_Numeral_Onumber__of(B,tc_nat),A),A) | C = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3953,b,3877,b)].
% 27.45/27.43 3954 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) # label(cls_Parity_Ozero__less__power__eq__number__of_5) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | c_Parity_Oeven(c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3954,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | -c_less(c_0,B,A) | c_Parity_Oeven(c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_0,c_Nat_Opower(B,c_Numeral_Onumber__of(C,tc_nat),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3954,b,3877,b)].
% 27.45/27.43 3955 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Opower(B,C,A) != c_0 | B = c_0 # label(cls_Power_Opower__eq__0__iff_0) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(A,B,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3955,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(B,C,A) != c_0 | B = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3955,b,3877,b)].
% 27.45/27.43 3956 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Opower(B,C,A) != c_0 | c_less(c_0,C,tc_nat) # label(cls_Power_Opower__eq__0__iff_1) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(A,B,tc_IntDef_Oint) != c_0 | c_less(c_0,B,tc_nat). [resolve(3956,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(B,C,A) != c_0 | c_less(c_0,C,tc_nat) | -class_Ring__and__Field_Oordered__field(A). [resolve(3956,b,3877,b)].
% 27.45/27.43 3957 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,tc_nat) | c_Nat_Opower(c_0,B,A) = c_0 # label(cls_Power_Opower__eq__0__iff_2) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,A,tc_nat) | c_Nat_Opower(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3957,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | -c_less(c_0,B,tc_nat) | c_Nat_Opower(c_0,B,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3957,b,3877,b)].
% 27.45/27.43 3958 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),C,A),A) # label(cls_Power_Ozero__le__power__abs_0) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3958,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),C,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3958,b,3877,b)].
% 27.45/27.43 3959 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,A),B,A),A) | B = c_0 # label(cls_Power_Ozero__less__power__abs__iff_0) # label(axiom). [assumption].
% 27.45/27.43 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3959,b,3876,a)].
% 27.45/27.43 Derived: -class_Power_Orecpower(A) | -c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,A),B,A),A) | B = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3959,b,3877,b)].
% 27.45/27.43 3960 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),C,A),A) | B = c_0 # label(cls_Power_Ozero__less__power__abs__iff_1) # label(axiom). [assumption].
% 27.45/27.45 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3960,b,3876,a)].
% 27.45/27.45 Derived: -class_Power_Orecpower(A) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),C,A),A) | B = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3960,b,3877,b)].
% 27.45/27.45 3961 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),c_0,A),A) # label(cls_Power_Ozero__less__power__abs__iff_2) # label(axiom). [assumption].
% 27.45/27.45 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3961,b,3876,a)].
% 27.45/27.45 Derived: -class_Power_Orecpower(A) | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(B,A),c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3961,b,3877,b)].
% 27.45/27.45 3962 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_1,A) = c_1 # label(cls_Ring__and__Field_Oabs__one_0) # label(axiom). [assumption].
% 27.45/27.45 Derived: c_HOL_Oabs(c_1,tc_IntDef_Oint) = c_1. [resolve(3962,a,3876,a)].
% 27.45/27.45 Derived: c_HOL_Oabs(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3962,a,3877,b)].
% 27.45/27.45 3963 -class_Ring__and__Field_Oordered__idom(A) | B != c_times(B,C,A) | B = c_0 | C = c_1 # label(cls_Ring__and__Field_Omult__cancel__left1_0) # label(axiom). [assumption].
% 27.45/27.45 Derived: A != c_times(A,B,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3963,a,3876,a)].
% 27.45/27.45 Derived: A != c_times(A,B,C) | A = c_0 | B = c_1 | -class_Ring__and__Field_Oordered__field(C). [resolve(3963,a,3877,b)].
% 27.45/27.45 3964 -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_times(c_0,B,A) # label(cls_Ring__and__Field_Omult__cancel__left1_1) # label(axiom). [assumption].
% 27.45/27.45 Derived: c_0 = c_times(c_0,A,tc_IntDef_Oint). [resolve(3964,a,3876,a)].
% 27.45/27.45 Derived: c_0 = c_times(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3964,a,3877,b)].
% 27.45/27.45 3965 -class_Ring__and__Field_Oordered__idom(A) | B = c_times(B,c_1,A) # label(cls_Ring__and__Field_Omult__cancel__left1_2) # label(axiom). [assumption].
% 27.45/27.45 Derived: A = c_times(A,c_1,tc_IntDef_Oint). [resolve(3965,a,3876,a)].
% 27.45/27.45 Derived: A = c_times(A,c_1,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3965,a,3877,b)].
% 27.45/27.45 3966 -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != B | B = c_0 | C = c_1 # label(cls_Ring__and__Field_Omult__cancel__left2_0) # label(axiom). [assumption].
% 27.45/27.45 Derived: c_times(A,B,tc_IntDef_Oint) != A | A = c_0 | B = c_1. [resolve(3966,a,3876,a)].
% 27.45/27.45 Derived: c_times(A,B,C) != A | A = c_0 | B = c_1 | -class_Ring__and__Field_Oordered__field(C). [resolve(3966,a,3877,b)].
% 27.45/27.45 3967 -class_Ring__and__Field_Oordered__idom(A) | B != c_times(C,B,A) | B = c_0 | C = c_1 # label(cls_Ring__and__Field_Omult__cancel__right1_0) # label(axiom). [assumption].
% 27.45/27.45 Derived: A != c_times(B,A,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3967,a,3876,a)].
% 27.45/27.45 Derived: A != c_times(B,A,C) | A = c_0 | B = c_1 | -class_Ring__and__Field_Oordered__field(C). [resolve(3967,a,3877,b)].
% 27.45/27.45 3968 -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_times(B,c_0,A) # label(cls_Ring__and__Field_Omult__cancel__right1_1) # label(axiom). [assumption].
% 27.45/27.45 Derived: c_0 = c_times(A,c_0,tc_IntDef_Oint). [resolve(3968,a,3876,a)].
% 27.45/27.45 Derived: c_0 = c_times(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3968,a,3877,b)].
% 27.45/27.45 3969 -class_Ring__and__Field_Oordered__idom(A) | B = c_times(c_1,B,A) # label(cls_Ring__and__Field_Omult__cancel__right1_2) # label(axiom). [assumption].
% 27.45/27.45 Derived: A = c_times(c_1,A,tc_IntDef_Oint). [resolve(3969,a,3876,a)].
% 27.45/27.45 Derived: A = c_times(c_1,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3969,a,3877,b)].
% 27.45/27.45 3970 -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != C | C = c_0 | B = c_1 # label(cls_Ring__and__Field_Omult__cancel__right2_0) # label(axiom). [assumption].
% 27.45/27.45 Derived: c_times(A,B,tc_IntDef_Oint) != B | B = c_0 | A = c_1. [resolve(3970,a,3876,a)].
% 27.45/27.45 Derived: c_times(A,B,C) != B | B = c_0 | A = c_1 | -class_Ring__and__Field_Oordered__field(C). [resolve(3970,a,3877,b)].
% 27.54/27.49 3971 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 27.54/27.49 3972 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 27.54/27.49 3973 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(34,a,22,b)].
% 27.54/27.49 3974 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(35,a,22,b)].
% 27.54/27.49 3975 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(36,a,22,b)].
% 27.54/27.49 3976 -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(37,a,22,b)].
% 27.54/27.49 3977 -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(38,a,22,b)].
% 27.54/27.49 3978 -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(39,a,22,b)].
% 27.54/27.49 3979 -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(40,a,22,b)].
% 27.54/27.49 3980 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(41,a,22,b)].
% 27.54/27.49 3981 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(42,a,22,b)].
% 27.54/27.49 3982 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(43,a,57,b)].
% 27.54/27.49 3983 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(63,a,57,b)].
% 27.54/27.49 3984 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(64,a,57,b)].
% 27.54/27.49 3985 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(65,a,57,b)].
% 27.54/27.49 3986 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(66,a,57,b)].
% 27.54/27.49 3987 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(67,a,57,b)].
% 27.54/27.49 3988 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(68,a,57,b)].
% 27.54/27.49 3989 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(69,a,57,b)].
% 27.54/27.49 3990 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(70,a,57,b)].
% 27.54/27.49 3991 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 27.54/27.49 3992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 27.54/27.49 3993 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 27.54/27.49 3994 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(108,b,88,b)].
% 27.54/27.49 3995 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(109,b,88,b)].
% 27.54/27.51 3996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 27.54/27.51 3997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 27.54/27.51 3998 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(221,c,201,b)].
% 27.54/27.51 3999 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(222,c,201,b)].
% 27.54/27.51 4000 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 27.54/27.51 4001 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 27.54/27.51 4002 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 27.54/27.51 4003 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 27.54/27.51 4004 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(307,a,295,b)].
% 27.54/27.51 4005 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(308,a,295,b)].
% 27.54/27.51 4006 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 27.54/27.51 4007 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 27.54/27.51 4008 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 27.54/27.51 4009 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 27.54/27.51 4010 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(389,c,364,b)].
% 27.54/27.51 4011 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(390,c,364,b)].
% 27.54/27.51 4012 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 27.54/27.51 4013 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 27.54/27.51 4014 -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(413,b,402,b)].
% 27.54/27.51 4015 -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(414,b,402,b)].
% 27.54/27.51 4016 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(415,a,402,b)].
% 27.54/27.51 4017 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(416,a,402,b)].
% 27.54/27.51 4018 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(417,a,402,b)].
% 27.54/27.51 4019 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 27.54/27.51 4020 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(428,c,402,b)].
% 27.54/27.51 4021 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(429,c,402,b)].
% 27.54/27.51 4022 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 27.54/27.51 4023 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 27.54/27.51 4024 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 27.54/27.51 4025 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 27.54/27.54 4026 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 27.54/27.54 4027 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(442,c,402,b)].
% 27.54/27.54 4028 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(443,c,402,b)].
% 27.54/27.54 4029 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 27.54/27.54 4030 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 27.54/27.54 4031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 27.54/27.54 4032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 27.54/27.54 4033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 27.54/27.54 4034 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(637,d,622,b)].
% 27.54/27.54 4035 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(638,d,622,b)].
% 27.54/27.54 4036 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(639,d,622,b)].
% 27.54/27.54 4037 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(640,d,622,b)].
% 27.54/27.54 4038 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(641,d,622,b)].
% 27.54/27.54 4039 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(642,d,622,b)].
% 27.54/27.54 4040 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(643,d,622,b)].
% 27.54/27.54 4041 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(644,d,622,b)].
% 27.54/27.54 4042 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(645,d,622,b)].
% 27.54/27.54 4043 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 27.54/27.54 4044 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 27.54/27.54 4045 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 27.54/27.54 4046 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 27.54/27.54 4047 -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(830,c,791,b)].
% 27.54/27.54 4048 -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(831,c,791,b)].
% 27.54/27.54 4049 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(832,b,791,b)].
% 27.54/27.54 4050 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(833,b,791,b)].
% 27.54/27.54 4051 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(834,b,791,b)].
% 27.54/27.54 4052 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(837,d,791,b)].
% 27.54/27.54 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4052,d,3877,b)].
% 27.54/27.55 4053 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(838,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4053,d,3877,b)].
% 27.54/27.55 4054 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(839,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4054,d,3877,b)].
% 27.54/27.55 4055 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(840,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4055,d,3877,b)].
% 27.54/27.55 4056 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(841,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4056,d,3877,b)].
% 27.54/27.55 4057 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(842,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4057,d,3877,b)].
% 27.54/27.55 4058 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(843,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4058,d,3877,b)].
% 27.54/27.55 4059 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(844,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4059,d,3877,b)].
% 27.54/27.55 4060 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(845,d,791,b)].
% 27.54/27.55 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4060,d,3877,b)].
% 27.54/27.55 4061 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 27.54/27.55 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4061,b,3877,b)].
% 27.54/27.55 4062 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 27.54/27.55 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4062,b,3877,b)].
% 27.54/27.55 4063 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 27.54/27.55 4064 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 27.54/27.55 4065 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 27.54/27.55 4066 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 27.54/27.55 4067 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 27.63/27.57 4068 -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(871,a,867,b)].
% 27.63/27.57 4069 -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(872,a,867,b)].
% 27.63/27.57 4070 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(873,a,867,b)].
% 27.63/27.57 4071 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(874,a,867,b)].
% 27.63/27.57 4072 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 27.63/27.57 4073 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(876,a,867,b)].
% 27.63/27.57 4074 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(877,a,867,b)].
% 27.63/27.57 4075 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 27.63/27.57 4076 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 27.63/27.57 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4076,b,3877,b)].
% 27.63/27.57 4077 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 27.63/27.57 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4077,b,3877,b)].
% 27.63/27.57 4078 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(947,a,944,b)].
% 27.63/27.57 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4078,d,3877,b)].
% 27.63/27.57 4079 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(948,a,944,b)].
% 27.63/27.57 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4079,d,3877,b)].
% 27.63/27.57 4080 -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(949,a,944,b)].
% 27.63/27.57 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4080,c,3877,b)].
% 27.63/27.57 4081 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(950,a,944,b)].
% 27.63/27.57 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4081,d,3877,b)].
% 27.63/27.57 4082 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 27.63/27.57 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4082,b,3877,b)].
% 27.63/27.57 4083 c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(952,a,944,b)].
% 27.63/27.57 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4083,b,3877,b)].
% 27.63/27.57 4084 c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(953,a,944,b)].
% 27.63/27.57 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4084,b,3877,b)].
% 27.63/27.57 4085 c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(954,a,944,b)].
% 27.63/27.57 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4085,b,3877,b)].
% 27.64/27.59 4086 c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(955,a,944,b)].
% 27.64/27.59 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4086,b,3877,b)].
% 27.64/27.59 4087 c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(956,a,944,b)].
% 27.64/27.59 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4087,b,3877,b)].
% 27.64/27.59 4088 c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(957,a,944,b)].
% 27.64/27.59 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4088,b,3877,b)].
% 27.64/27.59 4089 -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(958,a,944,b)].
% 27.64/27.59 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4089,c,3877,b)].
% 27.64/27.59 4090 -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(959,b,944,b)].
% 27.64/27.59 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4090,c,3877,b)].
% 27.64/27.59 4091 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(960,b,944,b)].
% 27.64/27.59 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4091,d,3877,b)].
% 27.64/27.59 4092 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(961,b,944,b)].
% 27.64/27.59 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4092,d,3877,b)].
% 27.64/27.59 4093 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(962,b,944,b)].
% 27.64/27.59 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4093,d,3877,b)].
% 27.64/27.59 4094 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(963,b,944,b)].
% 27.64/27.59 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4094,d,3877,b)].
% 27.64/27.59 4095 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 27.64/27.59 4096 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 27.67/27.61 4097 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 27.67/27.61 4098 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 27.67/27.61 4099 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 27.67/27.61 4100 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 27.67/27.61 4101 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1164,c,1143,b)].
% 27.67/27.61 4102 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1165,b,1143,b)].
% 27.67/27.61 4103 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1166,c,1143,b)].
% 27.67/27.61 4104 -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(1167,c,1143,b)].
% 27.67/27.61 4105 -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(1168,c,1143,b)].
% 27.67/27.61 4106 -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(1169,c,1143,b)].
% 27.67/27.61 4107 -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(1170,c,1143,b)].
% 27.67/27.61 4108 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1171,c,1143,b)].
% 27.67/27.61 4109 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(1172,b,1143,b)].
% 27.67/27.61 4110 -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(1185,a,1180,b)].
% 27.67/27.61 4111 -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(1186,a,1180,b)].
% 27.67/27.61 4112 -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(1187,a,1180,b)].
% 27.67/27.61 4113 -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(1188,a,1180,b)].
% 27.67/27.61 4114 -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(1189,a,1180,b)].
% 27.67/27.61 4115 -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(1190,a,1180,b)].
% 27.67/27.61 4116 -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(1191,a,1180,b)].
% 27.67/27.61 4117 -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(1192,a,1180,b)].
% 27.67/27.61 4118 -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(1193,a,1180,b)].
% 27.67/27.61 4119 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1194,a,1180,b)].
% 27.67/27.61 4120 -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(1195,a,1180,b)].
% 27.68/27.63 4121 -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(1196,a,1180,b)].
% 27.68/27.63 4122 -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(1197,a,1180,b)].
% 27.68/27.63 4123 -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(1198,a,1180,b)].
% 27.68/27.63 4124 -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(1199,a,1180,b)].
% 27.68/27.63 4125 -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(1200,a,1180,b)].
% 27.68/27.63 4126 -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(1201,a,1180,b)].
% 27.68/27.63 4127 -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(1202,a,1180,b)].
% 27.68/27.63 4128 -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(1203,a,1180,b)].
% 27.68/27.63 4129 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1204,a,1180,b)].
% 27.68/27.63 4130 -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(1205,a,1180,b)].
% 27.68/27.63 4131 -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(1206,a,1180,b)].
% 27.68/27.63 4132 -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(1207,a,1180,b)].
% 27.68/27.63 4133 -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(1208,b,1180,b)].
% 27.68/27.63 4134 -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(1209,b,1180,b)].
% 27.68/27.63 4135 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1210,a,1180,b)].
% 27.68/27.63 4136 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1211,a,1180,b)].
% 27.68/27.63 4137 -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(1212,a,1180,b)].
% 27.68/27.63 4138 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1213,a,1180,b)].
% 27.68/27.63 4139 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1214,a,1180,b)].
% 27.68/27.63 4140 -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(1215,a,1180,b)].
% 27.68/27.63 4141 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1216,a,1180,b)].
% 27.68/27.63 4142 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1217,a,1180,b)].
% 27.68/27.63 4143 -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(1218,a,1180,b)].
% 27.68/27.65 4144 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 27.68/27.65 4145 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(1220,a,1180,b)].
% 27.68/27.65 4146 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1221,a,1180,b)].
% 27.68/27.65 4147 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1222,a,1180,b)].
% 27.68/27.65 4148 -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(1223,a,1180,b)].
% 27.68/27.65 4149 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 27.68/27.65 4150 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(1225,a,1180,b)].
% 27.68/27.65 4151 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1180,b)].
% 27.68/27.65 4152 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1227,a,1180,b)].
% 27.68/27.65 4153 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1228,a,1180,b)].
% 27.68/27.65 4154 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1229,a,1180,b)].
% 27.68/27.65 4155 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1230,a,1180,b)].
% 27.68/27.65 4156 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1231,a,1180,b)].
% 27.68/27.65 4157 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1232,a,1180,b)].
% 27.68/27.65 4158 -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(1233,a,1180,b)].
% 27.68/27.65 4159 -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(1234,a,1180,b)].
% 27.68/27.65 4160 -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(1235,a,1180,b)].
% 27.68/27.65 4161 -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(1236,a,1180,b)].
% 27.68/27.65 4162 -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(1237,a,1180,b)].
% 27.68/27.65 4163 -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(1238,a,1180,b)].
% 27.68/27.65 4164 -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(1239,a,1180,b)].
% 27.68/27.65 4165 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1240,a,1180,b)].
% 27.68/27.65 4166 -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(1241,a,1180,b)].
% 27.68/27.65 4167 -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(1242,a,1180,b)].
% 27.68/27.65 4168 -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(1362,a,1357,b)].
% 27.68/27.69 4169 -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(1363,a,1357,b)].
% 27.68/27.69 4170 -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(1364,a,1357,b)].
% 27.68/27.69 4171 -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(1365,a,1357,b)].
% 27.68/27.69 4172 -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(1366,a,1357,b)].
% 27.68/27.69 4173 -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(1367,a,1357,b)].
% 27.68/27.69 4174 -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(1368,a,1357,b)].
% 27.68/27.69 4175 -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(1369,a,1357,b)].
% 27.68/27.69 4176 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 27.68/27.69 4177 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 27.68/27.69 4178 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 27.68/27.69 4179 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1389,c,1357,b)].
% 27.68/27.69 4180 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1390,b,1357,b)].
% 27.68/27.69 4181 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1391,c,1357,b)].
% 27.68/27.69 4182 -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(1392,c,1357,b)].
% 27.68/27.69 4183 -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(1393,c,1357,b)].
% 27.68/27.69 4184 -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(1394,c,1357,b)].
% 27.68/27.69 4185 -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(1395,c,1357,b)].
% 27.68/27.69 4186 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1396,c,1357,b)].
% 27.68/27.69 4187 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(1397,b,1357,b)].
% 27.68/27.69 4188 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1398,c,1357,b)].
% 27.68/27.69 4189 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1399,c,1357,b)].
% 27.68/27.69 4190 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 27.68/27.69 4191 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 27.68/27.69 4192 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 27.68/27.69 4193 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 27.68/27.69 4194 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 27.68/27.69 4195 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1633,c,1588,b)].
% 27.68/27.69 4196 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1634,b,1588,b)].
% 27.68/27.69 4197 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1635,c,1588,b)].
% 27.68/27.69 4198 -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(1636,c,1588,b)].
% 27.68/27.71 4199 -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(1637,c,1588,b)].
% 27.68/27.71 4200 -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(1638,c,1588,b)].
% 27.68/27.71 4201 -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(1639,c,1588,b)].
% 27.68/27.71 4202 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1640,c,1588,b)].
% 27.68/27.71 4203 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(1641,b,1588,b)].
% 27.68/27.71 4204 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 27.68/27.71 4205 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(1643,c,1588,b)].
% 27.68/27.71 4206 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(1644,c,1588,b)].
% 27.68/27.71 4207 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 27.68/27.71 4208 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 27.68/27.71 4209 -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(1706,e,1653,b)].
% 27.68/27.71 4210 -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(1707,d,1653,b)].
% 27.68/27.71 4211 -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(1708,d,1653,b)].
% 27.68/27.71 4212 -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(1709,f,1653,b)].
% 27.68/27.71 4213 -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(1710,e,1653,b)].
% 27.68/27.71 4214 -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(1711,e,1653,b)].
% 27.68/27.71 4215 -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(1712,f,1653,b)].
% 27.68/27.71 4216 -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(1713,e,1653,b)].
% 27.68/27.71 4217 -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(1714,e,1653,b)].
% 27.68/27.71 4218 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1715,b,1653,b)].
% 27.68/27.71 4219 -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(1716,f,1653,b)].
% 27.68/27.71 4220 -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(1717,e,1653,b)].
% 27.79/27.72 4221 -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(1718,e,1653,b)].
% 27.79/27.72 4222 -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(1719,f,1653,b)].
% 27.79/27.72 4223 -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(1720,e,1653,b)].
% 27.79/27.72 4224 -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(1721,e,1653,b)].
% 27.79/27.72 4225 -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(1722,d,1653,b)].
% 27.79/27.72 4226 -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(1723,d,1653,b)].
% 27.79/27.72 4227 -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(1724,e,1653,b)].
% 27.79/27.72 4228 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1725,b,1653,b)].
% 27.79/27.72 4229 -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(1726,d,1653,b)].
% 27.79/27.72 4230 -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(1727,e,1653,b)].
% 27.79/27.72 4231 -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(1728,e,1653,b)].
% 27.79/27.72 4232 -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(1729,d,1653,b)].
% 27.79/27.72 4233 -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(1730,d,1653,b)].
% 27.79/27.72 4234 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1731,c,1653,b)].
% 27.79/27.72 4235 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1732,c,1653,b)].
% 27.79/27.72 4236 -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(1733,d,1653,b)].
% 27.79/27.72 4237 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1734,c,1653,b)].
% 27.79/27.72 4238 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1735,c,1653,b)].
% 27.79/27.72 4239 -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(1736,d,1653,b)].
% 27.79/27.72 4240 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1737,c,1653,b)].
% 27.79/27.72 4241 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1738,c,1653,b)].
% 27.79/27.72 4242 -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(1739,d,1653,b)].
% 27.79/27.72 4243 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 27.79/27.72 4244 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(1741,b,1653,b)].
% 27.79/27.73 4245 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1742,c,1653,b)].
% 27.79/27.73 4246 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1743,c,1653,b)].
% 27.79/27.73 4247 -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(1744,d,1653,b)].
% 27.79/27.73 4248 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 27.79/27.73 4249 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(1746,b,1653,b)].
% 27.79/27.73 4250 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1747,b,1653,b)].
% 27.79/27.73 4251 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1748,b,1653,b)].
% 27.79/27.73 4252 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1749,b,1653,b)].
% 27.79/27.73 4253 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1750,b,1653,b)].
% 27.79/27.73 4254 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1751,c,1653,b)].
% 27.79/27.73 4255 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1752,c,1653,b)].
% 27.79/27.73 4256 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1753,c,1653,b)].
% 27.79/27.73 4257 -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(1754,c,1653,b)].
% 27.79/27.73 4258 -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(1755,c,1653,b)].
% 27.79/27.73 4259 -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(1756,c,1653,b)].
% 27.79/27.73 4260 -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(1757,d,1653,b)].
% 27.79/27.73 4261 -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(1758,d,1653,b)].
% 27.79/27.73 4262 -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(1759,c,1653,b)].
% 27.79/27.74 4263 -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(1760,d,1653,b)].
% 27.79/27.74 4264 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1761,c,1653,b)].
% 27.79/27.74 4265 -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(1762,c,1653,b)].
% 27.79/27.74 4266 -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(1763,c,1653,b)].
% 27.79/27.74 4267 -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(1765,c,1653,b)].
% 27.79/27.74 4268 -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(1766,c,1653,b)].
% 27.79/27.75 4269 -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(1767,c,1653,b)].
% 27.79/27.75 4270 -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(1768,c,1653,b)].
% 27.79/27.75 4271 -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(1769,c,1653,b)].
% 27.79/27.75 4272 -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(1770,c,1653,b)].
% 27.79/27.75 4273 -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(1771,c,1653,b)].
% 27.79/27.75 4274 -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(1772,c,1653,b)].
% 27.79/27.75 4275 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 27.79/27.75 4276 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1786,c,1653,b)].
% 27.79/27.75 4277 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1787,c,1653,b)].
% 27.79/27.75 4278 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 27.79/27.75 4279 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 27.79/27.75 4280 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 27.79/27.75 4281 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 27.79/27.75 4282 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 27.79/27.75 4283 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 27.79/27.75 4284 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 27.79/27.75 4285 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1800,c,1653,b)].
% 27.79/27.75 4286 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1801,b,1653,b)].
% 27.79/27.75 4287 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1802,c,1653,b)].
% 27.79/27.75 4288 -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(1803,c,1653,b)].
% 27.79/27.75 4289 -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(1804,c,1653,b)].
% 27.79/27.75 4290 -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(1805,c,1653,b)].
% 27.79/27.75 4291 -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(1806,c,1653,b)].
% 27.79/27.75 4292 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1807,c,1653,b)].
% 27.79/27.75 4293 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(1808,b,1653,b)].
% 27.79/27.75 4294 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 27.79/27.75 4295 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(1810,c,1653,b)].
% 27.79/27.75 4296 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(1811,c,1653,b)].
% 27.79/27.75 4297 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 27.86/27.80 4298 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 27.86/27.80 4299 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 27.86/27.80 4300 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2233,a,2231,b)].
% 27.86/27.80 4301 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2234,a,2231,b)].
% 27.86/27.80 4302 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2235,a,2231,b)].
% 27.86/27.80 4303 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2236,a,2231,b)].
% 27.86/27.80 4304 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2237,a,2231,b)].
% 27.86/27.80 4305 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2238,a,2231,b)].
% 27.86/27.80 4306 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2239,a,2231,b)].
% 27.86/27.80 4307 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2240,a,2231,b)].
% 27.86/27.80 4308 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 27.86/27.80 4309 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2242,a,2231,b)].
% 27.86/27.80 4310 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2243,a,2231,b)].
% 27.86/27.80 4311 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 27.86/27.80 4312 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2245,a,2231,b)].
% 27.86/27.80 4313 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 27.86/27.80 4314 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2247,a,2231,b)].
% 27.86/27.80 4315 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2248,a,2231,b)].
% 27.86/27.80 4316 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2249,a,2231,b)].
% 27.86/27.80 4317 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2250,a,2231,b)].
% 27.86/27.80 4318 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2251,a,2231,b)].
% 27.86/27.80 4319 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 27.86/27.80 4320 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 27.86/27.80 4321 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 27.86/27.80 4322 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2414,a,2424,b)].
% 27.86/27.80 4323 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2429,a,2424,b)].
% 27.86/27.80 4324 -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(2430,a,2424,b)].
% 27.86/27.80 4325 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2431,a,2424,b)].
% 27.86/27.80 4326 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2432,a,2424,b)].
% 27.86/27.80 4327 -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(2433,a,2424,b)].
% 27.86/27.84 4328 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2434,a,2424,b)].
% 27.86/27.84 4329 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2435,a,2424,b)].
% 27.86/27.84 4330 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2436,a,2424,b)].
% 27.86/27.84 4331 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2437,a,2424,b)].
% 27.86/27.84 4332 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2438,a,2424,b)].
% 27.86/27.84 4333 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2439,a,2424,b)].
% 27.86/27.84 4334 -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(2440,a,2424,b)].
% 27.86/27.84 4335 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2441,a,2424,b)].
% 27.86/27.84 4336 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2442,a,2424,b)].
% 27.86/27.84 4337 -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(2443,a,2424,b)].
% 27.86/27.84 4338 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2444,a,2424,b)].
% 27.86/27.84 4339 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2445,a,2424,b)].
% 27.86/27.84 4340 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2446,a,2424,b)].
% 27.86/27.84 4341 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2447,a,2424,b)].
% 27.86/27.84 4342 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 27.86/27.84 4343 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 27.86/27.84 4344 c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2519,a,2515,b)].
% 27.86/27.84 4345 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 27.86/27.84 4346 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 27.86/27.84 4347 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 27.86/27.84 4348 c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2523,a,2515,b)].
% 27.86/27.84 4349 -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2524,a,2515,b)].
% 27.86/27.84 4350 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 27.86/27.84 4351 c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2526,a,2515,b)].
% 27.86/27.84 4352 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 27.86/27.84 4353 -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2528,a,2515,b)].
% 27.86/27.84 4354 -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2529,a,2515,b)].
% 27.86/27.84 4355 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 27.86/27.84 4356 c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2531,a,2515,b)].
% 27.86/27.84 4357 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 27.86/27.84 4358 -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(2975,c,2849,b)].
% 27.86/27.85 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(4358,c,3876,a)].
% 27.86/27.85 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(4358,c,3877,b)].
% 27.86/27.85 4359 -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(2976,c,2849,b)].
% 27.86/27.85 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(4359,c,3876,a)].
% 27.86/27.85 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(4359,c,3877,b)].
% 27.86/27.85 4360 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2977,b,2849,b)].
% 27.86/27.85 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(4360,b,3876,a)].
% 27.86/27.85 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(4360,b,3877,b)].
% 27.86/27.85 4361 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2978,b,2849,b)].
% 27.86/27.85 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(4361,b,3876,a)].
% 27.86/27.85 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(4361,b,3877,b)].
% 27.86/27.85 4362 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2979,b,2849,b)].
% 27.86/27.85 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(4362,b,3876,a)].
% 27.86/27.85 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(4362,b,3877,b)].
% 27.86/27.85 4363 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 27.86/27.85 4364 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 27.86/27.85 4365 -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(2982,c,2849,b)].
% 27.86/27.85 4366 -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(2983,c,2849,b)].
% 27.86/27.85 4367 -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(2984,c,2849,b)].
% 27.86/27.85 4368 -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(2985,c,2849,b)].
% 27.86/27.85 4369 -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(2986,c,2849,b)].
% 27.86/27.85 4370 -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(2987,c,2849,b)].
% 27.86/27.85 4371 -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(2988,c,2849,b)].
% 27.86/27.85 4372 -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(2989,c,2849,b)].
% 27.86/27.85 4373 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 27.86/27.87 4374 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2991,c,2849,b)].
% 27.86/27.87 4375 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2992,c,2849,b)].
% 27.86/27.87 4376 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 27.86/27.87 4377 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 27.86/27.87 4378 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2995,c,2849,b)].
% 27.86/27.87 4379 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2996,b,2849,b)].
% 27.86/27.87 4380 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2997,c,2849,b)].
% 27.86/27.87 4381 -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(2998,c,2849,b)].
% 27.86/27.87 4382 -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(2999,c,2849,b)].
% 27.86/27.87 4383 -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(3000,c,2849,b)].
% 27.86/27.87 4384 -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(3001,c,2849,b)].
% 27.86/27.87 4385 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3002,c,2849,b)].
% 27.86/27.87 4386 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(3003,b,2849,b)].
% 27.86/27.87 4387 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 27.86/27.87 4388 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(3005,c,2849,b)].
% 27.86/27.87 4389 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(3006,c,2849,b)].
% 27.86/27.87 4390 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 27.86/27.87 4391 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 27.86/27.87 4392 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3052,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(4392,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4392,e,3877,b)].
% 27.86/27.87 4393 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3053,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(4393,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4393,e,3877,b)].
% 27.86/27.87 4394 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3054,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4394,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4394,e,3877,b)].
% 27.86/27.87 4395 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3055,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4395,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4395,e,3877,b)].
% 27.86/27.87 4396 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3056,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4396,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4396,e,3877,b)].
% 27.86/27.87 4397 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3057,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4397,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4397,e,3877,b)].
% 27.86/27.87 4398 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3058,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(4398,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4398,e,3877,b)].
% 27.86/27.87 4399 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3059,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(4399,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4399,e,3877,b)].
% 27.86/27.87 4400 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3060,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4400,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4400,e,3877,b)].
% 27.86/27.87 4401 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3061,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(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(4401,e,3876,a)].
% 27.86/27.87 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4401,e,3877,b)].
% 27.86/27.87 4402 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3062,b,3047,b)].
% 27.86/27.87 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(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(4402,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4402,e,3877,b)].
% 27.86/27.88 4403 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3063,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4403,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4403,e,3877,b)].
% 27.86/27.88 4404 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3064,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(4404,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4404,e,3877,b)].
% 27.86/27.88 4405 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3065,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,B,tc_IntDef_Oint). [resolve(4405,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4405,e,3877,b)].
% 27.86/27.88 4406 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3066,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4406,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4406,e,3877,b)].
% 27.86/27.88 4407 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3067,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4407,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4407,e,3877,b)].
% 27.86/27.88 4408 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3068,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4408,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4408,e,3877,b)].
% 27.86/27.88 4409 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3069,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4409,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4409,e,3877,b)].
% 27.86/27.88 4410 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3070,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(4410,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4410,e,3877,b)].
% 27.86/27.88 4411 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3071,b,3047,b)].
% 27.86/27.88 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint). [resolve(4411,e,3876,a)].
% 27.86/27.88 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4411,e,3877,b)].
% 27.86/27.88 4412 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3072,b,3047,b)].
% 27.97/27.89 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(4412,e,3876,a)].
% 27.97/27.89 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4412,e,3877,b)].
% 27.97/27.89 4413 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3073,b,3047,b)].
% 27.97/27.89 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4413,e,3876,a)].
% 27.97/27.89 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4413,e,3877,b)].
% 27.97/27.89 4414 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3074,b,3047,b)].
% 27.97/27.89 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4414,e,3876,a)].
% 27.97/27.89 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4414,e,3877,b)].
% 27.97/27.89 4415 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3075,b,3047,b)].
% 27.97/27.89 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4415,e,3876,a)].
% 27.97/27.89 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4415,e,3877,b)].
% 27.97/27.89 4416 c_times(A,B,C) != c_0 | B = c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(C). [resolve(3076,a,3047,b)].
% 27.97/27.89 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(4416,d,3876,a)].
% 27.97/27.89 Derived: c_times(A,B,C) != c_0 | B = c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(C). [resolve(4416,d,3877,b)].
% 27.97/27.89 4417 -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(3239,e,3047,b)].
% 27.97/27.89 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(4417,e,3876,a)].
% 27.97/27.89 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(4417,e,3877,b)].
% 27.97/27.90 4418 -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(3240,d,3047,b)].
% 27.97/27.90 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(4418,d,3876,a)].
% 27.97/27.90 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(4418,d,3877,b)].
% 27.97/27.90 4419 -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(3241,d,3047,b)].
% 27.97/27.90 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(4419,d,3876,a)].
% 27.97/27.90 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(4419,d,3877,b)].
% 27.97/27.90 4420 -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(3242,f,3047,b)].
% 27.97/27.90 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(4420,f,3876,a)].
% 27.97/27.90 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(4420,f,3877,b)].
% 27.97/27.90 4421 -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(3243,e,3047,b)].
% 27.97/27.90 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(4421,e,3876,a)].
% 27.97/27.90 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(4421,e,3877,b)].
% 27.97/27.90 4422 -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(3244,e,3047,b)].
% 27.97/27.90 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(4422,e,3876,a)].
% 27.97/27.90 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(4422,e,3877,b)].
% 27.97/27.90 4423 -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(3245,f,3047,b)].
% 27.97/27.90 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(4423,f,3876,a)].
% 27.97/27.90 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(4423,f,3877,b)].
% 27.97/27.90 4424 -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(3246,e,3047,b)].
% 27.97/27.90 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(4424,e,3876,a)].
% 27.97/27.90 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(4424,e,3877,b)].
% 27.97/27.90 4425 -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(3247,e,3047,b)].
% 27.97/27.90 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(4425,e,3876,a)].
% 27.97/27.90 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(4425,e,3877,b)].
% 27.97/27.90 4426 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3248,b,3047,b)].
% 27.97/27.90 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4426,b,3876,a)].
% 27.97/27.90 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4426,b,3877,b)].
% 27.97/27.90 4427 -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(3249,f,3047,b)].
% 27.97/27.90 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(4427,f,3876,a)].
% 27.97/27.90 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(4427,f,3877,b)].
% 27.97/27.90 4428 -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(3250,e,3047,b)].
% 27.97/27.90 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(4428,e,3876,a)].
% 27.97/27.90 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(4428,e,3877,b)].
% 27.97/27.90 4429 -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(3251,e,3047,b)].
% 27.97/27.90 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(4429,e,3876,a)].
% 27.97/27.90 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(4429,e,3877,b)].
% 27.97/27.90 4430 -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(3252,f,3047,b)].
% 27.97/27.91 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(4430,f,3876,a)].
% 27.97/27.91 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(4430,f,3877,b)].
% 27.97/27.91 4431 -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(3253,e,3047,b)].
% 27.97/27.91 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(4431,e,3876,a)].
% 27.97/27.91 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(4431,e,3877,b)].
% 27.97/27.91 4432 -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(3254,e,3047,b)].
% 27.97/27.91 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(4432,e,3876,a)].
% 27.97/27.91 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(4432,e,3877,b)].
% 27.97/27.91 4433 -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(3255,d,3047,b)].
% 27.97/27.91 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(4433,d,3876,a)].
% 27.97/27.91 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(4433,d,3877,b)].
% 27.97/27.91 4434 -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(3256,d,3047,b)].
% 27.97/27.91 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(4434,d,3876,a)].
% 27.97/27.91 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(4434,d,3877,b)].
% 27.97/27.91 4435 -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(3257,e,3047,b)].
% 27.97/27.91 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(4435,e,3876,a)].
% 27.97/27.91 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(4435,e,3877,b)].
% 27.97/27.91 4436 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3258,b,3047,b)].
% 27.97/27.91 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4436,b,3876,a)].
% 27.97/27.91 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4436,b,3877,b)].
% 27.97/27.91 4437 -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(3259,d,3047,b)].
% 27.97/27.91 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(4437,d,3876,a)].
% 27.97/27.91 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(4437,d,3877,b)].
% 27.97/27.91 4438 -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(3260,e,3047,b)].
% 27.97/27.91 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(4438,e,3876,a)].
% 27.97/27.91 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(4438,e,3877,b)].
% 27.97/27.91 4439 -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(3261,e,3047,b)].
% 27.97/27.91 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(4439,e,3876,a)].
% 27.97/27.91 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(4439,e,3877,b)].
% 27.97/27.91 4440 -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(3262,d,3047,b)].
% 27.97/27.91 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(4440,d,3876,a)].
% 27.97/27.91 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(4440,d,3877,b)].
% 27.97/27.91 4441 -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(3263,d,3047,b)].
% 27.97/27.91 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(4441,d,3876,a)].
% 27.97/27.91 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(4441,d,3877,b)].
% 27.97/27.91 4442 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3264,c,3047,b)].
% 27.97/27.91 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(4442,c,3876,a)].
% 27.97/27.91 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4442,c,3877,b)].
% 27.97/27.91 4443 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3265,c,3047,b)].
% 27.97/27.91 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(4443,c,3876,a)].
% 27.97/27.91 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4443,c,3877,b)].
% 27.97/27.91 4444 -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(3266,d,3047,b)].
% 27.97/27.91 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(4444,d,3876,a)].
% 27.97/27.91 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(4444,d,3877,b)].
% 27.97/27.92 4445 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3267,c,3047,b)].
% 27.97/27.92 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(4445,c,3876,a)].
% 27.97/27.92 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4445,c,3877,b)].
% 27.97/27.92 4446 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3268,c,3047,b)].
% 27.97/27.92 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(4446,c,3876,a)].
% 27.97/27.92 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4446,c,3877,b)].
% 27.97/27.92 4447 -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(3269,d,3047,b)].
% 27.97/27.92 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(4447,d,3876,a)].
% 27.97/27.92 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(4447,d,3877,b)].
% 27.97/27.92 4448 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3270,c,3047,b)].
% 27.97/27.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(4448,c,3876,a)].
% 27.97/27.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4448,c,3877,b)].
% 27.97/27.92 4449 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3271,c,3047,b)].
% 27.97/27.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(4449,c,3876,a)].
% 27.97/27.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4449,c,3877,b)].
% 27.97/27.92 4450 -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(3272,d,3047,b)].
% 27.97/27.92 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(4450,d,3876,a)].
% 27.97/27.92 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(4450,d,3877,b)].
% 27.97/27.92 4451 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 27.97/27.92 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(4451,b,3876,a)].
% 27.97/27.92 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4451,b,3877,b)].
% 27.97/27.92 4452 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(3274,b,3047,b)].
% 27.97/27.92 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(4452,b,3876,a)].
% 27.97/27.92 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(4452,b,3877,b)].
% 27.97/27.92 4453 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3275,c,3047,b)].
% 27.97/27.92 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(4453,c,3876,a)].
% 27.97/27.92 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4453,c,3877,b)].
% 27.97/27.92 4454 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3276,c,3047,b)].
% 27.97/27.92 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(4454,c,3876,a)].
% 27.97/27.92 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4454,c,3877,b)].
% 27.97/27.92 4455 -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(3277,d,3047,b)].
% 27.97/27.92 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(4455,d,3876,a)].
% 27.97/27.92 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(4455,d,3877,b)].
% 27.97/27.92 4456 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 27.97/27.92 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(4456,b,3876,a)].
% 27.97/27.92 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4456,b,3877,b)].
% 27.97/27.92 4457 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(3279,b,3047,b)].
% 27.97/27.93 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(4457,b,3876,a)].
% 27.97/27.93 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(4457,b,3877,b)].
% 27.97/27.93 4458 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3280,b,3047,b)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(4458,b,3876,a)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4458,b,3877,b)].
% 27.97/27.93 4459 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3281,b,3047,b)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(4459,b,3876,a)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4459,b,3877,b)].
% 27.97/27.93 4460 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3282,b,3047,b)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(4460,b,3876,a)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4460,b,3877,b)].
% 27.97/27.93 4461 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3283,b,3047,b)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(4461,b,3876,a)].
% 27.97/27.93 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4461,b,3877,b)].
% 27.97/27.93 4462 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3284,c,3047,b)].
% 27.97/27.93 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(4462,c,3876,a)].
% 27.97/27.93 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(4462,c,3877,b)].
% 27.97/27.93 4463 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3285,c,3047,b)].
% 27.97/27.93 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(4463,c,3876,a)].
% 27.97/27.93 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(4463,c,3877,b)].
% 27.97/27.93 4464 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3286,c,3047,b)].
% 27.97/27.93 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(4464,c,3876,a)].
% 27.97/27.93 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(4464,c,3877,b)].
% 27.97/27.93 4465 -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(3287,c,3047,b)].
% 27.97/27.93 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(4465,c,3876,a)].
% 27.97/27.93 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(4465,c,3877,b)].
% 27.97/27.93 4466 -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(3288,c,3047,b)].
% 27.97/27.93 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(4466,c,3876,a)].
% 27.97/27.93 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(4466,c,3877,b)].
% 27.97/27.93 4467 -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(3289,c,3047,b)].
% 27.97/27.93 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(4467,c,3876,a)].
% 27.97/27.93 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(4467,c,3877,b)].
% 27.97/27.93 4468 -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(3290,d,3047,b)].
% 27.97/27.93 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(4468,d,3876,a)].
% 27.97/27.93 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(4468,d,3877,b)].
% 27.97/27.93 4469 -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(3291,d,3047,b)].
% 27.97/27.93 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(4469,d,3876,a)].
% 27.97/27.93 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(4469,d,3877,b)].
% 27.97/27.93 4470 -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(3292,c,3047,b)].
% 27.97/27.93 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(4470,c,3876,a)].
% 27.97/27.94 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(4470,c,3877,b)].
% 27.97/27.94 4471 -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(3293,d,3047,b)].
% 27.97/27.94 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(4471,d,3876,a)].
% 27.97/27.94 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(4471,d,3877,b)].
% 27.97/27.94 4472 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3294,c,3047,b)].
% 27.97/27.94 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(4472,c,3876,a)].
% 27.97/27.94 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(4472,c,3877,b)].
% 27.97/27.94 4473 -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(3295,c,3047,b)].
% 27.97/27.94 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(4473,c,3876,a)].
% 27.97/27.94 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(4473,c,3877,b)].
% 27.97/27.94 4474 -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(3296,c,3047,b)].
% 27.97/27.94 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(4474,c,3876,a)].
% 27.97/27.94 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(4474,c,3877,b)].
% 27.97/27.94 4475 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(4475,b,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4475,b,3877,b)].
% 27.97/27.94 4476 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(4476,b,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4476,b,3877,b)].
% 27.97/27.94 4477 -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3329,c,3047,b)].
% 27.97/27.94 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(4477,c,3876,a)].
% 27.97/27.94 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4477,c,3877,b)].
% 27.97/27.94 4478 -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3330,c,3047,b)].
% 27.97/27.94 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4478,c,3876,a)].
% 27.97/27.94 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4478,c,3877,b)].
% 27.97/27.94 4479 c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3331,c,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4479,c,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4479,c,3877,b)].
% 27.97/27.94 4480 c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3332,b,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4480,b,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4480,b,3877,b)].
% 27.97/27.94 4481 c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3333,c,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4481,c,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Omeet(A,c_uminus(A,B),B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4481,c,3877,b)].
% 27.97/27.94 4482 c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3334,b,3047,b)].
% 27.97/27.94 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4482,b,3876,a)].
% 27.97/27.94 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4482,b,3877,b)].
% 27.97/27.94 4483 c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3335,b,3047,b)].
% 27.97/27.94 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(4483,b,3876,a)].
% 27.97/27.94 Derived: c_uminus(c_LOrder_Ojoin(A,B,C),C) = c_LOrder_Omeet(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4483,b,3877,b)].
% 27.97/27.94 4484 c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3336,b,3047,b)].
% 27.97/27.94 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(4484,b,3876,a)].
% 27.97/27.94 Derived: c_uminus(c_LOrder_Omeet(A,B,C),C) = c_LOrder_Ojoin(c_uminus(A,C),c_uminus(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4484,b,3877,b)].
% 27.97/27.94 4485 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 27.97/27.94 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4485,b,3876,a)].
% 27.97/27.94 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4485,b,3877,b)].
% 27.97/27.94 4486 -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3338,c,3047,b)].
% 27.97/27.94 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(4486,c,3876,a)].
% 27.97/27.94 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Onprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4486,c,3877,b)].
% 27.97/27.94 4487 -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3339,c,3047,b)].
% 27.97/27.94 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(4487,c,3876,a)].
% 27.97/27.94 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Onprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4487,c,3877,b)].
% 27.97/27.94 4488 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 27.97/27.94 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4488,b,3876,a)].
% 27.97/27.94 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4488,b,3877,b)].
% 27.97/27.94 4489 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3341,c,3047,b)].
% 27.97/27.94 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(4489,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Onprt(A,C),c_OrderedGroup_Onprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4489,c,3877,b)].
% 27.97/27.95 4490 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 27.97/27.95 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4490,b,3876,a)].
% 27.97/27.95 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4490,b,3877,b)].
% 27.97/27.95 4491 -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3343,c,3047,b)].
% 27.97/27.95 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(4491,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(A,c_0,B) | c_OrderedGroup_Opprt(A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4491,c,3877,b)].
% 27.97/27.95 4492 -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3344,c,3047,b)].
% 27.97/27.95 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(4492,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(c_0,A,B) | c_OrderedGroup_Opprt(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4492,c,3877,b)].
% 27.97/27.95 4493 -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3345,c,3047,b)].
% 27.97/27.95 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(4493,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(A,B,C) | c_lessequals(c_OrderedGroup_Opprt(A,C),c_OrderedGroup_Opprt(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4493,c,3877,b)].
% 27.97/27.95 4494 -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3346,c,3047,b)].
% 27.97/27.95 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(4494,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(c_0,c_plus(A,A,B),B) | c_lessequals(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4494,c,3877,b)].
% 27.97/27.95 4495 -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3347,c,3047,b)].
% 27.97/27.95 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4495,c,3876,a)].
% 27.97/27.95 Derived: -c_lessequals(c_0,A,B) | c_lessequals(c_0,c_plus(A,A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4495,c,3877,b)].
% 27.97/27.95 4496 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 27.97/27.95 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4496,b,3876,a)].
% 27.97/27.95 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4496,b,3877,b)].
% 27.97/27.95 4497 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 27.97/27.95 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(4497,b,3876,a)].
% 27.97/27.95 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4497,b,3877,b)].
% 27.97/27.95 4498 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 27.97/27.95 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(4498,b,3876,a)].
% 27.97/27.95 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4498,b,3877,b)].
% 27.97/27.95 4499 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3356,c,3047,b)].
% 27.97/27.95 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(4499,c,3876,a)].
% 27.97/27.95 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4499,c,3877,b)].
% 27.97/27.96 4500 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3357,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(4500,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4500,c,3877,b)].
% 27.97/27.96 4501 -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(3358,d,3047,b)].
% 27.97/27.96 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(4501,d,3876,a)].
% 27.97/27.96 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(4501,d,3877,b)].
% 27.97/27.96 4502 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3359,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(4502,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4502,c,3877,b)].
% 27.97/27.96 4503 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3360,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(4503,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4503,c,3877,b)].
% 27.97/27.96 4504 -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(3361,d,3047,b)].
% 27.97/27.96 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(4504,d,3876,a)].
% 27.97/27.96 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(4504,d,3877,b)].
% 27.97/27.96 4505 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3362,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(4505,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4505,c,3877,b)].
% 27.97/27.96 4506 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3363,c,3047,b)].
% 27.97/27.96 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4506,c,3876,a)].
% 27.97/27.96 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4506,c,3877,b)].
% 27.97/27.96 4507 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3364,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(4507,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4507,c,3877,b)].
% 27.97/27.96 4508 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3365,c,3047,b)].
% 27.97/27.96 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4508,c,3876,a)].
% 27.97/27.96 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4508,c,3877,b)].
% 27.97/27.96 4509 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3366,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(4509,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4509,c,3877,b)].
% 27.97/27.96 4510 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3367,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(4510,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4510,c,3877,b)].
% 27.97/27.96 4511 -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(3368,d,3047,b)].
% 27.97/27.96 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(4511,d,3876,a)].
% 27.97/27.96 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(4511,d,3877,b)].
% 27.97/27.96 4512 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3369,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(4512,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4512,c,3877,b)].
% 27.97/27.96 4513 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3370,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(4513,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4513,c,3877,b)].
% 27.97/27.96 4514 -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(3371,d,3047,b)].
% 27.97/27.96 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(4514,d,3876,a)].
% 27.97/27.96 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(4514,d,3877,b)].
% 27.97/27.96 4515 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3372,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(4515,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4515,c,3877,b)].
% 27.97/27.96 4516 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3373,c,3047,b)].
% 27.97/27.96 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4516,c,3876,a)].
% 27.97/27.96 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4516,c,3877,b)].
% 27.97/27.96 4517 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3374,c,3047,b)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(4517,c,3876,a)].
% 27.97/27.96 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4517,c,3877,b)].
% 27.97/27.96 4518 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3375,c,3047,b)].
% 27.97/27.97 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4518,c,3876,a)].
% 27.97/27.97 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4518,c,3877,b)].
% 27.97/27.97 4519 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 27.97/27.97 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(4519,c,3876,a)].
% 27.97/27.97 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4519,c,3877,b)].
% 27.97/27.97 4520 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 27.97/27.97 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(4520,b,3876,a)].
% 27.97/27.97 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4520,b,3877,b)].
% 27.97/27.97 4521 c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3378,b,3047,b)].
% 27.97/27.97 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(4521,b,3876,a)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B),B) = c_plus(c_HOL_Oabs(A,B),c_HOL_Oabs(C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4521,b,3877,b)].
% 27.97/27.97 4522 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 27.97/27.97 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4522,c,3876,a)].
% 27.97/27.97 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4522,c,3877,b)].
% 27.97/27.97 4523 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(4523,b,3876,a)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4523,b,3877,b)].
% 27.97/27.97 4524 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 27.97/27.97 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4524,b,3876,a)].
% 27.97/27.97 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4524,b,3877,b)].
% 27.97/27.97 4525 c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3382,b,3047,b)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(4525,b,3876,a)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_HOL_Oabs(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4525,b,3877,b)].
% 27.97/27.97 4526 -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3383,c,3047,b)].
% 27.97/27.97 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4526,c,3876,a)].
% 27.97/27.97 Derived: -c_lessequals(c_HOL_Oabs(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4526,c,3877,b)].
% 27.97/27.97 4527 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 27.97/27.97 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4527,b,3876,a)].
% 27.97/27.97 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4527,b,3877,b)].
% 27.97/27.97 4528 c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3385,b,3047,b)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(4528,b,3876,a)].
% 27.97/27.97 Derived: c_HOL_Oabs(c_uminus(A,B),B) = c_HOL_Oabs(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4528,b,3877,b)].
% 27.97/27.97 4529 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 27.97/27.97 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4529,b,3876,a)].
% 27.97/27.97 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4529,b,3877,b)].
% 27.97/27.98 4530 -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3387,c,3047,b)].
% 27.97/27.98 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(4530,c,3876,a)].
% 27.97/27.98 Derived: -c_lessequals(c_0,A,B) | c_HOL_Oabs(A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4530,c,3877,b)].
% 27.97/27.98 4531 -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3388,c,3047,b)].
% 27.97/27.98 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(4531,c,3876,a)].
% 27.97/27.98 Derived: -c_lessequals(A,c_0,B) | c_HOL_Oabs(A,B) = c_uminus(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4531,c,3877,b)].
% 27.97/27.98 4532 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 27.97/27.98 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4532,b,3876,a)].
% 27.97/27.98 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4532,b,3877,b)].
% 27.97/27.98 4533 c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3390,c,3047,b)].
% 27.97/27.98 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(4533,c,3876,a)].
% 27.97/27.98 Derived: c_less(c_0,c_HOL_Oabs(A,B),B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4533,c,3877,b)].
% 27.97/27.98 4534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 27.97/27.98 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(4534,b,3876,a)].
% 27.97/27.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4534,b,3877,b)].
% 27.97/27.98 4535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 27.97/27.98 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(4535,b,3876,a)].
% 27.97/27.98 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4535,b,3877,b)].
% 27.97/27.98 4536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 27.97/27.98 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(4536,b,3876,a)].
% 27.97/27.98 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4536,b,3877,b)].
% 27.97/27.98 4537 -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(3394,c,3047,b)].
% 27.97/27.98 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(4537,c,3876,a)].
% 27.97/27.98 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(4537,c,3877,b)].
% 27.97/27.98 4538 -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(3395,c,3047,b)].
% 27.97/27.98 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(4538,c,3876,a)].
% 27.97/27.98 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(4538,c,3877,b)].
% 27.97/27.98 4539 -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(3396,c,3047,b)].
% 27.97/27.98 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(4539,c,3876,a)].
% 27.97/27.98 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(4539,c,3877,b)].
% 27.97/27.98 4540 -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(3397,c,3047,b)].
% 27.97/27.98 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(4540,c,3876,a)].
% 27.97/27.98 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(4540,c,3877,b)].
% 27.97/27.99 4541 -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(3398,c,3047,b)].
% 27.97/27.99 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(4541,c,3876,a)].
% 27.97/27.99 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(4541,c,3877,b)].
% 27.97/27.99 4542 -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(3399,c,3047,b)].
% 27.97/27.99 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(4542,c,3876,a)].
% 27.97/27.99 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(4542,c,3877,b)].
% 27.97/27.99 4543 -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(3400,c,3047,b)].
% 27.97/27.99 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(4543,c,3876,a)].
% 27.97/27.99 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(4543,c,3877,b)].
% 27.97/27.99 4544 -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(3401,c,3047,b)].
% 27.97/27.99 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(4544,c,3876,a)].
% 27.97/27.99 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(4544,c,3877,b)].
% 27.97/27.99 4545 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 27.97/27.99 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(4545,b,3876,a)].
% 27.97/27.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4545,b,3877,b)].
% 27.97/27.99 4546 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(3403,c,3047,b)].
% 27.97/27.99 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4546,c,3876,a)].
% 27.97/27.99 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(4546,c,3877,b)].
% 27.97/27.99 4547 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(3404,c,3047,b)].
% 27.97/27.99 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4547,c,3876,a)].
% 27.97/27.99 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(4547,c,3877,b)].
% 27.97/27.99 4548 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 27.97/27.99 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(4548,b,3876,a)].
% 27.97/27.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4548,b,3877,b)].
% 27.97/27.99 4549 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 28.07/27.99 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(4549,b,3876,a)].
% 28.07/27.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4549,b,3877,b)].
% 28.07/27.99 4550 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3407,c,3047,b)].
% 28.07/27.99 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4550,c,3876,a)].
% 28.07/27.99 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(4550,c,3877,b)].
% 28.07/27.99 4551 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3408,b,3047,b)].
% 28.07/27.99 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(4551,b,3876,a)].
% 28.07/27.99 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4551,b,3877,b)].
% 28.07/27.99 4552 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3409,c,3047,b)].
% 28.07/27.99 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4552,c,3876,a)].
% 28.07/27.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(4552,c,3877,b)].
% 28.07/27.99 4553 -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(3410,c,3047,b)].
% 28.07/27.99 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(4553,c,3876,a)].
% 28.07/27.99 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(4553,c,3877,b)].
% 28.07/27.99 4554 -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(3411,c,3047,b)].
% 28.07/27.99 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(4554,c,3876,a)].
% 28.07/27.99 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(4554,c,3877,b)].
% 28.07/27.99 4555 -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(3412,c,3047,b)].
% 28.07/27.99 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(4555,c,3876,a)].
% 28.07/27.99 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(4555,c,3877,b)].
% 28.07/27.99 4556 -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(3413,c,3047,b)].
% 28.07/27.99 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(4556,c,3876,a)].
% 28.07/27.99 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(4556,c,3877,b)].
% 28.07/27.99 4557 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(3414,c,3047,b)].
% 28.07/27.99 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4557,c,3876,a)].
% 28.07/27.99 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(4557,c,3877,b)].
% 28.07/27.99 4558 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(3415,b,3047,b)].
% 28.07/27.99 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(4558,b,3876,a)].
% 28.07/27.99 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(4558,b,3877,b)].
% 28.07/27.99 4559 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 28.07/27.99 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(4559,b,3876,a)].
% 28.07/27.99 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4559,b,3877,b)].
% 28.07/27.99 4560 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(3417,c,3047,b)].
% 28.08/28.00 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(4560,c,3876,a)].
% 28.08/28.00 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4560,c,3877,b)].
% 28.08/28.00 4561 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(3418,c,3047,b)].
% 28.08/28.00 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(4561,c,3876,a)].
% 28.08/28.00 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4561,c,3877,b)].
% 28.08/28.00 4562 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 28.08/28.00 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(4562,b,3876,a)].
% 28.08/28.00 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4562,b,3877,b)].
% 28.08/28.00 4563 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 28.08/28.00 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(4563,b,3876,a)].
% 28.08/28.00 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4563,b,3877,b)].
% 28.08/28.00 4564 c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 28.08/28.00 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(4564,c,3876,a)].
% 28.08/28.00 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4564,c,3877,b)].
% 28.08/28.00 4565 c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 28.08/28.00 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(4565,b,3876,a)].
% 28.08/28.00 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4565,b,3877,b)].
% 28.08/28.00 4566 c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 28.08/28.00 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4566,b,3876,a)].
% 28.08/28.00 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4566,b,3877,b)].
% 28.08/28.00 4567 -c_less(c_0,c_NatArith_Oof__nat(A,B),B) | c_less(c_0,A,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3432,a,3425,b)].
% 28.08/28.00 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(4567,c,3876,a)].
% 28.08/28.00 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,B),B) | c_less(c_0,A,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(4567,c,3877,b)].
% 28.08/28.00 4568 -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3433,a,3425,b)].
% 28.08/28.00 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4568,c,3876,a)].
% 28.08/28.00 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4568,c,3877,b)].
% 28.08/28.00 4569 c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 28.08/28.00 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4569,c,3876,a)].
% 28.09/28.01 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4569,c,3877,b)].
% 28.09/28.01 4570 c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 28.09/28.01 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(4570,b,3876,a)].
% 28.09/28.01 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4570,b,3877,b)].
% 28.09/28.01 4571 c_NatArith_Oof__nat(A,B) != c_NatArith_Oof__nat(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(3436,a,3425,b)].
% 28.09/28.01 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(4571,c,3876,a)].
% 28.09/28.01 Derived: c_NatArith_Oof__nat(A,B) != c_NatArith_Oof__nat(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(4571,c,3877,b)].
% 28.09/28.01 4572 -c_lessequals(c_NatArith_Oof__nat(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3437,a,3425,b)].
% 28.09/28.01 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4572,c,3876,a)].
% 28.09/28.01 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_0,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4572,c,3877,b)].
% 28.09/28.01 4573 c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3438,a,3425,b)].
% 28.09/28.01 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4573,b,3876,a)].
% 28.09/28.01 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4573,b,3877,b)].
% 28.09/28.01 4574 -c_lessequals(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_lessequals(A,C,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3439,a,3425,b)].
% 28.09/28.01 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(4574,c,3876,a)].
% 28.09/28.01 Derived: -c_lessequals(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_lessequals(A,C,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(4574,c,3877,b)].
% 28.09/28.01 4575 -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3440,a,3425,b)].
% 28.09/28.01 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(4575,c,3876,a)].
% 28.09/28.01 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4575,c,3877,b)].
% 28.09/28.01 4576 -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 28.09/28.01 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4576,b,3876,a)].
% 28.09/28.01 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4576,b,3877,b)].
% 28.09/28.01 4577 -c_less(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_less(A,C,tc_nat) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3442,a,3425,b)].
% 28.09/28.01 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(4577,c,3876,a)].
% 28.09/28.01 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_NatArith_Oof__nat(C,B),B) | c_less(A,C,tc_nat) | -class_Ring__and__Field_Oordered__field(B). [resolve(4577,c,3877,b)].
% 28.09/28.01 4578 -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3443,a,3425,b)].
% 28.09/28.01 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(4578,c,3876,a)].
% 28.09/28.01 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4578,c,3877,b)].
% 28.09/28.01 4579 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3444,b,3425,b)].
% 28.09/28.02 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(4579,e,3876,a)].
% 28.09/28.02 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4579,e,3877,b)].
% 28.09/28.02 4580 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3445,b,3425,b)].
% 28.09/28.02 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(4580,e,3876,a)].
% 28.09/28.02 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4580,e,3877,b)].
% 28.09/28.02 4581 -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D | -class_Ring__and__Field_Oordered__idom(A). [resolve(3446,b,3425,b)].
% 28.09/28.02 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(4581,e,3876,a)].
% 28.09/28.02 Derived: -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D | -class_Ring__and__Field_Oordered__field(A). [resolve(4581,e,3877,b)].
% 28.09/28.02 4582 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3447,b,3425,b)].
% 28.09/28.02 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(4582,e,3876,a)].
% 28.09/28.02 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4582,e,3877,b)].
% 28.09/28.02 4583 -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) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3448,b,3425,b)].
% 28.09/28.02 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(4583,e,3876,a)].
% 28.09/28.02 Derived: -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) | -class_Ring__and__Field_Oordered__field(A). [resolve(4583,e,3877,b)].
% 28.09/28.02 4584 -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 28.09/28.02 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(4584,b,3876,a)].
% 28.09/28.02 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4584,b,3877,b)].
% 28.09/28.02 4585 -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 28.09/28.02 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(4585,b,3876,a)].
% 28.09/28.02 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4585,b,3877,b)].
% 28.09/28.02 4586 c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 28.09/28.02 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(4586,b,3876,a)].
% 28.09/28.02 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4586,b,3877,b)].
% 28.09/28.02 4587 c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 28.09/28.02 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(4587,b,3876,a)].
% 28.09/28.02 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4587,b,3877,b)].
% 28.09/28.02 4588 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 28.09/28.03 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4588,b,3876,a)].
% 28.09/28.03 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4588,b,3877,b)].
% 28.09/28.03 4589 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 28.09/28.03 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4589,b,3876,a)].
% 28.09/28.03 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4589,b,3877,b)].
% 28.09/28.03 4590 -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(3516,d,3425,b)].
% 28.09/28.03 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(4590,d,3876,a)].
% 28.09/28.03 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(4590,d,3877,b)].
% 28.09/28.03 4591 -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(3517,d,3425,b)].
% 28.09/28.03 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(4591,d,3876,a)].
% 28.09/28.03 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(4591,d,3877,b)].
% 28.09/28.03 4592 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3518,b,3425,b)].
% 28.09/28.03 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(4592,b,3876,a)].
% 28.09/28.03 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4592,b,3877,b)].
% 28.09/28.03 4593 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(3519,b,3425,b)].
% 28.09/28.03 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(4593,b,3876,a)].
% 28.09/28.03 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(4593,b,3877,b)].
% 28.09/28.03 4594 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 28.09/28.03 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(4594,b,3876,a)].
% 28.09/28.03 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4594,b,3877,b)].
% 28.09/28.03 4595 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(3521,b,3425,b)].
% 28.09/28.03 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(4595,b,3876,a)].
% 28.09/28.03 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(4595,b,3877,b)].
% 28.09/28.03 4596 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(3522,b,3425,b)].
% 28.09/28.03 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(4596,b,3876,a)].
% 28.09/28.03 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(4596,b,3877,b)].
% 28.09/28.03 4597 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 28.09/28.03 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(4597,b,3876,a)].
% 28.09/28.03 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4597,b,3877,b)].
% 32.07/32.00 4598 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 32.07/32.00 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(4598,b,3876,a)].
% 32.07/32.00 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4598,b,3877,b)].
% 32.07/32.00 4599 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 32.07/32.00 4600 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 32.07/32.00 4601 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 32.07/32.00 4602 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 32.07/32.00 4603 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 32.07/32.00 4604 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 32.07/32.00 4605 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(37,a,32,b)].
% 32.07/32.00 4606 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(38,a,32,b)].
% 32.07/32.00 4607 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(39,a,32,b)].
% 32.07/32.00 4608 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(40,a,32,b)].
% 32.07/32.00 4609 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 32.07/32.00 4610 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(42,a,32,b)].
% 32.07/32.00 4611 c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 32.07/32.00 4612 c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 32.07/32.00 4613 c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 32.07/32.00 4614 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 32.07/32.00 4615 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 32.07/32.00 4616 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 32.07/32.00 4617 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 32.07/32.00 4618 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1167,c,1147,b)].
% 32.07/32.00 4619 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1168,c,1147,b)].
% 32.07/32.00 4620 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1169,c,1147,b)].
% 32.07/32.00 4621 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1170,c,1147,b)].
% 32.07/32.00 4622 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 32.07/32.00 4623 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1172,b,1147,b)].
% 32.07/32.00 4624 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1185,a,1184,b)].
% 32.09/32.02 4625 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1186,a,1184,b)].
% 32.09/32.02 4626 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1187,a,1184,b)].
% 32.09/32.02 4627 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1188,a,1184,b)].
% 32.09/32.02 4628 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1189,a,1184,b)].
% 32.09/32.02 4629 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1190,a,1184,b)].
% 32.09/32.02 4630 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1191,a,1184,b)].
% 32.09/32.02 4631 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1192,a,1184,b)].
% 32.09/32.02 4632 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1193,a,1184,b)].
% 32.09/32.02 4633 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 32.09/32.02 4634 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1195,a,1184,b)].
% 32.09/32.02 4635 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1196,a,1184,b)].
% 32.09/32.02 4636 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1197,a,1184,b)].
% 32.09/32.02 4637 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1198,a,1184,b)].
% 32.09/32.02 4638 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1199,a,1184,b)].
% 32.09/32.02 4639 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1200,a,1184,b)].
% 32.09/32.02 4640 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1201,a,1184,b)].
% 32.09/32.02 4641 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1202,a,1184,b)].
% 32.09/32.02 4642 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1203,a,1184,b)].
% 32.09/32.02 4643 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 32.09/32.02 4644 -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_Wellfounded__Recursion_Owellorder(B). [resolve(1205,a,1184,b)].
% 32.11/32.03 4645 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1206,a,1184,b)].
% 32.11/32.03 4646 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1207,a,1184,b)].
% 32.11/32.03 4647 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1208,b,1184,b)].
% 32.11/32.03 4648 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1209,b,1184,b)].
% 32.11/32.03 4649 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1210,a,1184,b)].
% 32.11/32.03 4650 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1211,a,1184,b)].
% 32.11/32.03 4651 -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1212,a,1184,b)].
% 32.11/32.03 4652 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1213,a,1184,b)].
% 32.11/32.03 4653 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1214,a,1184,b)].
% 32.11/32.03 4654 -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1215,a,1184,b)].
% 32.11/32.03 4655 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1216,a,1184,b)].
% 32.11/32.03 4656 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(1217,a,1184,b)].
% 32.11/32.03 4657 -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1218,a,1184,b)].
% 32.11/32.03 4658 c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 32.11/32.03 4659 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1220,a,1184,b)].
% 32.11/32.03 4660 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1221,a,1184,b)].
% 32.11/32.03 4661 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1222,a,1184,b)].
% 32.11/32.03 4662 -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1223,a,1184,b)].
% 32.11/32.03 4663 c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 32.11/32.03 4664 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1225,a,1184,b)].
% 32.11/32.03 4665 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1226,a,1184,b)].
% 32.11/32.03 4666 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1227,a,1184,b)].
% 32.11/32.03 4667 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1228,a,1184,b)].
% 32.11/32.03 4668 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1229,a,1184,b)].
% 32.11/32.03 4669 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 32.11/32.03 4670 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 32.11/32.03 4671 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 32.20/32.12 4672 -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1233,a,1184,b)].
% 32.20/32.12 4673 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1234,a,1184,b)].
% 32.20/32.12 4674 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1235,a,1184,b)].
% 32.20/32.12 4675 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1236,a,1184,b)].
% 32.20/32.12 4676 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1237,a,1184,b)].
% 32.20/32.12 4677 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1238,a,1184,b)].
% 32.20/32.12 4678 -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_Wellfounded__Recursion_Owellorder(C). [resolve(1239,a,1184,b)].
% 32.20/32.12 4679 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 32.20/32.12 4680 -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1241,a,1184,b)].
% 32.20/32.12 4681 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1242,a,1184,b)].
% 32.20/32.12 4682 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2414,a,2428,b)].
% 32.20/32.12 4683 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2429,a,2428,b)].
% 32.20/32.12 4684 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2430,a,2428,b)].
% 32.20/32.12 4685 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2431,a,2428,b)].
% 32.20/32.12 4686 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2432,a,2428,b)].
% 32.20/32.12 4687 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2433,a,2428,b)].
% 32.20/32.12 4688 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2434,a,2428,b)].
% 32.20/32.12 4689 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2435,a,2428,b)].
% 32.20/32.12 4690 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2436,a,2428,b)].
% 32.20/32.12 4691 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2437,a,2428,b)].
% 32.20/32.12 4692 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2438,a,2428,b)].
% 32.20/32.12 4693 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2439,a,2428,b)].
% 32.20/32.12 4694 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2440,a,2428,b)].
% 32.96/32.90 4695 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2441,a,2428,b)].
% 32.96/32.90 4696 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Wellfounded__Recursion_Owellorder(D). [resolve(2442,a,2428,b)].
% 32.96/32.90 4697 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2443,a,2428,b)].
% 32.96/32.90 4698 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2444,a,2428,b)].
% 32.96/32.90 4699 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2445,a,2428,b)].
% 32.96/32.90 4700 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2446,a,2428,b)].
% 32.96/32.90 4701 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(2447,a,2428,b)].
% 32.96/32.90 4702 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ofield(A) # label(clsrel_Ring__and__Field_Oordered__field_0) # label(axiom). [assumption].
% 32.96/32.90 4703 -class_Ring__and__Field_Ofield(A) | class_HOL_Oinverse(A) # label(clsrel_Ring__and__Field_Ofield_30) # label(axiom). [assumption].
% 32.96/32.90 4704 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ofield_4) # label(axiom). [assumption].
% 32.96/32.90 4705 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse(c_Numeral_Onumber__of(B,A),A) = c_divide(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Oinverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: -class_Numeral_Onumber(A) | c_HOL_Oinverse(c_Numeral_Onumber__of(B,A),A) = c_divide(c_1,c_Numeral_Onumber__of(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4705,b,4702,b)].
% 32.96/32.90 4706 -class_Ring__and__Field_Ofield(A) | c_divide(B,c_1,A) = B # label(cls_Ring__and__Field_Odivide__1_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_divide(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4706,a,4702,b)].
% 32.96/32.90 4707 -class_Ring__and__Field_Ofield(A) | c_divide(c_uminus(B,A),C,A) = c_uminus(c_divide(B,C,A),A) # label(cls_Ring__and__Field_Odivide__minus__left_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_divide(c_uminus(A,B),C,B) = c_uminus(c_divide(A,C,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4707,a,4702,b)].
% 32.96/32.90 4708 -class_Ring__and__Field_Ofield(A) | B = c_0 | c_times(c_HOL_Oinverse(B,A),B,A) = c_1 # label(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: A = c_0 | c_times(c_HOL_Oinverse(A,B),A,B) = c_1 | -class_Ring__and__Field_Oordered__field(B). [resolve(4708,a,4702,b)].
% 32.96/32.90 4709 -class_Ring__and__Field_Ofield(A) | c_times(B,C,A) != c_times(B,D,A) | C = D | B = c_0 # label(cls_Ring__and__Field_Ofield__mult__cancel__left_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_times(A,B,C) != c_times(A,D,C) | B = D | A = c_0 | -class_Ring__and__Field_Oordered__field(C). [resolve(4709,a,4702,b)].
% 32.96/32.90 4710 -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_times(c_0,C,A) # label(cls_Ring__and__Field_Ofield__mult__cancel__left_1) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_times(c_0,A,B) = c_times(c_0,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4710,a,4702,b)].
% 32.96/32.90 4711 -class_Ring__and__Field_Ofield(A) | c_times(B,C,A) != c_times(D,C,A) | B = D | C = c_0 # label(cls_Ring__and__Field_Ofield__mult__cancel__right_0) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_times(A,B,C) != c_times(D,B,C) | A = D | B = c_0 | -class_Ring__and__Field_Oordered__field(C). [resolve(4711,a,4702,b)].
% 32.96/32.90 4712 -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_times(C,c_0,A) # label(cls_Ring__and__Field_Ofield__mult__cancel__right_1) # label(axiom). [assumption].
% 32.96/32.90 Derived: c_times(A,c_0,B) = c_times(C,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4712,a,4702,b)].
% 32.96/32.90 4713 -class_Ring__and__Field_Ofield(A) | B = c_0 | c_times(B,c_HOL_Oinverse(B,A),A) = c_1 # label(cls_Ring__and__Field_Oright__inverse_0) # label(axiom). [assumption].
% 32.99/32.93 Derived: A = c_0 | c_times(A,c_HOL_Oinverse(A,B),B) = c_1 | -class_Ring__and__Field_Oordered__field(B). [resolve(4713,a,4702,b)].
% 32.99/32.93 4714 -class_Ring__and__Field_Ofield(A) | c_times(B,c_divide(C,D,A),A) = c_divide(c_times(B,C,A),D,A) # label(cls_Ring__and__Field_Otimes__divide__eq__1_0) # label(axiom). [assumption].
% 32.99/32.93 Derived: c_times(A,c_divide(B,C,D),D) = c_divide(c_times(A,B,D),C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(4714,a,4702,b)].
% 32.99/32.93 4715 -class_Ring__and__Field_Ofield(A) | c_times(c_divide(B,C,A),D,A) = c_divide(c_times(B,D,A),C,A) # label(cls_Ring__and__Field_Otimes__divide__eq__2_0) # label(axiom). [assumption].
% 32.99/32.93 Derived: c_times(c_divide(A,B,C),D,C) = c_divide(c_times(A,D,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4715,a,4702,b)].
% 32.99/32.93 4716 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(43,a,54,b)].
% 32.99/32.93 4717 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(63,a,54,b)].
% 32.99/32.93 4718 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(64,a,54,b)].
% 32.99/32.93 4719 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(65,a,54,b)].
% 32.99/32.93 4720 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(66,a,54,b)].
% 32.99/32.93 4721 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(67,a,54,b)].
% 32.99/32.93 4722 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(68,a,54,b)].
% 32.99/32.93 4723 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(69,a,54,b)].
% 32.99/32.93 4724 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(70,a,54,b)].
% 32.99/32.93 4725 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(108,b,83,b)].
% 32.99/32.93 4726 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(109,b,83,b)].
% 32.99/32.93 4727 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 32.99/32.93 4728 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 32.99/32.93 4729 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(221,c,196,b)].
% 32.99/32.93 4730 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(222,c,196,b)].
% 32.99/32.93 4731 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 32.99/32.93 4732 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 32.99/32.93 4733 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 32.99/32.93 4734 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 32.99/32.93 4735 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 32.99/32.93 4736 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 33.03/32.94 4737 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 33.03/32.94 4738 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 33.03/32.94 4739 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 33.03/32.94 4740 -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(413,b,398,b)].
% 33.03/32.94 4741 -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(414,b,398,b)].
% 33.03/32.94 4742 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(415,a,398,b)].
% 33.03/32.94 4743 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(416,a,398,b)].
% 33.03/32.94 4744 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(417,a,398,b)].
% 33.03/32.94 4745 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(428,c,398,b)].
% 33.03/32.94 4746 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(429,c,398,b)].
% 33.03/32.94 4747 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 33.03/32.94 4748 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 33.03/32.94 4749 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 33.03/32.94 4750 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 33.03/32.94 4751 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 33.03/32.94 4752 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 33.03/32.94 4753 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 33.03/32.94 4754 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 33.03/32.94 4755 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(637,d,619,b)].
% 33.03/32.94 4756 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(638,d,619,b)].
% 33.03/32.94 4757 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(639,d,619,b)].
% 33.03/32.94 4758 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(640,d,619,b)].
% 33.03/32.94 4759 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(641,d,619,b)].
% 33.03/32.94 4760 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(642,d,619,b)].
% 33.03/32.94 4761 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(643,d,619,b)].
% 33.03/32.94 4762 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(644,d,619,b)].
% 33.03/32.94 4763 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(645,d,619,b)].
% 33.03/32.94 4764 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 33.03/32.95 4765 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 33.03/32.95 4766 -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(830,c,788,b)].
% 33.03/32.95 4767 -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(831,c,788,b)].
% 33.03/32.95 4768 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(832,b,788,b)].
% 33.03/32.95 4769 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(833,b,788,b)].
% 33.03/32.95 4770 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(834,b,788,b)].
% 33.03/32.95 4771 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(837,d,788,b)].
% 33.03/32.95 4772 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(838,d,788,b)].
% 33.03/32.95 4773 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(839,d,788,b)].
% 33.03/32.95 4774 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(840,d,788,b)].
% 33.03/32.95 4775 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(841,d,788,b)].
% 33.03/32.95 4776 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(842,d,788,b)].
% 33.03/32.95 4777 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(843,d,788,b)].
% 33.03/32.95 4778 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(844,d,788,b)].
% 33.03/32.95 4779 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(845,d,788,b)].
% 33.03/32.95 4780 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 33.03/32.95 4781 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 33.03/32.95 4782 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 33.03/32.95 4783 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 33.03/32.95 4784 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 33.03/32.95 4785 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 33.03/32.95 4786 -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(871,a,864,b)].
% 33.03/32.95 4787 -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(872,a,864,b)].
% 33.03/32.95 4788 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 33.03/32.95 4789 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(874,a,864,b)].
% 33.03/32.95 4790 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 33.03/32.95 4791 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(876,a,864,b)].
% 33.03/32.95 4792 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(877,a,864,b)].
% 33.19/33.14 4793 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 33.19/33.14 4794 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 33.19/33.14 4795 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 33.19/33.14 4796 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(947,a,941,b)].
% 33.19/33.14 4797 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(948,a,941,b)].
% 33.19/33.14 4798 -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(949,a,941,b)].
% 33.19/33.14 4799 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(950,a,941,b)].
% 33.19/33.14 4800 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 33.19/33.14 4801 c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(952,a,941,b)].
% 33.19/33.14 4802 c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(953,a,941,b)].
% 33.19/33.14 4803 c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(954,a,941,b)].
% 33.19/33.14 4804 c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(955,a,941,b)].
% 33.19/33.14 4805 c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(956,a,941,b)].
% 33.19/33.14 4806 c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(957,a,941,b)].
% 33.19/33.14 4807 -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(958,a,941,b)].
% 33.19/33.14 4808 -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Ofield(A). [resolve(959,b,941,b)].
% 33.19/33.14 4809 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(960,b,941,b)].
% 33.19/33.14 4810 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(961,b,941,b)].
% 33.19/33.14 4811 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Ofield(A). [resolve(962,b,941,b)].
% 33.19/33.14 4812 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(963,b,941,b)].
% 33.19/33.14 4813 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 33.19/33.14 4814 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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(3798,c,3753,b)].
% 33.19/33.14 4815 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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(3799,c,3753,b)].
% 33.19/33.14 4816 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 33.19/33.14 4817 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 33.19/33.14 4818 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 33.19/33.14 4819 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 33.19/33.14 4820 -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(3825,c,3753,b)].
% 33.19/33.14 4821 -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(3826,c,3753,b)].
% 33.19/33.14 4822 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B). [resolve(3827,b,3753,b)].
% 33.19/33.14 4823 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3828,b,3753,b)].
% 33.19/33.14 4824 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3829,b,3753,b)].
% 33.19/33.14 4825 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3830,d,3753,b)].
% 33.19/33.14 4826 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3831,d,3753,b)].
% 33.19/33.14 4827 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3832,d,3753,b)].
% 33.19/33.14 4828 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3833,d,3753,b)].
% 33.19/33.14 4829 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3834,d,3753,b)].
% 33.19/33.14 4830 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3835,d,3753,b)].
% 33.19/33.14 4831 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3836,d,3753,b)].
% 33.19/33.14 4832 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3837,d,3753,b)].
% 33.19/33.14 4833 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3838,d,3753,b)].
% 33.19/33.14 4834 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 33.19/33.14 4835 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 33.19/33.14 4836 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 33.19/33.14 4837 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 33.19/33.14 4838 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 33.19/33.14 4839 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 33.19/33.14 4840 -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(3846,d,3753,b)].
% 33.19/33.14 4841 -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(3847,d,3753,b)].
% 33.19/33.14 4842 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 33.19/33.14 4843 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(3849,b,3753,b)].
% 33.19/33.14 4844 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 33.19/33.14 4845 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(3851,b,3753,b)].
% 34.62/34.59 4846 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(3852,b,3753,b)].
% 34.62/34.59 4847 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 34.62/34.59 4848 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 34.62/34.59 4849 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 34.62/34.59 4850 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3856,d,3753,b)].
% 34.62/34.59 4851 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3857,d,3753,b)].
% 34.62/34.59 4852 -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3858,c,3753,b)].
% 34.62/34.59 4853 -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3859,d,3753,b)].
% 34.62/34.59 4854 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 34.62/34.59 4855 c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3861,b,3753,b)].
% 34.62/34.59 4856 c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3862,b,3753,b)].
% 34.62/34.59 4857 c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3863,b,3753,b)].
% 34.62/34.59 4858 c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3864,b,3753,b)].
% 34.62/34.59 4859 c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3865,b,3753,b)].
% 34.62/34.59 4860 c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3866,b,3753,b)].
% 34.62/34.59 4861 -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3867,c,3753,b)].
% 34.62/34.59 4862 -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Ofield(A). [resolve(3868,c,3753,b)].
% 34.62/34.59 4863 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3869,d,3753,b)].
% 34.62/34.59 4864 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3870,d,3753,b)].
% 34.62/34.59 4865 -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3871,d,3753,b)].
% 34.62/34.59 4866 -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3872,d,3753,b)].
% 34.62/34.59
% 34.62/34.59 ============================== end predicate elimination =============
% 34.62/34.59
% 34.62/34.59 Auto_denials: (non-Horn, no changes).
% 34.62/34.59
% 34.62/34.59 Term ordering decisions:
% 34.62/34.59 Function symbol KB weights: tc_IntDef_Oint=1. tc_nat=1. c_0=1. c_1=1. c_emptyset=1. tc_Message_Omsg=1. c_Finite__Set_OFinites=1. c_List_Olist_ONil=1. tc_Event_Oevent=1. c_Numeral_OPls=1. c_IntDef_ONats=1. c_Numeral_Obit_OB1=1. c_Numeral_Obit_OB0=1. c_UNIV=1. c_IntDef_OInts=1. c_Message_Oagent_OSpy=1. c_Numeral_OMin=1. c_Yahalom_Oyahalom=1. c_Message_Oagent_OServer=1. tc_List_Onibble=1. tc_Message_Oagent=1. c_Relation_OId=1. c_Event_Obad=1. c_IntDef_Ointrel=1. c_Message_OsymKeys=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. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. v_B=1. v_evs3=1. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. tc_Product__Type_Ounit=1. tc_Public_Okeymode=1. v_Aa=1. v_Ba=1. v_NB=1. tc_List_Ochar=1. tc_bool=1. v_A=1. v_KAB=1. v_NA=1. v_NAa=1. c_Numeral_Onumber__of=1. c_uminus=1. c_NatArith_Oof__nat=1. tc_prod=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. c_Message_Omsg_OMPair=1. c_Numeral_OBit=1. c_Nat_Osize=1. tc_Datatype__Universe_Onode=1. c_SetInterval_OlessThan=1. c_Finite__Set_OMax=1. c_Finite__Set_OMin=1. c_HOL_Oabs=1. c_List_Oset=1. c_SetInterval_OgreaterThan=1. c_IntDef_Oof__int=1. c_Numeral_Obin__add=1. c_Message_Omsg_OCrypt=1. c_Event_Oknows=1. c_List_Orev=1. c_Union=1. c_List_Olists=1. c_Message_OHPair=1. c_OrderedGroup_Onprt=1. c_OrderedGroup_Opprt=1. c_Transitive__Closure_Ortrancl=1. c_Event_Oevent_OGets=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_Event_Oevent_ONotes=1. c_List_Olistrel=1. c_Public_OpublicKey=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. v_sko__uhi=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_fun=1. tc_set=1. tc_List_Olist=1. c_Suc=1. c_Message_Oanalz=1. c_Message_Osynth=1. c_Message_Oparts=1. c_Message_Omsg_OKey=1. c_Numeral_Obin__minus=1. c_IntDef_Oint=1. c_Public_OshrK=1. c_Message_Omsg_OAgent=1. c_Message_Omsg_ONonce=1. c_Message_OkeysFor=1. c_IntDef_Onat=1. c_Message_Omsg_OHash=1. c_GCD_Ogcd=1. c_Message_OinvKey=1. c_Event_Oused=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Message_Omsg_ONumber=1. c_Numeral_Obin__pred=1. c_IntDiv_OnegateSnd=1. c_Numeral_Obin__succ=1. c_Event_OinitState=1. c_IntDef_OAbs__Integ=1. c_Message_Oagent_OFriend=1. tc_Datatype_Ooption=1. v_sko__2VY=1. c_IntDef_ORep__Integ=1. c_plus=1. c_times=1. c_insert=1. c_minus=1. c_SetInterval_OatLeastLessThan=1. c_List_Olist_OCons=1. c_Nat_Opower=1. c_Orderings_Omin=1. c_Orderings_Omax=1. c_Divides_Oop_Amod=1. c_SetInterval_OatLeastAtMost=1. c_append=1. c_div=1. c_union=1. c_SetInterval_OgreaterThanAtMost=1. c_inter=1. c_Event_Oevent_OSays=1. c_SetInterval_OgreaterThanLessThan=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=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_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_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_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__UnivCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------